The Average Number of Occurrences of Patterns in 132-avoiding permutations For ALL patterns of length , 10 By Shalosh B. Ekhad In this article, C(n) denotes the n-th Catalan number (i.e. (2n)!/(n!(n+1)!)\ 1/2 ), and m denotes, n The purpose of this article is to provide (easily) rigorously-provable expressions, in n, for the total number of occurrences of a given pattern in ALL 132-avoiding permutations of length n, that immediately yield the expression for the average of the r.v. "number of occurrences of the pattern" in the above set, upon dividing by the cardinality, the Catalan number, C(n) There are, 16796, 132-avoiding patterns of length, 10 but obviously you get the same average for a pattern and its inverse so we only have to consider one member for each such pair (unless, of course, if it is an involution) Hence we should expect, 8524, such different expressions Another trivial equivalence was discovered by Miklos Bona in the prestigious\ journal Electronic J. of Combinatorics v. 19 (2012), #P62, and taking this into acco\ unt, there are, 8095, of them Nevertheless, SURPRISE, SURPIRSE!, there are only, 42, of them! Here they all are in decreasing order of (asymptotic) abundance For the, 1, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}} is given by the following expression / 92499341 508130747 2 31558709 3 51179257 4 6930407 5 |- 1/2 - -------- n - --------- n - -------- n - -------- n - -------- n \ 55050240 220200960 18874368 75497472 47185920 2791789 6 72215 7 2431 8\ n / 7241 - --------- n - --------- n - --------- n | 4 + |1/2 + ---- n 188743680 132120576 528482304 / \ 2520 224057 2 753013 3 4436197 4 65983 5 862681 6 5963 7 + ------ n + ------ n + ------- n + ----- n + ------- n + ----- n 33600 90720 725760 24192 1209600 60480 1441 8 41 9 10\ + ------ n + ------ n + 1/3628800 n | C(n) 241920 362880 / and in Maple input form: (-1/2-92499341/55050240*n-508130747/220200960*n^2-31558709/18874368*n^3-\ 51179257/75497472*n^4-6930407/47185920*n^5-2791789/188743680*n^6-72215/ 132120576*n^7-2431/528482304*n^8)*4^n+(1/2+7241/2520*n+224057/33600*n^2+753013/ 90720*n^3+4436197/725760*n^4+65983/24192*n^5+862681/1209600*n^6+5963/60480*n^7+ 1441/241920*n^8+41/362880*n^9+1/3628800*n^10)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 20 1/2 19 18 1/2 17 16 m 2431 Pi m 41 m 2332759 Pi m 1441 m ------- - -------------- + ------ - ----------------- + -------- 3628800 528482304 362880 4227858432 241920 1/2 15 14 1/2 13 12 81419767 Pi m 5963 m 49379825 Pi m 862681 m - ------------------ + -------- - ------------------ + ---------- 5284823040 60480 301989888 1209600 1/2 11 10 1/2 9 8 79567487 Pi m 65983 m 1470492001 Pi m 4436197 m - ------------------ + --------- - ------------------- + ---------- 94371840 24192 603979776 725760 1/2 7 6 1/2 5 4 7378710421 Pi m 753013 m 1506631127 Pi m 224057 m - ------------------- + --------- - ------------------- + --------- 1761607680 90720 352321536 33600 1/2 3 2 1/2 350898343 Pi m 7241 m 9 Pi m - ------------------ + ------- - --------- + 1/2 146800640 2520 16 and in Maple input form: 1/3628800*m^20-2431/528482304*Pi^(1/2)*m^19+41/362880*m^18-2332759/4227858432* Pi^(1/2)*m^17+1441/241920*m^16-81419767/5284823040*Pi^(1/2)*m^15+5963/60480*m^ 14-49379825/301989888*Pi^(1/2)*m^13+862681/1209600*m^12-79567487/94371840*Pi^(1 /2)*m^11+65983/24192*m^10-1470492001/603979776*Pi^(1/2)*m^9+4436197/725760*m^8-\ 7378710421/1761607680*Pi^(1/2)*m^7+753013/90720*m^6-1506631127/352321536*Pi^(1/ 2)*m^5+224057/33600*m^4-350898343/146800640*Pi^(1/2)*m^3+7241/2520*m^2-9/16*Pi^ (1/2)*m+1/2 For the, 2, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 8, 7, 6, 5, 4, 3, 2, 1, 10]}, {[10, 9, 8, 7, 5, 6, 4, 3, 2, 1]}, {[9, 10, 8, 7, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 4, 3, 1, 2]}, {[10, 8, 9, 7, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 4, 2, 3, 1]}, {[10, 9, 7, 8, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 3, 4, 2, 1]}, {[10, 9, 8, 6, 7, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 5, 3, 2, 1]}} is given by the following expression / 86994317 439142267 2 121198361 3 33062393 4 3450589 5 |1/2 + -------- n + --------- n + --------- n + -------- n + -------- n \ 55050240 220200960 94371840 75497472 47185920 948629 6 68783 7 143 8\ n / 6989 + --------- n + --------- n + --------- n | 4 + |- 1/2 - ---- n 188743680 660602880 528482304 / \ 2520 123307 2 128729 3 25475 4 222743 5 5287 6 487 7 - ------ n - ------ n - ----- n - ------ n - ----- n - ----- n 20160 18144 5376 120960 13440 12096 25 8 9\ - ----- n - 1/72576 n | C(n) 16128 / and in Maple input form: (1/2+86994317/55050240*n+439142267/220200960*n^2+121198361/94371840*n^3+ 33062393/75497472*n^4+3450589/47185920*n^5+948629/188743680*n^6+68783/660602880 *n^7+143/528482304*n^8)*4^n+(-1/2-6989/2520*n-123307/20160*n^2-128729/18144*n^3 -25475/5376*n^4-222743/120960*n^5-5287/13440*n^6-487/12096*n^7-25/16128*n^8-1/ 72576*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 19 18 1/2 17 16 1/2 15 143 Pi m m 2207491 Pi m 25 m 27180659 Pi m ------------- - ----- + ----------------- - ------ + ------------------ 528482304 72576 21139292160 16128 5284823040 14 1/2 13 12 1/2 11 487 m 118956509 Pi m 5287 m 98183633 Pi m - ------- + ------------------- - -------- + ------------------ 12096 1509949440 13440 188743680 10 1/2 9 8 1/2 7 222743 m 5366155237 Pi m 25475 m 6058303717 Pi m - ---------- + ------------------- - -------- + ------------------- 120960 3019898880 5376 1761607680 6 1/2 5 4 1/2 3 128729 m 6736098547 Pi m 123307 m 334383271 Pi m - --------- + ------------------- - --------- + ------------------ 18144 1761607680 20160 146800640 2 1/2 6989 m 9 Pi m - ------- + --------- - 1/2 2520 16 and in Maple input form: 143/528482304*Pi^(1/2)*m^19-1/72576*m^18+2207491/21139292160*Pi^(1/2)*m^17-25/ 16128*m^16+27180659/5284823040*Pi^(1/2)*m^15-487/12096*m^14+118956509/ 1509949440*Pi^(1/2)*m^13-5287/13440*m^12+98183633/188743680*Pi^(1/2)*m^11-\ 222743/120960*m^10+5366155237/3019898880*Pi^(1/2)*m^9-25475/5376*m^8+6058303717 /1761607680*Pi^(1/2)*m^7-128729/18144*m^6+6736098547/1761607680*Pi^(1/2)*m^5-\ 123307/20160*m^4+334383271/146800640*Pi^(1/2)*m^3-6989/2520*m^2+9/16*Pi^(1/2)*m -1/2 For the, 3, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 8, 7, 6, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 4, 3, 2, 1, 9]}, {[9, 8, 10, 7, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 4, 2, 1, 3]}, {[10, 8, 7, 9, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 3, 2, 4, 1]}, {[10, 9, 7, 6, 8, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 3, 5, 2, 1]}, {[10, 9, 8, 6, 5, 7, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 6, 3, 2, 1]}} is given by the following expression / 327641 14155373 2 2821189 3 2486627 4 89489 5 |-------- n + --------- n + -------- n + -------- n + -------- n \36700160 440401920 62914560 83886080 10485760 111577 6 10967 7 143 8\ n / 1429 + --------- n + --------- n + ---------- n | 4 + |- ------ n 125829120 440401920 1761607680 / \ 160160 6673 2 204627 3 6082291 4 4125767 5 729803 6 - ------ n - ------- n - -------- n - -------- n - -------- n 124800 1601600 38438400 38438400 19219200 114841 7 1129 8 9\ - -------- n - ------- n - 1/268800 n | C(n) 19219200 3494400 / and in Maple input form: (327641/36700160*n+14155373/440401920*n^2+2821189/62914560*n^3+2486627/83886080 *n^4+89489/10485760*n^5+111577/125829120*n^6+10967/440401920*n^7+143/1761607680 *n^8)*4^n+(-1429/160160*n-6673/124800*n^2-204627/1601600*n^3-6082291/38438400*n ^4-4125767/38438400*n^5-729803/19219200*n^6-114841/19219200*n^7-1129/3494400*n^ 8-1/268800*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 19 18 1/2 17 16 1/2 15 143 Pi m m 352231 Pi m 1129 m 3222859 Pi m ------------- - ------ + ---------------- - -------- + ----------------- 1761607680 268800 14092861440 3494400 3523215360 14 1/2 13 12 1/2 11 114841 m 3198379 Pi m 729803 m 823007 Pi m - ---------- + ----------------- - ---------- + ---------------- 19219200 335544320 19219200 20971520 10 1/2 9 8 1/2 7 4125767 m 157416977 Pi m 6082291 m 290977891 Pi m - ----------- + ------------------ - ---------- + ------------------ 38438400 2013265920 38438400 3523215360 6 1/2 5 4 1/2 3 2 204627 m 52950631 Pi m 6673 m 2948769 Pi m 1429 m - --------- + ----------------- - ------- + ---------------- - ------- 1601600 1174405120 124800 293601280 160160 and in Maple input form: 143/1761607680*Pi^(1/2)*m^19-1/268800*m^18+352231/14092861440*Pi^(1/2)*m^17-\ 1129/3494400*m^16+3222859/3523215360*Pi^(1/2)*m^15-114841/19219200*m^14+3198379 /335544320*Pi^(1/2)*m^13-729803/19219200*m^12+823007/20971520*Pi^(1/2)*m^11-\ 4125767/38438400*m^10+157416977/2013265920*Pi^(1/2)*m^9-6082291/38438400*m^8+ 290977891/3523215360*Pi^(1/2)*m^7-204627/1601600*m^6+52950631/1174405120*Pi^(1/ 2)*m^5-6673/124800*m^4+2948769/293601280*Pi^(1/2)*m^3-1429/160160*m^2 For the, 4, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[10, 8, 7, 6, 5, 4, 3, 2, 9, 1]}, {[10, 9, 8, 6, 5, 4, 7, 3, 2, 1]}, {[9, 8, 7, 6, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 4, 3, 2, 1, 8]}, {[9, 8, 7, 10, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 3, 2, 1, 4]}, {[10, 8, 7, 6, 9, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 3, 2, 5, 1]}, {[10, 9, 7, 6, 5, 8, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 3, 6, 2, 1]}} is given by the following expression / 161311 6165163 2 117211 3 2321311 4 11897 5 |-------- n + --------- n + ------- n + -------- n + ------- n \13762560 165150720 2621440 94371840 1966080 26987 6 283 7 11 8\ n / 16 470627 2 + -------- n + -------- n + --------- n | 4 + |- ---- n - ------- n 47185920 18350080 220200960 / \ 1365 7207200 1193 3 4501667 4 110821 5 204293 6 19189 7 - ---- n - -------- n - ------- n - ------- n - ------- n 8400 28828800 1201200 7207200 4804800 1951 8 9\ - ------- n - 1/436800 n | C(n) 9609600 / and in Maple input form: (161311/13762560*n+6165163/165150720*n^2+117211/2621440*n^3+2321311/94371840*n^ 4+11897/1966080*n^5+26987/47185920*n^6+283/18350080*n^7+11/220200960*n^8)*4^n+( -16/1365*n-470627/7207200*n^2-1193/8400*n^3-4501667/28828800*n^4-110821/1201200 *n^5-204293/7207200*n^6-19189/4804800*n^7-1951/9609600*n^8-1/436800*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 19 18 1/2 17 16 1/2 15 11 Pi m m 9089 Pi m 1951 m 778559 Pi m ------------ - ------ + -------------- - -------- + ---------------- 220200960 436800 587202560 9609600 1321205760 14 1/2 13 12 1/2 11 19189 m 842369 Pi m 204293 m 2963749 Pi m - --------- + ---------------- - ---------- + ----------------- 4804800 125829120 7207200 94371840 10 1/2 9 8 1/2 7 110821 m 6072063 Pi m 4501667 m 115779941 Pi m - ---------- + ---------------- - ---------- + ------------------ 1201200 83886080 28828800 1321205760 6 1/2 5 4 1/2 3 2 1193 m 23657441 Pi m 470627 m 483933 Pi m 16 m - ------- + ----------------- - --------- + --------------- - ----- 8400 440401920 7207200 36700160 1365 and in Maple input form: 11/220200960*Pi^(1/2)*m^19-1/436800*m^18+9089/587202560*Pi^(1/2)*m^17-1951/ 9609600*m^16+778559/1321205760*Pi^(1/2)*m^15-19189/4804800*m^14+842369/ 125829120*Pi^(1/2)*m^13-204293/7207200*m^12+2963749/94371840*Pi^(1/2)*m^11-\ 110821/1201200*m^10+6072063/83886080*Pi^(1/2)*m^9-4501667/28828800*m^8+ 115779941/1321205760*Pi^(1/2)*m^7-1193/8400*m^6+23657441/440401920*Pi^(1/2)*m^5 -470627/7207200*m^4+483933/36700160*Pi^(1/2)*m^3-16/1365*m^2 For the, 5, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 8, 7, 6, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 4, 3, 2, 1, 7]}, {[9, 8, 7, 6, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 3, 2, 1, 5]}, {[10, 8, 7, 6, 5, 4, 3, 9, 2, 1], [10, 9, 7, 6, 5, 4, 3, 2, 8, 1]}, {[10, 8, 7, 6, 5, 9, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 3, 2, 6, 1]}, {[10, 9, 7, 6, 5, 4, 8, 3, 2, 1], [10, 9, 8, 6, 5, 4, 3, 7, 2, 1]}} is given by the following expression /117113 772393 2 4017811 3 1599571 4 233717 5 |------- n + -------- n + -------- n + -------- n + -------- n \7864320 18874368 94371840 75497472 47185920 17315 6 1159 7 8\ n / 511 22045 2 + -------- n + -------- n + 1/25165824 n | 4 + |- ----- n - ------ n 37748736 94371840 / \ 34320 288288 868717 3 1727521 4 72041 5 27169 6 9299 7 - ------- n - -------- n - ------ n - ------- n - ------- n 5765760 11531520 887040 1153152 2882880 89 8 9\ - ------ n - 1/549120 n | C(n) 549120 / and in Maple input form: (117113/7864320*n+772393/18874368*n^2+4017811/94371840*n^3+1599571/75497472*n^4 +233717/47185920*n^5+17315/37748736*n^6+1159/94371840*n^7+1/25165824*n^8)*4^n+( -511/34320*n-22045/288288*n^2-868717/5765760*n^3-1727521/11531520*n^4-72041/ 887040*n^5-27169/1153152*n^6-9299/2882880*n^7-89/549120*n^8-1/549120*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 19 18 1/2 17 16 1/2 15 14 Pi m m 37223 Pi m 89 m 356731 Pi m 9299 m --------- - ------ + --------------- - ------ + ---------------- - -------- 25165824 549120 3019898880 549120 754974720 2882880 1/2 13 12 1/2 11 10 8258119 Pi m 27169 m 2525327 Pi m 72041 m + ----------------- - --------- + ----------------- - --------- 1509949440 1153152 94371840 887040 1/2 9 8 1/2 7 6 200550647 Pi m 1727521 m 67056019 Pi m 868717 m + ------------------ - ---------- + ----------------- - --------- 3019898880 11531520 754974720 5765760 1/2 5 4 1/2 3 2 15333511 Pi m 22045 m 351339 Pi m 511 m + ----------------- - -------- + --------------- - ------ 251658240 288288 20971520 34320 and in Maple input form: 1/25165824*Pi^(1/2)*m^19-1/549120*m^18+37223/3019898880*Pi^(1/2)*m^17-89/549120 *m^16+356731/754974720*Pi^(1/2)*m^15-9299/2882880*m^14+8258119/1509949440*Pi^(1 /2)*m^13-27169/1153152*m^12+2525327/94371840*Pi^(1/2)*m^11-72041/887040*m^10+ 200550647/3019898880*Pi^(1/2)*m^9-1727521/11531520*m^8+67056019/754974720*Pi^(1 /2)*m^7-868717/5765760*m^6+15333511/251658240*Pi^(1/2)*m^5-22045/288288*m^4+ 351339/20971520*Pi^(1/2)*m^3-511/34320*m^2 For the, 6, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[10, 9, 7, 6, 5, 4, 3, 8, 2, 1]}, {[9, 8, 7, 6, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 3, 2, 1, 6]}, {[10, 8, 7, 6, 5, 4, 9, 3, 2, 1], [10, 9, 8, 6, 5, 4, 3, 2, 7, 1]}} is given by the following expression / 21539 44017 2 1953739 3 3792463 4 54859 5 |------- n + ------- n + -------- n + --------- n + -------- n \1310720 1048576 47185920 188743680 11796480 8095 6 541 7 8\ n / 47 390107 2 + -------- n + -------- n + 7/188743680 n | 4 + |- ---- n - ------- n 18874368 47185920 / \ 2860 4804800 735689 3 8445161 4 318883 5 49201 6 1979 7 - ------- n - -------- n - ------- n - ------- n - ------ n 4804800 57657600 4118400 2217600 655200 1247 8 9\ - ------- n - 7/4118400 n | C(n) 8236800 / and in Maple input form: (21539/1310720*n+44017/1048576*n^2+1953739/47185920*n^3+3792463/188743680*n^4+ 54859/11796480*n^5+8095/18874368*n^6+541/47185920*n^7+7/188743680*n^8)*4^n+(-47 /2860*n-390107/4804800*n^2-735689/4804800*n^3-8445161/57657600*n^4-318883/ 4118400*n^5-49201/2217600*n^6-1979/655200*n^7-1247/8236800*n^8-7/4118400*n^9)*C (n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 19 18 1/2 17 16 1/2 15 14 7 Pi m 7 m 3475 Pi m 1247 m 166769 Pi m 1979 m ----------- - ------- + -------------- - -------- + ---------------- - -------- 188743680 4118400 301989888 8236800 377487360 655200 1/2 13 12 1/2 11 10 3875251 Pi m 49201 m 955985 Pi m 318883 m + ----------------- - --------- + ---------------- - ---------- 754974720 2217600 37748736 4118400 1/2 9 8 1/2 7 6 19330363 Pi m 8445161 m 3714419 Pi m 735689 m + ----------------- - ---------- + ---------------- - --------- 301989888 57657600 41943040 4804800 1/2 5 4 1/2 3 2 2670013 Pi m 390107 m 193851 Pi m 47 m + ---------------- - --------- + --------------- - ----- 41943040 4804800 10485760 2860 and in Maple input form: 7/188743680*Pi^(1/2)*m^19-7/4118400*m^18+3475/301989888*Pi^(1/2)*m^17-1247/ 8236800*m^16+166769/377487360*Pi^(1/2)*m^15-1979/655200*m^14+3875251/754974720* Pi^(1/2)*m^13-49201/2217600*m^12+955985/37748736*Pi^(1/2)*m^11-318883/4118400*m ^10+19330363/301989888*Pi^(1/2)*m^9-8445161/57657600*m^8+3714419/41943040*Pi^(1 /2)*m^7-735689/4804800*m^6+2670013/41943040*Pi^(1/2)*m^5-390107/4804800*m^4+ 193851/10485760*Pi^(1/2)*m^3-47/2860*m^2 For the, 7, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[8, 7, 6, 5, 4, 3, 2, 1, 9, 10]}, {[9, 10, 8, 7, 6, 5, 4, 3, 1, 2]}, {[10, 8, 9, 7, 6, 5, 4, 2, 3, 1]}, {[10, 9, 7, 8, 6, 5, 3, 4, 2, 1]}, {[10, 9, 8, 6, 7, 4, 5, 3, 2, 1]}, {[8, 9, 7, 6, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 4, 3, 1, 2, 10]}, {[8, 9, 10, 7, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 4, 1, 2, 3]}, {[9, 7, 8, 6, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 4, 2, 3, 1, 10]}, {[9, 8, 6, 7, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 3, 4, 2, 1, 10]}, {[9, 8, 7, 5, 6, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 5, 3, 2, 1, 10]}, {[9, 10, 7, 8, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 3, 4, 1, 2]}, {[9, 10, 8, 6, 7, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 5, 3, 1, 2]}, {[9, 10, 8, 7, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 4, 3, 1, 2]}, {[10, 7, 8, 9, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 2, 3, 4, 1]}, {[10, 8, 9, 6, 7, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 5, 2, 3, 1]}, {[10, 8, 9, 7, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 4, 2, 3, 1]}, {[10, 8, 9, 7, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 4, 2, 3, 1]}, {[10, 8, 9, 7, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 4, 2, 3, 1]}, {[10, 9, 6, 7, 8, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 3, 4, 5, 2, 1]}, {[10, 9, 7, 8, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 3, 4, 2, 1]}, {[10, 9, 7, 8, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 3, 4, 2, 1]}, {[10, 9, 8, 5, 6, 7, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 6, 3, 2, 1]}} is given by the following expression / 5061619 660043 2 15327 3 134843 4 245803 5 2123 6 |- 1/2 - ------- n - ------ n - ----- n - ------ n - ------- n - ------- n \ 3440640 393216 16384 524288 7864320 1572864 143 7\ n / 1920203 2722457 2 127916771 3 - -------- n | 4 + |1/2 + ------- n + ------- n + --------- n 11010048 / \ 720720 491400 21621600 19008313 4 66644269 5 148999 6 131609 7 8 + -------- n + -------- n + ------ n + ------- n + 7/23400 n 5405400 57657600 772200 9609600 9\ + 1/1209600 n | C(n) / and in Maple input form: (-1/2-5061619/3440640*n-660043/393216*n^2-15327/16384*n^3-134843/524288*n^4-\ 245803/7864320*n^5-2123/1572864*n^6-143/11010048*n^7)*4^n+(1/2+1920203/720720*n +2722457/491400*n^2+127916771/21621600*n^3+19008313/5405400*n^4+66644269/ 57657600*n^5+148999/772200*n^6+131609/9609600*n^7+7/23400*n^8+1/1209600*n^9)*C( n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 18 1/2 17 16 1/2 15 14 m 143 Pi m 7 m 120175 Pi m 131609 m ------- - ------------- + ----- - ---------------- + ---------- 1209600 11010048 23400 88080384 9609600 1/2 13 12 1/2 11 10 2061959 Pi m 148999 m 6131129 Pi m 66644269 m - ----------------- + ---------- - ----------------- + ------------ 62914560 772200 20971520 57657600 1/2 9 8 1/2 7 6 5137299 Pi m 19008313 m 67117 Pi m 127916771 m - ---------------- + ----------- - -------------- + ------------ 4194304 5405400 24576 21621600 1/2 5 4 1/2 3 2 369885353 Pi m 2722457 m 19772377 Pi m 1920203 m - ------------------ + ---------- - ----------------- + ---------- 110100480 491400 9175040 720720 1/2 9 Pi m - --------- + 1/2 16 and in Maple input form: 1/1209600*m^18-143/11010048*Pi^(1/2)*m^17+7/23400*m^16-120175/88080384*Pi^(1/2) *m^15+131609/9609600*m^14-2061959/62914560*Pi^(1/2)*m^13+148999/772200*m^12-\ 6131129/20971520*Pi^(1/2)*m^11+66644269/57657600*m^10-5137299/4194304*Pi^(1/2)* m^9+19008313/5405400*m^8-67117/24576*Pi^(1/2)*m^7+127916771/21621600*m^6-\ 369885353/110100480*Pi^(1/2)*m^5+2722457/491400*m^4-19772377/9175040*Pi^(1/2)*m ^3+1920203/720720*m^2-9/16*Pi^(1/2)*m+1/2 For the, 8, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 8, 7, 5, 4, 6, 3, 2, 1, 10]}, {[10, 9, 8, 5, 4, 6, 7, 3, 2, 1]}, {[8, 7, 9, 6, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 4, 2, 1, 3, 10]}, {[8, 7, 9, 10, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 2, 1, 3, 4]}, {[8, 9, 7, 6, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 4, 3, 1, 2, 9]}, {[8, 9, 7, 10, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 3, 1, 2, 4]}, {[9, 7, 6, 8, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 3, 2, 4, 1, 10]}, {[9, 7, 8, 6, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 4, 2, 3, 1, 9]}, {[9, 7, 8, 10, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 2, 3, 1, 4]}, {[9, 8, 6, 5, 7, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 3, 5, 2, 1, 10]}, {[9, 8, 6, 7, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 3, 4, 2, 1, 9]}, {[9, 8, 7, 5, 6, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 5, 3, 2, 1, 9]}, {[9, 8, 7, 6, 4, 5, 3, 2, 10, 1], [10, 8, 7, 5, 6, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 5, 3, 4, 2, 10, 1], [10, 8, 6, 7, 5, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 5, 4, 2, 3, 10, 1], [10, 7, 8, 6, 5, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 5, 4, 3, 10, 1, 2], [9, 10, 7, 6, 5, 4, 3, 2, 1, 8]}, {[9, 8, 10, 6, 7, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 5, 2, 1, 3]}, {[9, 8, 10, 7, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 5, 4, 2, 1, 3]}, {[9, 10, 7, 6, 8, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 3, 5, 1, 2]}, {[9, 10, 8, 6, 5, 7, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 6, 3, 1, 2]}, {[9, 10, 8, 7, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 5, 4, 3, 1, 2]}, {[10, 7, 6, 8, 9, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 3, 2, 4, 5, 1]}, {[10, 7, 8, 6, 9, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 2, 3, 5, 1]}, {[10, 8, 6, 7, 9, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 3, 4, 2, 5, 1]}, {[10, 8, 7, 9, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 3, 2, 4, 1]}, {[10, 8, 7, 9, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 3, 2, 4, 1]}, {[10, 8, 7, 9, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 3, 2, 4, 1]}, {[10, 8, 7, 9, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 3, 2, 4, 1]}, {[10, 8, 9, 6, 5, 7, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 6, 2, 3, 1]}, {[10, 8, 9, 7, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 4, 2, 3, 1]}, {[10, 8, 9, 7, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 4, 2, 3, 1]}, {[10, 9, 6, 5, 7, 8, 4, 3, 2, 1], [10, 9, 8, 7, 4, 3, 5, 6, 2, 1]}, {[10, 9, 6, 7, 5, 8, 4, 3, 2, 1], [10, 9, 8, 7, 5, 3, 4, 6, 2, 1]}, {[10, 9, 7, 5, 6, 8, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 3, 6, 2, 1]}, {[10, 9, 7, 6, 8, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 3, 5, 2, 1]}, {[10, 9, 7, 6, 8, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 3, 5, 2, 1]}, {[10, 9, 7, 8, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 3, 4, 2, 1]}, {[10, 9, 8, 5, 6, 4, 7, 3, 2, 1], [10, 9, 8, 6, 4, 5, 7, 3, 2, 1]}, { [8, 7, 6, 5, 4, 3, 2, 9, 1, 10], [8, 7, 6, 5, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 4, 3, 2, 1, 8, 10], [10, 7, 6, 5, 4, 3, 2, 1, 8, 9]}} is given by the following expression / 6791 12567 2 15119 3 6215 4 6117 5 377 6 |- ------ n - ------ n - ------ n - ------ n - ------- n - ------- n \ 573440 327680 327680 262144 1310720 1310720 33 7\ n / 237 480143 2 789067 3 353351 4 - ------- n | 4 + |----- n + ------- n + ------- n + ------- n 9175040 / \20020 7207200 5405400 2217600 969571 5 19193 6 108049 7 2117 8 9\ + -------- n + ------ n + -------- n + -------- n + 1/3931200 n | C(n) 10810800 800800 43243200 28828800 / and in Maple input form: (-6791/573440*n-12567/327680*n^2-15119/327680*n^3-6215/262144*n^4-6117/1310720* n^5-377/1310720*n^6-33/9175040*n^7)*4^n+(237/20020*n+480143/7207200*n^2+789067/ 5405400*n^3+353351/2217600*n^4+969571/10810800*n^5+19193/800800*n^6+108049/ 43243200*n^7+2117/28828800*n^8+1/3931200*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 18 1/2 17 16 1/2 15 14 m 33 Pi m 2117 m 21409 Pi m 108049 m ------- - ------------ + -------- - --------------- + ---------- 3931200 9175040 28828800 73400320 43243200 1/2 13 12 1/2 11 10 52329 Pi m 19193 m 303653 Pi m 969571 m - --------------- + --------- - ---------------- + ---------- 10485760 800800 10485760 10810800 1/2 9 8 1/2 7 6 763483 Pi m 353351 m 236607 Pi m 789067 m - --------------- + --------- - --------------- + --------- 10485760 2217600 2621440 5405400 1/2 5 4 1/2 3 2 1009033 Pi m 480143 m 61119 Pi m 237 m - ---------------- + --------- - -------------- + ------ 18350080 7207200 4587520 20020 and in Maple input form: 1/3931200*m^18-33/9175040*Pi^(1/2)*m^17+2117/28828800*m^16-21409/73400320*Pi^(1 /2)*m^15+108049/43243200*m^14-52329/10485760*Pi^(1/2)*m^13+19193/800800*m^12-\ 303653/10485760*Pi^(1/2)*m^11+969571/10810800*m^10-763483/10485760*Pi^(1/2)*m^9 +353351/2217600*m^8-236607/2621440*Pi^(1/2)*m^7+789067/5405400*m^6-1009033/ 18350080*Pi^(1/2)*m^5+480143/7207200*m^4-61119/4587520*Pi^(1/2)*m^3+237/20020*m ^2 For the, 9, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 7, 6, 5, 4, 3, 2, 8, 1, 10]}, {[10, 7, 6, 5, 4, 3, 2, 8, 9, 1]}, {[8, 7, 6, 5, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 4, 3, 2, 1, 7, 10]}, {[8, 7, 6, 5, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 4, 3, 2, 1, 7, 8]}, {[8, 7, 6, 9, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 3, 2, 1, 4, 10]}, {[8, 7, 6, 9, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 3, 2, 1, 4, 5]}, {[8, 9, 7, 6, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 4, 3, 1, 2, 8]}, {[8, 9, 7, 6, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 3, 1, 2, 5]}, {[9, 7, 6, 5, 8, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 3, 2, 5, 1, 10]}, {[9, 7, 8, 6, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 4, 2, 3, 1, 8]}, {[9, 7, 8, 6, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 2, 3, 1, 5]}, {[9, 8, 6, 5, 4, 7, 3, 2, 1, 10], [9, 8, 7, 5, 4, 3, 6, 2, 1, 10]}, {[9, 8, 6, 7, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 3, 4, 2, 1, 8]}, {[9, 8, 6, 7, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 3, 4, 2, 1, 5]}, {[9, 8, 7, 5, 6, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 5, 3, 2, 1, 8]}, {[9, 8, 7, 6, 4, 5, 3, 10, 2, 1], [10, 9, 7, 5, 6, 4, 3, 2, 1, 8]}, {[9, 8, 7, 6, 5, 3, 4, 10, 2, 1], [10, 9, 6, 7, 5, 4, 3, 2, 1, 8]}, {[9, 8, 7, 6, 5, 4, 10, 2, 3, 1], [10, 8, 9, 6, 5, 4, 3, 2, 1, 7]}, {[9, 8, 7, 6, 5, 4, 10, 3, 1, 2], [9, 10, 8, 6, 5, 4, 3, 2, 1, 7]}, {[9, 8, 7, 10, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 5, 3, 2, 1, 4]}, {[9, 10, 7, 6, 5, 4, 3, 2, 8, 1], [10, 8, 7, 6, 5, 4, 3, 9, 1, 2]}, {[9, 10, 7, 6, 5, 8, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 3, 6, 1, 2]}, {[9, 10, 8, 6, 5, 4, 7, 3, 2, 1], [10, 9, 8, 6, 5, 4, 7, 3, 1, 2]}, {[9, 10, 8, 7, 5, 4, 3, 6, 2, 1], [10, 9, 7, 6, 5, 8, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 5, 4, 3, 1, 2]}, {[10, 7, 6, 5, 8, 9, 4, 3, 2, 1], [10, 9, 8, 7, 4, 3, 2, 5, 6, 1]}, {[10, 7, 8, 6, 5, 4, 3, 2, 9, 1], [10, 8, 7, 6, 5, 4, 2, 3, 9, 1]}, {[10, 7, 8, 6, 5, 9, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 2, 3, 6, 1]}, {[10, 8, 6, 7, 5, 4, 3, 2, 9, 1], [10, 8, 7, 6, 5, 3, 4, 2, 9, 1]}, {[10, 8, 6, 7, 5, 9, 4, 3, 2, 1], [10, 9, 8, 7, 5, 3, 4, 2, 6, 1]}, {[10, 8, 7, 5, 6, 4, 3, 2, 9, 1], [10, 8, 7, 6, 4, 5, 3, 2, 9, 1]}, {[10, 8, 7, 5, 6, 9, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 3, 2, 6, 1]}, {[10, 8, 7, 6, 9, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 3, 2, 5, 1]}, {[10, 8, 7, 6, 9, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 3, 2, 5, 1]}, {[10, 8, 7, 6, 9, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 3, 2, 5, 1]}, {[10, 8, 9, 6, 5, 4, 7, 3, 2, 1], [10, 9, 8, 6, 5, 4, 7, 2, 3, 1]}, {[10, 8, 9, 7, 5, 4, 3, 6, 2, 1], [10, 9, 7, 6, 5, 8, 4, 2, 3, 1]}, {[10, 9, 6, 5, 4, 7, 8, 3, 2, 1], [10, 9, 8, 5, 4, 3, 6, 7, 2, 1]}, {[10, 9, 6, 7, 5, 4, 8, 3, 2, 1], [10, 9, 8, 6, 5, 3, 4, 7, 2, 1]}, {[10, 9, 7, 5, 6, 4, 8, 3, 2, 1], [10, 9, 8, 6, 4, 5, 3, 7, 2, 1]}, {[10, 9, 7, 6, 4, 5, 8, 3, 2, 1], [10, 9, 8, 5, 6, 4, 3, 7, 2, 1]}, {[10, 9, 7, 6, 5, 8, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 3, 6, 2, 1]}} is given by the following expression / 1289 2859 2 14273 3 4891 4 4241 5 49 6 |- ----- n - ----- n - ------ n - ------ n - ------- n - ------ n \ 81920 65536 327680 262144 1310720 262144 7\ n / 585041 2 3431551 3 1190383 4 - 3/1310720 n | 4 + |9/572 n + ------- n + -------- n + ------- n / \ 7207200 21621600 7862400 20483 5 375707 6 23981 7 581 8 9\ + ------ n + -------- n + -------- n + -------- n + 1/6177600 n | C(n) 277200 21621600 14414400 12355200 / and in Maple input form: (-1289/81920*n-2859/65536*n^2-14273/327680*n^3-4891/262144*n^4-4241/1310720*n^5 -49/262144*n^6-3/1310720*n^7)*4^n+(9/572*n+585041/7207200*n^2+3431551/21621600* n^3+1190383/7862400*n^4+20483/277200*n^5+375707/21621600*n^6+23981/14414400*n^7 +581/12355200*n^8+1/6177600*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 18 1/2 17 16 1/2 15 14 1/2 13 m 3 Pi m 581 m 1987 Pi m 23981 m 36133 Pi m ------- - ----------- + -------- - -------------- + --------- - --------------- 6177600 1310720 12355200 10485760 14414400 10485760 12 1/2 11 10 1/2 9 8 375707 m 233809 Pi m 20483 m 676831 Pi m 1190383 m + ---------- - ---------------- + --------- - --------------- + ---------- 21621600 10485760 277200 10485760 7862400 1/2 7 6 1/2 5 4 242817 Pi m 3431551 m 169903 Pi m 585041 m - --------------- + ---------- - --------------- + --------- 2621440 21621600 2621440 7207200 1/2 3 2 11601 Pi m 9 m - -------------- + ---- 655360 572 and in Maple input form: 1/6177600*m^18-3/1310720*Pi^(1/2)*m^17+581/12355200*m^16-1987/10485760*Pi^(1/2) *m^15+23981/14414400*m^14-36133/10485760*Pi^(1/2)*m^13+375707/21621600*m^12-\ 233809/10485760*Pi^(1/2)*m^11+20483/277200*m^10-676831/10485760*Pi^(1/2)*m^9+ 1190383/7862400*m^8-242817/2621440*Pi^(1/2)*m^7+3431551/21621600*m^6-169903/ 2621440*Pi^(1/2)*m^5+585041/7207200*m^4-11601/655360*Pi^(1/2)*m^3+9/572*m^2 For the, 10, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 8, 6, 5, 4, 3, 7, 2, 1, 10]}, {[10, 9, 6, 5, 4, 3, 7, 8, 2, 1]}, {[8, 7, 6, 5, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 4, 3, 2, 1, 6, 10]}, {[8, 7, 6, 5, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 4, 3, 2, 1, 6, 7]}, {[8, 7, 6, 5, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 3, 2, 1, 5, 10]}, {[8, 7, 6, 5, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 3, 2, 1, 5, 6]}, {[8, 9, 7, 6, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 4, 3, 1, 2, 7]}, {[8, 9, 7, 6, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 3, 1, 2, 6]}, {[9, 7, 6, 5, 4, 3, 8, 2, 1, 10], [9, 8, 6, 5, 4, 3, 2, 7, 1, 10]}, {[9, 7, 6, 5, 4, 8, 3, 2, 1, 10], [9, 8, 7, 5, 4, 3, 2, 6, 1, 10]}, {[9, 7, 8, 6, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 4, 2, 3, 1, 7]}, {[9, 7, 8, 6, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 2, 3, 1, 6]}, {[9, 8, 6, 7, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 3, 4, 2, 1, 7]}, {[9, 8, 6, 7, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 3, 4, 2, 1, 6]}, {[9, 8, 7, 5, 6, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 5, 3, 2, 1, 7]}, {[9, 8, 7, 5, 6, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 3, 2, 1, 6]}, {[9, 8, 7, 6, 4, 5, 10, 3, 2, 1], [10, 9, 8, 5, 6, 4, 3, 2, 1, 7]}, {[9, 8, 7, 6, 5, 10, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 3, 2, 1, 6]}, {[9, 8, 7, 6, 5, 10, 4, 2, 3, 1], [10, 8, 9, 7, 5, 4, 3, 2, 1, 6]}, {[9, 8, 7, 6, 5, 10, 4, 3, 1, 2], [9, 10, 8, 7, 5, 4, 3, 2, 1, 6]}, {[9, 8, 7, 6, 10, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 4, 3, 2, 1, 5]}, {[9, 10, 7, 6, 5, 4, 3, 8, 2, 1], [10, 9, 7, 6, 5, 4, 3, 8, 1, 2]}, {[9, 10, 7, 6, 5, 4, 8, 3, 2, 1], [10, 9, 8, 6, 5, 4, 3, 7, 1, 2]}, {[9, 10, 8, 6, 5, 4, 3, 2, 7, 1], [10, 8, 7, 6, 5, 4, 9, 3, 1, 2]}, {[9, 10, 8, 6, 5, 4, 3, 7, 2, 1], [10, 9, 7, 6, 5, 4, 8, 3, 1, 2]}, {[9, 10, 8, 7, 5, 4, 3, 2, 6, 1], [10, 8, 7, 6, 5, 9, 4, 3, 1, 2]}, {[10, 7, 6, 5, 4, 3, 8, 9, 2, 1], [10, 9, 6, 5, 4, 3, 2, 7, 8, 1]}, {[10, 7, 6, 5, 4, 8, 9, 3, 2, 1], [10, 9, 8, 5, 4, 3, 2, 6, 7, 1]}, {[10, 7, 8, 6, 5, 4, 3, 9, 2, 1], [10, 9, 7, 6, 5, 4, 2, 3, 8, 1]}, {[10, 7, 8, 6, 5, 4, 9, 3, 2, 1], [10, 9, 8, 6, 5, 4, 2, 3, 7, 1]}, {[10, 8, 6, 7, 5, 4, 3, 9, 2, 1], [10, 9, 7, 6, 5, 3, 4, 2, 8, 1]}, {[10, 8, 6, 7, 5, 4, 9, 3, 2, 1], [10, 9, 8, 6, 5, 3, 4, 2, 7, 1]}, {[10, 8, 7, 5, 6, 4, 3, 9, 2, 1], [10, 9, 7, 6, 4, 5, 3, 2, 8, 1]}, {[10, 8, 7, 5, 6, 4, 9, 3, 2, 1], [10, 9, 8, 6, 4, 5, 3, 2, 7, 1]}, {[10, 8, 7, 6, 4, 5, 3, 9, 2, 1], [10, 9, 7, 5, 6, 4, 3, 2, 8, 1]}, {[10, 8, 7, 6, 4, 5, 9, 3, 2, 1], [10, 9, 8, 5, 6, 4, 3, 2, 7, 1]}, {[10, 8, 7, 6, 5, 3, 4, 9, 2, 1], [10, 9, 6, 7, 5, 4, 3, 2, 8, 1]}, {[10, 8, 7, 6, 5, 4, 9, 2, 3, 1], [10, 8, 9, 6, 5, 4, 3, 2, 7, 1]}, {[10, 8, 7, 6, 5, 9, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 3, 2, 6, 1]}, {[10, 8, 7, 6, 5, 9, 4, 2, 3, 1], [10, 8, 9, 7, 5, 4, 3, 2, 6, 1]}, {[10, 8, 9, 6, 5, 4, 3, 7, 2, 1], [10, 9, 7, 6, 5, 4, 8, 2, 3, 1]}, {[10, 9, 6, 7, 5, 4, 3, 8, 2, 1], [10, 9, 7, 6, 5, 3, 4, 8, 2, 1]}, {[10, 9, 7, 5, 6, 4, 3, 8, 2, 1], [10, 9, 7, 6, 4, 5, 3, 8, 2, 1]}} is given by the following expression / 9367 90509 2 2003 3 25579 4 7171 5 1229 6 |- ------ n - ------- n - ----- n - ------- n - ------- n - ------- n \ 491520 1966080 49152 1572864 2621440 7864320 7\ n /109 791471 2 96701 3 1656071 4 - 1/524288 n | 4 + |---- n + ------- n + ------ n + -------- n / \5720 8648640 589680 11531520 75599 5 85531 6 929 7 1357 8 9\ + ------- n + ------- n + ------ n + -------- n + 1/7413120 n | C(n) 1153152 5765760 665280 34594560 / and in Maple input form: (-9367/491520*n-90509/1966080*n^2-2003/49152*n^3-25579/1572864*n^4-7171/2621440 *n^5-1229/7864320*n^6-1/524288*n^7)*4^n+(109/5720*n+791471/8648640*n^2+96701/ 589680*n^3+1656071/11531520*n^4+75599/1153152*n^5+85531/5765760*n^6+929/665280* n^7+1357/34594560*n^8+1/7413120*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 18 1/2 17 16 1/2 15 14 1/2 13 m Pi m 1357 m 9967 Pi m 929 m 12211 Pi m ------- - --------- + -------- - -------------- + ------- - --------------- 7413120 524288 34594560 62914560 665280 4194304 12 1/2 11 10 1/2 9 8 85531 m 1216777 Pi m 75599 m 742979 Pi m 1656071 m + --------- - ----------------- + --------- - --------------- + ---------- 5765760 62914560 1153152 12582912 11531520 1/2 7 6 1/2 5 4 1/2 3 45161 Pi m 96701 m 222865 Pi m 791471 m 28101 Pi m - -------------- + -------- - --------------- + --------- - -------------- 491520 589680 3145728 8648640 1310720 2 109 m + ------ 5720 and in Maple input form: 1/7413120*m^18-1/524288*Pi^(1/2)*m^17+1357/34594560*m^16-9967/62914560*Pi^(1/2) *m^15+929/665280*m^14-12211/4194304*Pi^(1/2)*m^13+85531/5765760*m^12-1216777/ 62914560*Pi^(1/2)*m^11+75599/1153152*m^10-742979/12582912*Pi^(1/2)*m^9+1656071/ 11531520*m^8-45161/491520*Pi^(1/2)*m^7+96701/589680*m^6-222865/3145728*Pi^(1/2) *m^5+791471/8648640*m^4-28101/1310720*Pi^(1/2)*m^3+109/5720*m^2 For the, 11, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 8, 10, 7, 6, 5, 4, 2, 1, 3]}, {[10, 8, 7, 9, 6, 5, 3, 2, 4, 1]}, {[10, 9, 7, 6, 8, 4, 3, 5, 2, 1]}, {[8, 7, 6, 5, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 4, 3, 2, 1, 7, 9]}, {[8, 7, 9, 6, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 4, 2, 1, 3, 9]}, {[8, 7, 9, 6, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 2, 1, 3, 5]}, {[9, 7, 6, 5, 4, 3, 2, 8, 10, 1], [10, 7, 6, 5, 4, 3, 2, 8, 1, 9]}, {[9, 7, 6, 8, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 3, 2, 4, 1, 9]}, {[9, 7, 6, 8, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 3, 2, 4, 1, 5]}, {[9, 8, 6, 5, 7, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 3, 5, 2, 1, 9]}, {[9, 8, 7, 5, 4, 6, 3, 2, 10, 1], [10, 8, 7, 5, 4, 6, 3, 2, 1, 9]}, {[9, 8, 7, 6, 4, 3, 5, 2, 10, 1], [10, 8, 6, 5, 7, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 5, 3, 2, 4, 10, 1], [10, 7, 6, 8, 5, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 5, 4, 10, 2, 1, 3], [9, 8, 10, 6, 5, 4, 3, 2, 1, 7]}, {[9, 8, 10, 6, 5, 7, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 6, 2, 1, 3]}, {[9, 8, 10, 7, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 5, 4, 2, 1, 3]}, {[10, 7, 6, 8, 5, 9, 4, 3, 2, 1], [10, 9, 8, 7, 5, 3, 2, 4, 6, 1]}, {[10, 8, 6, 5, 7, 9, 4, 3, 2, 1], [10, 9, 8, 7, 4, 3, 5, 2, 6, 1]}, {[10, 8, 7, 9, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 3, 2, 4, 1]}, {[10, 8, 7, 9, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 3, 2, 4, 1]}, {[10, 9, 6, 5, 7, 4, 8, 3, 2, 1], [10, 9, 8, 6, 4, 3, 5, 7, 2, 1]}, {[10, 9, 7, 5, 4, 6, 8, 3, 2, 1], [10, 9, 8, 5, 4, 6, 3, 7, 2, 1]}} is given by the following expression / 37 2 233 3 629 4 569 5 35 6 |7/30720 n + ----- n + ------ n - ------ n - ------ n - ------ n \ 36864 491520 589824 983040 589824 7\ n / 5501 2 12049 3 8753 4 - 1/983040 n | 4 + |-1/4290 n - ------- n - ------- n - -------- n / \ 3603600 3931200 12355200 82961 5 95867 6 233 7 223 8 9\ + -------- n + -------- n + ------ n + -------- n + 1/12355200 n | 28828800 43243200 554400 12355200 / C(n) and in Maple input form: (7/30720*n+37/36864*n^2+233/491520*n^3-629/589824*n^4-569/983040*n^5-35/589824* n^6-1/983040*n^7)*4^n+(-1/4290*n-5501/3603600*n^2-12049/3931200*n^3-8753/ 12355200*n^4+82961/28828800*n^5+95867/43243200*n^6+233/554400*n^7+223/12355200* n^8+1/12355200*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 18 1/2 17 16 1/2 15 14 1/2 13 m Pi m 223 m 1427 Pi m 233 m 5077 Pi m -------- - --------- + -------- - -------------- + ------- - -------------- 12355200 983040 12355200 23592960 554400 7864320 12 1/2 11 10 1/2 9 8 95867 m 40523 Pi m 82961 m 5707 Pi m 8753 m + --------- - --------------- + --------- - ------------- - -------- 43243200 23592960 28828800 7864320 12355200 1/2 7 6 1/2 5 4 1/2 3 2 18131 Pi m 12049 m 667 Pi m 5501 m 21 Pi m m + -------------- - -------- + ------------ - ------- + ----------- - ---- 11796480 3931200 491520 3603600 81920 4290 and in Maple input form: 1/12355200*m^18-1/983040*Pi^(1/2)*m^17+223/12355200*m^16-1427/23592960*Pi^(1/2) *m^15+233/554400*m^14-5077/7864320*Pi^(1/2)*m^13+95867/43243200*m^12-40523/ 23592960*Pi^(1/2)*m^11+82961/28828800*m^10-5707/7864320*Pi^(1/2)*m^9-8753/ 12355200*m^8+18131/11796480*Pi^(1/2)*m^7-12049/3931200*m^6+667/491520*Pi^(1/2)* m^5-5501/3603600*m^4+21/81920*Pi^(1/2)*m^3-1/4290*m^2 For the, 12, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[10, 8, 7, 5, 4, 6, 3, 2, 9, 1]}, {[10, 9, 7, 5, 4, 6, 3, 8, 2, 1]}, {[8, 7, 6, 5, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 4, 3, 2, 1, 6, 9]}, {[8, 7, 6, 5, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 4, 3, 2, 1, 6, 8]}, {[8, 7, 6, 9, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 3, 2, 1, 4, 9]}, {[8, 7, 6, 9, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 3, 2, 1, 4, 6]}, {[8, 7, 9, 6, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 4, 2, 1, 3, 8]}, {[8, 7, 9, 6, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 2, 1, 3, 6]}, {[9, 7, 6, 5, 4, 3, 8, 2, 10, 1], [10, 8, 6, 5, 4, 3, 2, 7, 1, 9]}, {[9, 7, 6, 5, 4, 3, 8, 10, 2, 1], [10, 9, 6, 5, 4, 3, 2, 7, 1, 8]}, {[9, 7, 6, 5, 8, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 3, 2, 5, 1, 9]}, {[9, 7, 6, 5, 8, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 3, 2, 5, 1, 6]}, {[9, 7, 6, 8, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 3, 2, 4, 1, 8]}, {[9, 7, 6, 8, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 3, 2, 4, 1, 6]}, {[9, 8, 6, 5, 4, 3, 2, 7, 10, 1], [10, 7, 6, 5, 4, 3, 8, 2, 1, 9]}, {[9, 8, 6, 5, 4, 7, 3, 2, 10, 1], [10, 8, 7, 5, 4, 3, 6, 2, 1, 9]}, {[9, 8, 6, 5, 7, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 3, 5, 2, 1, 8]}, {[9, 8, 6, 5, 7, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 3, 5, 2, 1, 6]}, {[9, 8, 7, 5, 4, 3, 6, 2, 10, 1], [10, 8, 6, 5, 4, 7, 3, 2, 1, 9]}, {[9, 8, 7, 5, 4, 6, 3, 10, 2, 1], [10, 9, 7, 5, 4, 6, 3, 2, 1, 8]}, {[9, 8, 7, 6, 4, 3, 2, 5, 10, 1], [10, 7, 6, 5, 8, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 4, 3, 5, 10, 2, 1], [10, 9, 6, 5, 7, 4, 3, 2, 1, 8]}, {[9, 8, 7, 6, 5, 10, 3, 2, 1, 4], [9, 8, 7, 10, 5, 4, 3, 2, 1, 6]}, {[9, 8, 7, 6, 5, 10, 3, 2, 4, 1], [10, 8, 7, 9, 5, 4, 3, 2, 1, 6]}, {[9, 8, 7, 6, 5, 10, 4, 2, 1, 3], [9, 8, 10, 7, 5, 4, 3, 2, 1, 6]}, {[9, 8, 7, 10, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 5, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 5, 4, 2, 1, 3], [9, 8, 10, 7, 6, 5, 3, 2, 1, 4]}, {[9, 8, 10, 6, 5, 4, 3, 2, 7, 1], [10, 8, 7, 6, 5, 4, 9, 2, 1, 3]}, {[9, 8, 10, 6, 5, 4, 7, 3, 2, 1], [10, 9, 8, 6, 5, 4, 7, 2, 1, 3]}, {[9, 8, 10, 7, 5, 4, 3, 6, 2, 1], [10, 9, 7, 6, 5, 8, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 5, 4, 2, 1, 3]}, {[10, 7, 6, 5, 4, 3, 8, 2, 9, 1], [10, 8, 6, 5, 4, 3, 2, 7, 9, 1]}, {[10, 7, 6, 5, 8, 4, 9, 3, 2, 1], [10, 9, 8, 6, 4, 3, 2, 5, 7, 1]}, {[10, 7, 6, 8, 5, 4, 3, 2, 9, 1], [10, 8, 7, 6, 5, 3, 2, 4, 9, 1]}, {[10, 7, 6, 8, 5, 4, 9, 3, 2, 1], [10, 9, 8, 6, 5, 3, 2, 4, 7, 1]}, {[10, 8, 6, 5, 4, 7, 9, 3, 2, 1], [10, 9, 8, 5, 4, 3, 6, 2, 7, 1]}, {[10, 8, 6, 5, 7, 4, 3, 2, 9, 1], [10, 8, 7, 6, 4, 3, 5, 2, 9, 1]}, {[10, 8, 6, 5, 7, 4, 9, 3, 2, 1], [10, 9, 8, 6, 4, 3, 5, 2, 7, 1]}, {[10, 8, 7, 5, 4, 6, 9, 3, 2, 1], [10, 9, 8, 5, 4, 6, 3, 2, 7, 1]}, {[10, 8, 7, 6, 9, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 4, 3, 2, 5, 1]}, {[10, 8, 7, 6, 9, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 4, 3, 2, 5, 1]}, {[10, 8, 7, 9, 5, 4, 3, 6, 2, 1], [10, 9, 7, 6, 5, 8, 3, 2, 4, 1]}, {[10, 9, 6, 5, 4, 7, 3, 8, 2, 1], [10, 9, 7, 5, 4, 3, 6, 8, 2, 1]}, {[10, 9, 6, 5, 7, 4, 3, 8, 2, 1], [10, 9, 7, 6, 4, 3, 5, 8, 2, 1]}} is given by the following expression / 43 59 2 379 3 19 4 163 5 6 |----- n + ----- n - ------- n - ----- n - ------ n - 1/24576 n \61440 49152 1474560 16384 368640 7\ n / 31037 2 402223 3 87721 4 - 1/1474560 n | 4 + |-1/1430 n - -------- n - --------- n + -------- n / \ 10810800 129729600 86486400 151391 5 79763 6 4307 7 1049 8 9\ + -------- n + -------- n + -------- n + -------- n + 1/18532800 n | 43243200 43243200 14414400 86486400 / C(n) and in Maple input form: (43/61440*n+59/49152*n^2-379/1474560*n^3-19/16384*n^4-163/368640*n^5-1/24576*n^ 6-1/1474560*n^7)*4^n+(-1/1430*n-31037/10810800*n^2-402223/129729600*n^3+87721/ 86486400*n^4+151391/43243200*n^5+79763/43243200*n^6+4307/14414400*n^7+1049/ 86486400*n^8+1/18532800*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 18 1/2 17 16 1/2 15 14 1/2 13 m Pi m 1049 m 163 Pi m 4307 m 1439 Pi m -------- - --------- + -------- - ------------- + -------- - -------------- 18532800 1474560 86486400 3932160 14414400 2949120 12 1/2 11 10 1/2 9 8 79763 m 543 Pi m 151391 m 9211 Pi m 87721 m + --------- - ------------- + ---------- - ------------- + -------- 43243200 327680 43243200 5898240 86486400 1/2 7 6 1/2 5 4 1/2 3 3583 Pi m 402223 m 4031 Pi m 31037 m 129 Pi m + ------------- - --------- + ------------- - -------- + ------------ 3932160 129729600 1966080 10810800 163840 2 m - ---- 1430 and in Maple input form: 1/18532800*m^18-1/1474560*Pi^(1/2)*m^17+1049/86486400*m^16-163/3932160*Pi^(1/2) *m^15+4307/14414400*m^14-1439/2949120*Pi^(1/2)*m^13+79763/43243200*m^12-543/ 327680*Pi^(1/2)*m^11+151391/43243200*m^10-9211/5898240*Pi^(1/2)*m^9+87721/ 86486400*m^8+3583/3932160*Pi^(1/2)*m^7-402223/129729600*m^6+4031/1966080*Pi^(1/ 2)*m^5-31037/10810800*m^4+129/163840*Pi^(1/2)*m^3-1/1430*m^2 For the, 13, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 8, 7, 6, 10, 4, 3, 2, 1, 5]}, {[8, 7, 6, 5, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 3, 2, 1, 5, 9]}, {[8, 7, 6, 5, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 3, 2, 1, 5, 7]}, {[8, 7, 9, 6, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 4, 2, 1, 3, 7]}, {[9, 7, 6, 5, 4, 8, 3, 2, 10, 1], [10, 8, 7, 5, 4, 3, 2, 6, 1, 9]}, {[9, 7, 6, 5, 4, 8, 10, 3, 2, 1], [10, 9, 8, 5, 4, 3, 2, 6, 1, 7]}, {[9, 7, 6, 8, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 3, 2, 4, 1, 7]}, {[9, 8, 6, 5, 4, 3, 7, 2, 10, 1], [10, 8, 6, 5, 4, 3, 7, 2, 1, 9]}, {[9, 8, 6, 5, 7, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 3, 5, 2, 1, 7]}, {[9, 8, 7, 5, 4, 3, 2, 6, 10, 1], [10, 7, 6, 5, 4, 8, 3, 2, 1, 9]}, {[9, 8, 7, 5, 4, 6, 10, 3, 2, 1], [10, 9, 8, 5, 4, 6, 3, 2, 1, 7]}, {[9, 8, 7, 6, 10, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 5, 4, 2, 1, 3], [9, 8, 10, 7, 6, 4, 3, 2, 1, 5]}, {[9, 8, 10, 6, 5, 4, 3, 7, 2, 1], [10, 9, 7, 6, 5, 4, 8, 2, 1, 3]}, {[9, 8, 10, 7, 5, 4, 3, 2, 6, 1], [10, 8, 7, 6, 5, 9, 4, 2, 1, 3]}, {[10, 7, 6, 5, 4, 8, 3, 9, 2, 1], [10, 9, 7, 5, 4, 3, 2, 6, 8, 1]}, {[10, 7, 6, 8, 5, 4, 3, 9, 2, 1], [10, 9, 7, 6, 5, 3, 2, 4, 8, 1]}, {[10, 8, 6, 5, 4, 3, 7, 9, 2, 1], [10, 9, 6, 5, 4, 3, 7, 2, 8, 1]}, {[10, 8, 6, 5, 7, 4, 3, 9, 2, 1], [10, 9, 7, 6, 4, 3, 5, 2, 8, 1]}, {[10, 8, 7, 5, 4, 6, 3, 9, 2, 1], [10, 9, 7, 5, 4, 6, 3, 2, 8, 1]}, {[10, 8, 7, 6, 4, 3, 5, 9, 2, 1], [10, 9, 6, 5, 7, 4, 3, 2, 8, 1]}, {[10, 8, 7, 6, 5, 9, 3, 2, 4, 1], [10, 8, 7, 9, 5, 4, 3, 2, 6, 1]}} is given by the following expression / 163 2 319 3 1333 4 2371 5 43 6 |9/8960 n + ------ n - ------ n - ------- n - ------- n - ------- n \ 147456 589824 1179648 5898240 1179648 7\ n / 11 2323 2 10451 3 61487 4 - 5/8257536 n | 4 + |- ----- n - ------ n - ------- n + -------- n / \ 10920 665280 3706560 34594560 41029 5 29467 6 4651 7 25 8 9\ + -------- n + -------- n + -------- n + ------- n + 1/20756736 n | 11531520 17297280 17297280 2306304 / C(n) and in Maple input form: (9/8960*n+163/147456*n^2-319/589824*n^3-1333/1179648*n^4-2371/5898240*n^5-43/ 1179648*n^6-5/8257536*n^7)*4^n+(-11/10920*n-2323/665280*n^2-10451/3706560*n^3+ 61487/34594560*n^4+41029/11531520*n^5+29467/17297280*n^6+4651/17297280*n^7+25/ 2306304*n^8+1/20756736*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 18 1/2 17 16 1/2 15 14 1/2 13 m 5 Pi m 25 m 2453 Pi m 4651 m 20903 Pi m -------- - ----------- + ------- - -------------- + -------- - --------------- 20756736 8257536 2306304 66060288 17297280 47185920 12 1/2 11 10 1/2 9 8 29467 m 74659 Pi m 41029 m 17101 Pi m 61487 m + --------- - --------------- + --------- - -------------- + -------- 17297280 47185920 11531520 9437184 34594560 1/2 7 6 1/2 5 4 1/2 3 2345 Pi m 10451 m 10313 Pi m 2323 m 81 Pi m + ------------- - -------- + -------------- - ------- + ----------- 4718592 3706560 4587520 665280 71680 2 11 m - ----- 10920 and in Maple input form: 1/20756736*m^18-5/8257536*Pi^(1/2)*m^17+25/2306304*m^16-2453/66060288*Pi^(1/2)* m^15+4651/17297280*m^14-20903/47185920*Pi^(1/2)*m^13+29467/17297280*m^12-74659/ 47185920*Pi^(1/2)*m^11+41029/11531520*m^10-17101/9437184*Pi^(1/2)*m^9+61487/ 34594560*m^8+2345/4718592*Pi^(1/2)*m^7-10451/3706560*m^6+10313/4587520*Pi^(1/2) *m^5-2323/665280*m^4+81/71680*Pi^(1/2)*m^3-11/10920*m^2 For the, 14, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 8, 7, 10, 6, 5, 3, 2, 1, 4]}, {[10, 8, 6, 5, 4, 3, 7, 2, 9, 1]}, {[10, 8, 7, 6, 9, 4, 3, 2, 5, 1]}, {[8, 7, 6, 5, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 3, 2, 1, 5, 8]}, {[8, 7, 6, 9, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 3, 2, 1, 4, 8]}, {[8, 7, 6, 9, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 3, 2, 1, 4, 7]}, {[9, 7, 6, 5, 4, 8, 3, 10, 2, 1], [10, 9, 7, 5, 4, 3, 2, 6, 1, 8]}, {[9, 7, 6, 5, 8, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 3, 2, 5, 1, 8]}, {[9, 7, 6, 5, 8, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 3, 2, 5, 1, 7]}, {[9, 8, 6, 5, 4, 3, 7, 10, 2, 1], [10, 9, 6, 5, 4, 3, 7, 2, 1, 8]}, {[9, 8, 6, 5, 4, 7, 3, 10, 2, 1], [10, 9, 7, 5, 4, 3, 6, 2, 1, 8]}, {[9, 8, 6, 5, 4, 7, 10, 3, 2, 1], [10, 9, 8, 5, 4, 3, 6, 2, 1, 7]}, {[9, 8, 7, 5, 4, 3, 6, 10, 2, 1], [10, 9, 6, 5, 4, 7, 3, 2, 1, 8]}, {[9, 8, 7, 6, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 4, 3, 2, 1, 5]}, {[9, 8, 7, 10, 5, 4, 3, 2, 6, 1], [10, 8, 7, 6, 5, 9, 3, 2, 1, 4]}, {[9, 8, 7, 10, 5, 4, 3, 6, 2, 1], [10, 9, 7, 6, 5, 8, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 5, 3, 2, 1, 4]}, {[10, 7, 6, 5, 4, 8, 3, 2, 9, 1], [10, 8, 7, 5, 4, 3, 2, 6, 9, 1]}, {[10, 7, 6, 5, 8, 4, 3, 2, 9, 1], [10, 8, 7, 6, 4, 3, 2, 5, 9, 1]}, {[10, 7, 6, 5, 8, 4, 3, 9, 2, 1], [10, 9, 7, 6, 4, 3, 2, 5, 8, 1]}, {[10, 8, 6, 5, 4, 7, 3, 2, 9, 1], [10, 8, 7, 5, 4, 3, 6, 2, 9, 1]}, {[10, 8, 6, 5, 4, 7, 3, 9, 2, 1], [10, 9, 7, 5, 4, 3, 6, 2, 8, 1]}, {[10, 8, 7, 5, 4, 3, 6, 9, 2, 1], [10, 9, 6, 5, 4, 7, 3, 2, 8, 1]}} is given by the following expression / 487 887 2 229 3 173 4 131 5 11 6 |------ n + ------ n - ------ n - ------ n - ------ n - ------ n \430080 737280 294912 147456 368640 368640 7\ n / 17 2111 2 74983 3 4447 4 - 1/2064384 n | 4 + |- ----- n - ------ n - -------- n + ------- n / \ 15015 540540 25945920 1921920 10943 5 39 6 1957 7 151 8 9\ + ------- n + ----- n + ------- n + -------- n + 1/25945920 n | C(n) 2882880 24640 8648640 17297280 / and in Maple input form: (487/430080*n+887/737280*n^2-229/294912*n^3-173/147456*n^4-131/368640*n^5-11/ 368640*n^6-1/2064384*n^7)*4^n+(-17/15015*n-2111/540540*n^2-74983/25945920*n^3+ 4447/1921920*n^4+10943/2882880*n^5+39/24640*n^6+1957/8648640*n^7+151/17297280*n ^8+1/25945920*n^9)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 18 1/2 17 16 1/2 15 14 1/2 13 m Pi m 151 m 2509 Pi m 1957 m 1147 Pi m -------- - --------- + -------- - -------------- + -------- - -------------- 25945920 2064384 17297280 82575360 8648640 2949120 12 1/2 11 10 1/2 9 8 39 m 4639 Pi m 10943 m 2473 Pi m 4447 m + ------ - -------------- + --------- - ------------- + ------- 24640 2949120 2882880 1179648 1921920 1/2 7 6 1/2 5 4 1/2 3 3887 Pi m 74983 m 34211 Pi m 2111 m 1461 Pi m + ------------- - -------- + -------------- - ------- + ------------- 11796480 25945920 13762560 540540 1146880 2 17 m - ----- 15015 and in Maple input form: 1/25945920*m^18-1/2064384*Pi^(1/2)*m^17+151/17297280*m^16-2509/82575360*Pi^(1/2 )*m^15+1957/8648640*m^14-1147/2949120*Pi^(1/2)*m^13+39/24640*m^12-4639/2949120* Pi^(1/2)*m^11+10943/2882880*m^10-2473/1179648*Pi^(1/2)*m^9+4447/1921920*m^8+ 3887/11796480*Pi^(1/2)*m^7-74983/25945920*m^6+34211/13762560*Pi^(1/2)*m^5-2111/ 540540*m^4+1461/1146880*Pi^(1/2)*m^3-17/15015*m^2 For the, 15, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[7, 6, 5, 4, 3, 2, 1, 8, 9, 10]}, {[8, 7, 6, 4, 5, 3, 2, 1, 9, 10]}, {[8, 9, 7, 6, 5, 4, 3, 1, 2, 10]}, {[9, 7, 8, 6, 5, 4, 2, 3, 1, 10]}, {[9, 8, 6, 7, 5, 3, 4, 2, 1, 10]}, {[9, 8, 7, 4, 5, 6, 3, 2, 1, 10]}, {[9, 10, 8, 7, 5, 6, 4, 3, 1, 2]}, {[10, 8, 9, 7, 5, 6, 4, 2, 3, 1]}, {[10, 9, 7, 8, 5, 6, 3, 4, 2, 1]}, {[10, 9, 8, 4, 5, 6, 7, 3, 2, 1]}, {[7, 8, 6, 5, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 4, 3, 1, 2, 9, 10]}, {[7, 8, 9, 6, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 4, 1, 2, 3, 10]}, {[7, 8, 9, 10, 6, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 5, 1, 2, 3, 4]}, {[8, 6, 7, 5, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 4, 2, 3, 1, 9, 10]}, {[8, 7, 5, 6, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 3, 4, 2, 1, 9, 10]}, {[8, 9, 6, 7, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 3, 4, 1, 2, 10]}, {[8, 9, 7, 5, 6, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 5, 3, 1, 2, 10]}, {[8, 9, 7, 6, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 4, 3, 1, 2, 10]}, {[8, 9, 7, 6, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 4, 3, 1, 2, 10]}, {[8, 9, 7, 6, 5, 4, 2, 3, 1, 10], [9, 7, 8, 6, 5, 4, 3, 1, 2, 10]}, {[8, 9, 10, 6, 7, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 5, 1, 2, 3]}, {[8, 9, 10, 7, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 5, 4, 1, 2, 3]}, {[9, 6, 7, 8, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 2, 3, 4, 1, 10]}, {[9, 7, 8, 5, 6, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 5, 2, 3, 1, 10]}, {[9, 7, 8, 6, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 4, 2, 3, 1, 10]}, {[9, 7, 8, 6, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 4, 2, 3, 1, 10]}, {[9, 8, 5, 6, 7, 4, 3, 2, 1, 10], [9, 8, 7, 6, 3, 4, 5, 2, 1, 10]}, {[9, 8, 6, 7, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 3, 4, 2, 1, 10]}, {[9, 10, 6, 7, 8, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 3, 4, 5, 1, 2]}, {[9, 10, 7, 8, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 5, 3, 4, 1, 2]}, {[9, 10, 8, 5, 6, 7, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 6, 3, 1, 2]}, {[9, 10, 8, 6, 7, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 5, 3, 1, 2]}, {[9, 10, 8, 6, 7, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 5, 3, 1, 2]}, {[9, 10, 8, 6, 7, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 5, 3, 1, 2]}, {[9, 10, 8, 6, 7, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 4, 5, 3, 1, 2]}, {[9, 10, 8, 7, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 6, 3, 4, 2, 1], [10, 9, 7, 8, 5, 6, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 6, 4, 2, 3, 1], [10, 8, 9, 7, 5, 6, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 5, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 5, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 5, 4, 3, 1, 2]}, {[10, 6, 7, 8, 9, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 2, 3, 4, 5, 1]}, {[10, 7, 8, 9, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 2, 3, 4, 1]}, {[10, 7, 8, 9, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 2, 3, 4, 1]}, {[10, 7, 8, 9, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 2, 3, 4, 1]}, {[10, 7, 8, 9, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 2, 3, 4, 1]}, {[10, 8, 9, 5, 6, 7, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 6, 2, 3, 1]}, {[10, 8, 9, 6, 7, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 5, 2, 3, 1]}, {[10, 8, 9, 6, 7, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 5, 2, 3, 1]}, {[10, 8, 9, 6, 7, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 5, 2, 3, 1]}, {[10, 8, 9, 7, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 4, 2, 3, 1]}, {[10, 8, 9, 7, 5, 6, 3, 4, 2, 1], [10, 9, 7, 8, 5, 6, 4, 2, 3, 1]}, {[10, 8, 9, 7, 6, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 5, 4, 2, 3, 1]}, {[10, 9, 5, 6, 7, 8, 4, 3, 2, 1], [10, 9, 8, 7, 3, 4, 5, 6, 2, 1]}, {[10, 9, 6, 7, 8, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 3, 4, 5, 2, 1]}, {[10, 9, 6, 7, 8, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 3, 4, 5, 2, 1]}, {[10, 9, 7, 8, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 3, 4, 2, 1]}} is given by the following expression / 581489 167821 2 208577 3 52811 4 7287 5 529 6 |1/2 + ------ n + ------ n + ------ n + ------ n + ------ n + ------- n \ 430080 122880 327680 393216 655360 1966080 11 7\ n / 1834379 69403 2 2760031 3 + -------- n | 4 + |- 1/2 - ------- n - ----- n - ------- n 13762560 / \ 720720 14040 576576 2140147 4 957317 5 3173 6 2147 7 8\ - ------- n - ------- n - ----- n - ------ n - 1/26208 n | C(n) 864864 1441440 38610 576576 / and in Maple input form: (1/2+581489/430080*n+167821/122880*n^2+208577/327680*n^3+52811/393216*n^4+7287/ 655360*n^5+529/1966080*n^6+11/13762560*n^7)*4^n+(-1/2-1834379/720720*n-69403/ 14040*n^2-2760031/576576*n^3-2140147/864864*n^4-957317/1441440*n^5-3173/38610*n ^6-2147/576576*n^7-1/26208*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 17 16 1/2 15 14 1/2 13 12 11 Pi m m 29723 Pi m 2147 m 59883 Pi m 3173 m ------------ - ----- + --------------- - -------- + --------------- - -------- 13762560 26208 110100480 576576 5242880 38610 1/2 11 10 1/2 9 8 2309189 Pi m 957317 m 4129397 Pi m 2140147 m + ----------------- - ---------- + ---------------- - ---------- 15728640 1441440 5242880 864864 1/2 7 6 1/2 5 4 16372123 Pi m 2760031 m 19876547 Pi m 69403 m + ----------------- - ---------- + ----------------- - -------- 7864320 576576 6881280 14040 1/2 3 2 1/2 2317907 Pi m 1834379 m 9 Pi m + ---------------- - ---------- + --------- - 1/2 1146880 720720 16 and in Maple input form: 11/13762560*Pi^(1/2)*m^17-1/26208*m^16+29723/110100480*Pi^(1/2)*m^15-2147/ 576576*m^14+59883/5242880*Pi^(1/2)*m^13-3173/38610*m^12+2309189/15728640*Pi^(1/ 2)*m^11-957317/1441440*m^10+4129397/5242880*Pi^(1/2)*m^9-2140147/864864*m^8+ 16372123/7864320*Pi^(1/2)*m^7-2760031/576576*m^6+19876547/6881280*Pi^(1/2)*m^5-\ 69403/14040*m^4+2317907/1146880*Pi^(1/2)*m^3-1834379/720720*m^2+9/16*Pi^(1/2)*m -1/2 For the, 16, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[7, 6, 5, 4, 3, 2, 8, 1, 9, 10], [8, 6, 5, 4, 3, 2, 1, 7, 9, 10]}, {[7, 6, 8, 5, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 4, 2, 1, 3, 9, 10]}, {[7, 6, 8, 9, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 2, 1, 3, 4, 5]}, {[7, 8, 6, 9, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 3, 1, 2, 4, 10]}, {[7, 8, 6, 9, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 3, 1, 2, 4, 5]}, {[7, 8, 9, 6, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 4, 1, 2, 3, 9]}, {[7, 8, 9, 6, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 4, 1, 2, 3, 5]}, {[8, 6, 5, 7, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 3, 2, 4, 1, 9, 10]}, {[8, 6, 7, 9, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 2, 3, 1, 4, 10]}, {[8, 6, 7, 9, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 2, 3, 1, 4, 5]}, {[8, 7, 5, 4, 6, 3, 2, 1, 9, 10], [8, 7, 6, 4, 3, 5, 2, 1, 9, 10]}, {[8, 7, 6, 5, 4, 3, 9, 1, 2, 10], [8, 9, 6, 5, 4, 3, 2, 1, 7, 10]}, {[8, 7, 6, 5, 4, 3, 9, 10, 1, 2], [9, 10, 6, 5, 4, 3, 2, 1, 7, 8]}, {[8, 7, 9, 5, 6, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 5, 2, 1, 3, 10]}, {[8, 7, 9, 6, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 4, 2, 1, 3, 10]}, {[8, 7, 9, 6, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 4, 2, 1, 3, 10]}, {[8, 7, 9, 6, 5, 4, 2, 3, 1, 10], [9, 7, 8, 6, 5, 4, 2, 1, 3, 10]}, {[8, 7, 9, 6, 5, 4, 3, 1, 2, 10], [8, 9, 7, 6, 5, 4, 2, 1, 3, 10]}, {[8, 7, 9, 10, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 2, 1, 3, 4]}, {[8, 7, 9, 10, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 2, 1, 3, 4]}, {[8, 7, 9, 10, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 2, 1, 3, 4]}, {[8, 7, 9, 10, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 2, 1, 3, 4]}, {[8, 7, 9, 10, 6, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 5, 2, 1, 3, 4]}, {[8, 9, 6, 5, 7, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 3, 5, 1, 2, 10]}, {[8, 9, 6, 7, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 3, 4, 1, 2, 9]}, {[8, 9, 6, 7, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 3, 4, 1, 2, 5]}, {[8, 9, 7, 5, 4, 6, 3, 2, 1, 10], [9, 8, 7, 5, 4, 6, 3, 1, 2, 10]}, {[8, 9, 7, 5, 6, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 5, 3, 1, 2, 9]}, {[8, 9, 7, 6, 4, 3, 5, 2, 1, 10], [9, 8, 6, 5, 7, 4, 3, 1, 2, 10]}, {[8, 9, 7, 6, 4, 5, 3, 2, 10, 1], [10, 8, 7, 5, 6, 4, 3, 1, 2, 9]}, {[8, 9, 7, 6, 5, 3, 2, 4, 1, 10], [9, 7, 6, 8, 5, 4, 3, 1, 2, 10]}, {[8, 9, 7, 6, 5, 3, 4, 2, 10, 1], [10, 8, 6, 7, 5, 4, 3, 1, 2, 9]}, {[8, 9, 7, 6, 5, 4, 2, 3, 10, 1], [10, 7, 8, 6, 5, 4, 3, 1, 2, 9]}, {[8, 9, 7, 6, 5, 4, 3, 10, 1, 2], [9, 10, 7, 6, 5, 4, 3, 1, 2, 8]}, {[8, 9, 7, 10, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 3, 1, 2, 4]}, {[8, 9, 7, 10, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 3, 1, 2, 4]}, {[8, 9, 7, 10, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 3, 1, 2, 4]}, {[8, 9, 7, 10, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 3, 1, 2, 4]}, {[8, 9, 7, 10, 6, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 5, 3, 1, 2, 4]}, {[8, 9, 10, 6, 5, 4, 3, 2, 1, 7], [9, 8, 7, 6, 5, 4, 10, 1, 2, 3]}, {[8, 9, 10, 6, 5, 7, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 6, 1, 2, 3]}, {[8, 9, 10, 7, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 5, 4, 2, 1, 3], [9, 8, 10, 7, 6, 5, 4, 1, 2, 3]}, {[9, 6, 5, 7, 8, 4, 3, 2, 1, 10], [9, 8, 7, 6, 3, 2, 4, 5, 1, 10]}, {[9, 6, 7, 5, 8, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 2, 3, 5, 1, 10]}, {[9, 6, 7, 8, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 2, 3, 4, 1, 9]}, {[9, 6, 7, 8, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 2, 3, 4, 1, 5]}, {[9, 7, 5, 6, 8, 4, 3, 2, 1, 10], [9, 8, 7, 6, 3, 4, 2, 5, 1, 10]}, {[9, 7, 6, 8, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 3, 2, 4, 1, 10]}, {[9, 7, 6, 8, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 3, 2, 4, 1, 10]}, {[9, 7, 6, 8, 5, 4, 2, 3, 1, 10], [9, 7, 8, 6, 5, 3, 2, 4, 1, 10]}, {[9, 7, 8, 5, 4, 6, 3, 2, 1, 10], [9, 8, 7, 5, 4, 6, 2, 3, 1, 10]}, {[9, 7, 8, 5, 6, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 5, 2, 3, 1, 9]}, {[9, 7, 8, 6, 4, 3, 5, 2, 1, 10], [9, 8, 6, 5, 7, 4, 2, 3, 1, 10]}, {[9, 7, 8, 6, 4, 5, 3, 2, 10, 1], [10, 8, 7, 5, 6, 4, 2, 3, 1, 9]}, {[9, 7, 8, 6, 5, 3, 4, 2, 10, 1], [10, 8, 6, 7, 5, 4, 2, 3, 1, 9]}, {[9, 7, 8, 6, 5, 4, 2, 3, 10, 1], [10, 7, 8, 6, 5, 4, 2, 3, 1, 9]}, {[9, 7, 8, 6, 5, 4, 3, 10, 1, 2], [9, 10, 7, 6, 5, 4, 2, 3, 1, 8]}, {[9, 7, 8, 10, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 2, 3, 1, 4]}, {[9, 7, 8, 10, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 2, 3, 1, 4]}, {[9, 7, 8, 10, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 2, 3, 1, 4]}, {[9, 7, 8, 10, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 2, 3, 1, 4]}, {[9, 7, 8, 10, 6, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 5, 2, 3, 1, 4]}, {[9, 8, 5, 4, 6, 7, 3, 2, 1, 10], [9, 8, 7, 4, 3, 5, 6, 2, 1, 10]}, {[9, 8, 5, 6, 4, 7, 3, 2, 1, 10], [9, 8, 7, 5, 3, 4, 6, 2, 1, 10]}, {[9, 8, 5, 6, 7, 4, 3, 2, 10, 1], [10, 8, 7, 6, 3, 4, 5, 2, 1, 9]}, {[9, 8, 6, 4, 5, 7, 3, 2, 1, 10], [9, 8, 7, 4, 5, 3, 6, 2, 1, 10]}, {[9, 8, 6, 5, 7, 3, 4, 2, 1, 10], [9, 8, 6, 7, 4, 3, 5, 2, 1, 10]}, {[9, 8, 6, 7, 4, 5, 3, 2, 10, 1], [10, 8, 7, 5, 6, 3, 4, 2, 1, 9]}, {[9, 8, 6, 7, 5, 3, 4, 2, 10, 1], [10, 8, 6, 7, 5, 3, 4, 2, 1, 9]}, {[9, 8, 6, 7, 5, 4, 2, 3, 10, 1], [10, 7, 8, 6, 5, 3, 4, 2, 1, 9]}, {[9, 8, 6, 7, 5, 4, 3, 10, 1, 2], [9, 10, 7, 6, 5, 3, 4, 2, 1, 8]}, {[9, 8, 7, 4, 5, 6, 3, 2, 10, 1], [10, 8, 7, 4, 5, 6, 3, 2, 1, 9]}, {[9, 8, 7, 5, 6, 3, 4, 2, 10, 1], [10, 8, 6, 7, 4, 5, 3, 2, 1, 9]}, {[9, 8, 7, 5, 6, 4, 2, 3, 10, 1], [10, 7, 8, 6, 4, 5, 3, 2, 1, 9]}, {[9, 8, 7, 5, 6, 4, 3, 10, 1, 2], [9, 10, 7, 6, 4, 5, 3, 2, 1, 8]}, {[9, 8, 7, 6, 3, 4, 5, 2, 10, 1], [10, 8, 5, 6, 7, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 4, 5, 2, 3, 10, 1], [10, 7, 8, 5, 6, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 4, 5, 3, 10, 1, 2], [9, 10, 7, 5, 6, 4, 3, 2, 1, 8]}, {[9, 8, 7, 6, 5, 2, 3, 4, 10, 1], [10, 6, 7, 8, 5, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 5, 3, 4, 10, 1, 2], [9, 10, 6, 7, 5, 4, 3, 2, 1, 8]}, {[9, 8, 10, 5, 6, 7, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 6, 2, 1, 3]}, {[9, 8, 10, 6, 7, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 5, 2, 1, 3]}, {[9, 8, 10, 6, 7, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 5, 2, 1, 3]}, {[9, 8, 10, 6, 7, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 5, 2, 1, 3]}, {[9, 8, 10, 6, 7, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 4, 5, 2, 1, 3]}, {[9, 8, 10, 7, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 4, 2, 1, 3]}, {[9, 8, 10, 7, 5, 6, 3, 4, 2, 1], [10, 9, 7, 8, 5, 6, 4, 2, 1, 3]}, {[9, 8, 10, 7, 5, 6, 4, 2, 3, 1], [10, 8, 9, 7, 5, 6, 4, 2, 1, 3]}, {[9, 8, 10, 7, 5, 6, 4, 3, 1, 2], [9, 10, 8, 7, 5, 6, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 4, 5, 3, 1, 2], [9, 10, 8, 6, 7, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 5, 3, 4, 1, 2], [9, 10, 7, 8, 6, 5, 4, 2, 1, 3]}, {[9, 10, 6, 5, 7, 8, 4, 3, 2, 1], [10, 9, 8, 7, 4, 3, 5, 6, 1, 2]}, {[9, 10, 6, 7, 5, 8, 4, 3, 2, 1], [10, 9, 8, 7, 5, 3, 4, 6, 1, 2]}, {[9, 10, 7, 5, 6, 8, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 3, 6, 1, 2]}, {[9, 10, 7, 6, 8, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 3, 5, 1, 2]}, {[9, 10, 7, 6, 8, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 3, 5, 1, 2]}, {[9, 10, 7, 6, 8, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 3, 5, 1, 2]}, {[9, 10, 7, 6, 8, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 4, 3, 5, 1, 2]}, {[9, 10, 7, 8, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 5, 3, 4, 1, 2]}, {[9, 10, 8, 5, 4, 6, 7, 3, 2, 1], [10, 9, 8, 5, 4, 6, 7, 3, 1, 2]}, {[9, 10, 8, 5, 6, 4, 7, 3, 2, 1], [10, 9, 8, 6, 4, 5, 7, 3, 1, 2]}, {[9, 10, 8, 6, 4, 5, 7, 3, 2, 1], [10, 9, 8, 5, 6, 4, 7, 3, 1, 2]}, {[9, 10, 8, 6, 5, 7, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 6, 3, 1, 2]}, {[9, 10, 8, 6, 5, 7, 4, 2, 3, 1], [10, 8, 9, 7, 5, 4, 6, 3, 1, 2]}, {[9, 10, 8, 6, 5, 7, 4, 3, 1, 2], [9, 10, 8, 7, 5, 4, 6, 3, 1, 2]}, {[9, 10, 8, 6, 7, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 4, 5, 3, 1, 2]}, {[9, 10, 8, 6, 7, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 4, 5, 3, 1, 2]}, {[9, 10, 8, 7, 4, 3, 5, 6, 2, 1], [10, 9, 6, 5, 7, 8, 4, 3, 1, 2]}, {[9, 10, 8, 7, 4, 5, 3, 6, 2, 1], [10, 9, 7, 5, 6, 8, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 3, 4, 6, 2, 1], [10, 9, 6, 7, 5, 8, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 4, 6, 2, 3, 1], [10, 8, 9, 6, 5, 7, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 6, 3, 2, 4, 1], [10, 8, 7, 9, 5, 6, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 3, 2, 4, 5, 1], [10, 7, 6, 8, 9, 5, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 3, 4, 2, 5, 1], [10, 8, 6, 7, 9, 5, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 4, 2, 3, 5, 1], [10, 7, 8, 6, 9, 5, 4, 3, 1, 2]}, {[10, 6, 5, 7, 8, 9, 4, 3, 2, 1], [10, 9, 8, 7, 3, 2, 4, 5, 6, 1]}, {[10, 6, 7, 5, 8, 9, 4, 3, 2, 1], [10, 9, 8, 7, 4, 2, 3, 5, 6, 1]}, {[10, 6, 7, 8, 5, 9, 4, 3, 2, 1], [10, 9, 8, 7, 5, 2, 3, 4, 6, 1]}, {[10, 7, 5, 6, 8, 9, 4, 3, 2, 1], [10, 9, 8, 7, 3, 4, 2, 5, 6, 1]}, {[10, 7, 6, 8, 9, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 3, 2, 4, 5, 1]}, {[10, 7, 6, 8, 9, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 3, 2, 4, 5, 1]}, {[10, 7, 6, 8, 9, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 3, 2, 4, 5, 1]}, {[10, 7, 8, 5, 6, 9, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 2, 3, 6, 1]}, {[10, 7, 8, 6, 9, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 2, 3, 5, 1]}, {[10, 7, 8, 6, 9, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 2, 3, 5, 1]}, {[10, 7, 8, 6, 9, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 2, 3, 5, 1]}, {[10, 7, 8, 9, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 2, 3, 4, 1]}, {[10, 7, 8, 9, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 2, 3, 4, 1]}, {[10, 7, 8, 9, 6, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 5, 2, 3, 4, 1]}, {[10, 8, 5, 6, 7, 9, 4, 3, 2, 1], [10, 9, 8, 7, 3, 4, 5, 2, 6, 1]}, {[10, 8, 6, 7, 9, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 3, 4, 2, 5, 1]}, {[10, 8, 6, 7, 9, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 3, 4, 2, 5, 1]}, {[10, 8, 6, 7, 9, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 3, 4, 2, 5, 1]}, {[10, 8, 7, 9, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 3, 2, 4, 1]}, {[10, 8, 7, 9, 5, 6, 3, 4, 2, 1], [10, 9, 7, 8, 5, 6, 3, 2, 4, 1]}, {[10, 8, 7, 9, 5, 6, 4, 2, 3, 1], [10, 8, 9, 7, 5, 6, 3, 2, 4, 1]}, {[10, 8, 7, 9, 6, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 5, 3, 2, 4, 1]}, {[10, 8, 7, 9, 6, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 5, 3, 2, 4, 1]}, {[10, 8, 9, 5, 4, 6, 7, 3, 2, 1], [10, 9, 8, 5, 4, 6, 7, 2, 3, 1]}, {[10, 8, 9, 5, 6, 4, 7, 3, 2, 1], [10, 9, 8, 6, 4, 5, 7, 2, 3, 1]}, {[10, 8, 9, 6, 4, 5, 7, 3, 2, 1], [10, 9, 8, 5, 6, 4, 7, 2, 3, 1]}, {[10, 8, 9, 6, 5, 7, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 6, 2, 3, 1]}, {[10, 8, 9, 6, 5, 7, 4, 2, 3, 1], [10, 8, 9, 7, 5, 4, 6, 2, 3, 1]}, {[10, 8, 9, 6, 7, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 4, 5, 2, 3, 1]}, {[10, 8, 9, 7, 4, 3, 5, 6, 2, 1], [10, 9, 6, 5, 7, 8, 4, 2, 3, 1]}, {[10, 8, 9, 7, 4, 5, 3, 6, 2, 1], [10, 9, 7, 5, 6, 8, 4, 2, 3, 1]}, {[10, 8, 9, 7, 5, 3, 4, 6, 2, 1], [10, 9, 6, 7, 5, 8, 4, 2, 3, 1]}, {[10, 9, 5, 4, 6, 7, 8, 3, 2, 1], [10, 9, 8, 4, 3, 5, 6, 7, 2, 1]}, {[10, 9, 5, 6, 4, 7, 8, 3, 2, 1], [10, 9, 8, 5, 3, 4, 6, 7, 2, 1]}, {[10, 9, 5, 6, 7, 4, 8, 3, 2, 1], [10, 9, 8, 6, 3, 4, 5, 7, 2, 1]}, {[10, 9, 6, 4, 5, 7, 8, 3, 2, 1], [10, 9, 8, 4, 5, 3, 6, 7, 2, 1]}, {[10, 9, 6, 5, 7, 8, 3, 4, 2, 1], [10, 9, 7, 8, 4, 3, 5, 6, 2, 1]}, {[10, 9, 6, 7, 4, 5, 8, 3, 2, 1], [10, 9, 8, 5, 6, 3, 4, 7, 2, 1]}, {[10, 9, 6, 7, 5, 8, 3, 4, 2, 1], [10, 9, 7, 8, 5, 3, 4, 6, 2, 1]}, {[10, 9, 6, 7, 8, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 3, 4, 5, 2, 1]}, {[10, 9, 7, 4, 5, 6, 8, 3, 2, 1], [10, 9, 8, 4, 5, 6, 3, 7, 2, 1]}, {[10, 9, 7, 5, 6, 8, 3, 4, 2, 1], [10, 9, 7, 8, 4, 5, 3, 6, 2, 1]}, { [7, 6, 5, 4, 3, 2, 8, 9, 1, 10], [7, 6, 5, 4, 3, 2, 8, 9, 10, 1], [9, 6, 5, 4, 3, 2, 1, 7, 8, 10], [10, 6, 5, 4, 3, 2, 1, 7, 8, 9]}, { [7, 8, 6, 5, 4, 3, 2, 9, 1, 10], [7, 8, 6, 5, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 4, 3, 1, 2, 8, 10], [10, 7, 6, 5, 4, 3, 1, 2, 8, 9]}, { [8, 6, 7, 5, 4, 3, 2, 9, 1, 10], [8, 6, 7, 5, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 4, 2, 3, 1, 8, 10], [10, 7, 6, 5, 4, 2, 3, 1, 8, 9]}, { [8, 7, 5, 6, 4, 3, 2, 9, 1, 10], [8, 7, 5, 6, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 3, 4, 2, 1, 8, 10], [10, 7, 6, 5, 3, 4, 2, 1, 8, 9]}, { [8, 7, 6, 4, 5, 3, 2, 9, 1, 10], [8, 7, 6, 4, 5, 3, 2, 9, 10, 1], [9, 7, 6, 4, 5, 3, 2, 1, 8, 10], [10, 7, 6, 4, 5, 3, 2, 1, 8, 9]}, { [8, 7, 6, 5, 3, 4, 2, 9, 1, 10], [8, 7, 6, 5, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 4, 3, 2, 1, 8, 10], [10, 7, 5, 6, 4, 3, 2, 1, 8, 9]}, { [8, 7, 6, 5, 4, 2, 3, 9, 1, 10], [8, 7, 6, 5, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 4, 3, 2, 1, 8, 10], [10, 6, 7, 5, 4, 3, 2, 1, 8, 9]}} is given by the following expression / 3979 26915 2 43751 3 38987 4 8171 5 161 6 |------ n + ------ n + ------ n + ------- n + ------- n + ------- n \245760 589824 983040 2359296 3932160 2359296 7\ n / 139 121409 2 39601 3 881117 4 + 1/3932160 n | 4 + |- ---- n - ------- n - ------ n - ------- n / \ 8580 1441440 240240 5765760 65477 5 53 6 113 7 8\ - ------ n - ---- n - ------ n - 1/91520 n | C(n) 960960 4095 137280 / and in Maple input form: (3979/245760*n+26915/589824*n^2+43751/983040*n^3+38987/2359296*n^4+8171/3932160 *n^5+161/2359296*n^6+1/3932160*n^7)*4^n+(-139/8580*n-121409/1441440*n^2-39601/ 240240*n^3-881117/5765760*n^4-65477/960960*n^5-53/4095*n^6-113/137280*n^7-1/ 91520*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 17 16 1/2 15 14 1/2 13 12 Pi m m 6467 Pi m 113 m 67783 Pi m 53 m --------- - ----- + -------------- - ------- + --------------- - ------ 3932160 91520 94371840 137280 31457280 4095 1/2 11 10 1/2 9 8 1780097 Pi m 65477 m 1984837 Pi m 881117 m + ----------------- - --------- + ---------------- - --------- 94371840 960960 31457280 5765760 1/2 7 6 1/2 5 4 2257877 Pi m 39601 m 531053 Pi m 121409 m + ---------------- - -------- + --------------- - --------- 23592960 240240 7864320 1441440 1/2 3 2 11937 Pi m 139 m + -------------- - ------ 655360 8580 and in Maple input form: 1/3932160*Pi^(1/2)*m^17-1/91520*m^16+6467/94371840*Pi^(1/2)*m^15-113/137280*m^ 14+67783/31457280*Pi^(1/2)*m^13-53/4095*m^12+1780097/94371840*Pi^(1/2)*m^11-\ 65477/960960*m^10+1984837/31457280*Pi^(1/2)*m^9-881117/5765760*m^8+2257877/ 23592960*Pi^(1/2)*m^7-39601/240240*m^6+531053/7864320*Pi^(1/2)*m^5-121409/ 1441440*m^4+11937/655360*Pi^(1/2)*m^3-139/8580*m^2 For the, 17, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[8, 6, 5, 4, 3, 2, 7, 1, 9, 10]}, {[8, 7, 5, 4, 3, 6, 2, 1, 9, 10]}, {[9, 6, 5, 4, 3, 2, 7, 8, 1, 10]}, {[9, 7, 6, 4, 5, 3, 2, 8, 1, 10]}, {[9, 8, 5, 4, 3, 6, 7, 2, 1, 10]}, {[9, 8, 6, 4, 5, 3, 7, 2, 1, 10]}, {[9, 10, 7, 6, 5, 4, 3, 8, 1, 2]}, {[9, 10, 8, 6, 5, 4, 7, 3, 1, 2]}, {[10, 6, 5, 4, 3, 2, 7, 8, 9, 1]}, {[10, 7, 6, 4, 5, 3, 2, 8, 9, 1]}, {[10, 7, 8, 6, 5, 4, 2, 3, 9, 1]}, {[10, 8, 6, 7, 5, 3, 4, 2, 9, 1]}, {[10, 8, 7, 4, 5, 6, 3, 2, 9, 1]}, {[10, 8, 9, 6, 5, 4, 7, 2, 3, 1]}, {[10, 9, 5, 4, 3, 6, 7, 8, 2, 1]}, {[10, 9, 6, 4, 5, 3, 7, 8, 2, 1]}, {[10, 9, 6, 7, 5, 3, 4, 8, 2, 1]}, {[10, 9, 7, 4, 5, 6, 3, 8, 2, 1]}, {[7, 6, 5, 4, 3, 8, 2, 1, 9, 10], [8, 7, 5, 4, 3, 2, 1, 6, 9, 10]}, {[7, 6, 5, 4, 3, 8, 9, 2, 1, 10], [9, 8, 5, 4, 3, 2, 1, 6, 7, 10]}, {[7, 6, 5, 4, 3, 8, 9, 10, 2, 1], [10, 9, 5, 4, 3, 2, 1, 6, 7, 8]}, {[7, 6, 5, 8, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 3, 2, 1, 4, 9, 10]}, {[7, 6, 5, 8, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 3, 2, 1, 4, 5, 10]}, {[7, 6, 5, 8, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 3, 2, 1, 4, 5, 6]}, {[7, 8, 6, 5, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 4, 3, 1, 2, 7, 10]}, {[7, 8, 6, 5, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 4, 3, 1, 2, 7, 8]}, {[7, 8, 6, 5, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 3, 1, 2, 5, 10]}, {[7, 8, 6, 5, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 3, 1, 2, 5, 6]}, {[7, 8, 9, 6, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 4, 1, 2, 3, 8]}, {[7, 8, 9, 6, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 4, 1, 2, 3, 6]}, {[8, 6, 5, 4, 7, 3, 2, 1, 9, 10], [8, 7, 6, 4, 3, 2, 5, 1, 9, 10]}, {[8, 6, 7, 5, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 4, 2, 3, 1, 7, 10]}, {[8, 6, 7, 5, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 4, 2, 3, 1, 7, 8]}, {[8, 6, 7, 5, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 2, 3, 1, 5, 10]}, {[8, 6, 7, 5, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 2, 3, 1, 5, 6]}, {[8, 7, 5, 6, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 3, 4, 2, 1, 7, 10]}, {[8, 7, 5, 6, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 3, 4, 2, 1, 7, 8]}, {[8, 7, 5, 6, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 3, 4, 2, 1, 5, 10]}, {[8, 7, 5, 6, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 3, 4, 2, 1, 5, 6]}, {[8, 7, 6, 4, 5, 3, 9, 2, 1, 10], [9, 8, 6, 4, 5, 3, 2, 1, 7, 10]}, {[8, 7, 6, 4, 5, 3, 9, 10, 2, 1], [10, 9, 6, 4, 5, 3, 2, 1, 7, 8]}, {[8, 7, 6, 5, 3, 4, 9, 2, 1, 10], [9, 8, 5, 6, 4, 3, 2, 1, 7, 10]}, {[8, 7, 6, 5, 3, 4, 9, 10, 2, 1], [10, 9, 5, 6, 4, 3, 2, 1, 7, 8]}, {[8, 7, 6, 5, 4, 9, 2, 3, 1, 10], [9, 7, 8, 5, 4, 3, 2, 1, 6, 10]}, {[8, 7, 6, 5, 4, 9, 3, 1, 2, 10], [8, 9, 7, 5, 4, 3, 2, 1, 6, 10]}, {[8, 7, 6, 5, 4, 9, 10, 2, 3, 1], [10, 8, 9, 5, 4, 3, 2, 1, 6, 7]}, {[8, 7, 6, 5, 4, 9, 10, 3, 1, 2], [9, 10, 8, 5, 4, 3, 2, 1, 6, 7]}, {[8, 7, 6, 9, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 3, 2, 1, 4, 10]}, {[8, 7, 6, 9, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 3, 2, 1, 4, 10]}, {[8, 7, 6, 9, 5, 4, 2, 3, 1, 10], [9, 7, 8, 6, 5, 3, 2, 1, 4, 10]}, {[8, 7, 6, 9, 5, 4, 3, 1, 2, 10], [8, 9, 7, 6, 5, 3, 2, 1, 4, 10]}, {[8, 7, 6, 9, 10, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 3, 2, 1, 4, 5]}, {[8, 7, 6, 9, 10, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 3, 2, 1, 4, 5]}, {[8, 7, 6, 9, 10, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 3, 2, 1, 4, 5]}, {[8, 7, 6, 9, 10, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 3, 2, 1, 4, 5]}, {[8, 9, 6, 5, 4, 3, 2, 7, 1, 10], [9, 7, 6, 5, 4, 3, 8, 1, 2, 10]}, {[8, 9, 6, 5, 4, 7, 3, 2, 1, 10], [9, 8, 7, 5, 4, 3, 6, 1, 2, 10]}, {[8, 9, 6, 7, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 3, 4, 1, 2, 8]}, {[8, 9, 6, 7, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 3, 4, 1, 2, 6]}, {[8, 9, 7, 5, 4, 3, 6, 2, 1, 10], [9, 8, 6, 5, 4, 7, 3, 1, 2, 10]}, {[8, 9, 7, 5, 6, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 5, 3, 1, 2, 8]}, {[8, 9, 7, 5, 6, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 3, 1, 2, 6]}, {[8, 9, 7, 6, 4, 3, 2, 5, 1, 10], [9, 7, 6, 5, 8, 4, 3, 1, 2, 10]}, {[8, 9, 7, 6, 4, 5, 3, 10, 2, 1], [10, 9, 7, 5, 6, 4, 3, 1, 2, 8]}, {[8, 9, 7, 6, 5, 3, 4, 10, 2, 1], [10, 9, 6, 7, 5, 4, 3, 1, 2, 8]}, {[8, 9, 7, 6, 5, 4, 10, 2, 3, 1], [10, 8, 9, 6, 5, 4, 3, 1, 2, 7]}, {[8, 9, 7, 6, 5, 4, 10, 3, 1, 2], [9, 10, 8, 6, 5, 4, 3, 1, 2, 7]}, {[8, 9, 7, 6, 10, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 3, 1, 2, 5]}, {[8, 9, 7, 6, 10, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 3, 1, 2, 5]}, {[8, 9, 7, 6, 10, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 3, 1, 2, 5]}, {[8, 9, 7, 6, 10, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 4, 3, 1, 2, 5]}, {[8, 9, 10, 6, 5, 4, 3, 2, 7, 1], [10, 8, 7, 6, 5, 4, 9, 1, 2, 3]}, {[8, 9, 10, 6, 5, 4, 7, 3, 2, 1], [10, 9, 8, 6, 5, 4, 7, 1, 2, 3]}, {[8, 9, 10, 7, 5, 4, 3, 2, 1, 6], [9, 8, 7, 6, 5, 10, 4, 1, 2, 3]}, {[8, 9, 10, 7, 5, 4, 3, 6, 2, 1], [10, 9, 7, 6, 5, 8, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 5, 4, 1, 2, 3]}, {[9, 6, 5, 4, 7, 8, 3, 2, 1, 10], [9, 8, 7, 4, 3, 2, 5, 6, 1, 10]}, {[9, 6, 7, 5, 4, 3, 2, 8, 1, 10], [9, 7, 6, 5, 4, 2, 3, 8, 1, 10]}, {[9, 6, 7, 5, 4, 8, 3, 2, 1, 10], [9, 8, 7, 5, 4, 2, 3, 6, 1, 10]}, {[9, 6, 7, 8, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 2, 3, 4, 1, 8]}, {[9, 6, 7, 8, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 2, 3, 4, 1, 6]}, {[9, 7, 5, 6, 4, 3, 2, 8, 1, 10], [9, 7, 6, 5, 3, 4, 2, 8, 1, 10]}, {[9, 7, 5, 6, 4, 8, 3, 2, 1, 10], [9, 8, 7, 5, 3, 4, 2, 6, 1, 10]}, {[9, 7, 6, 4, 5, 8, 3, 2, 1, 10], [9, 8, 7, 4, 5, 3, 2, 6, 1, 10]}, {[9, 7, 6, 5, 8, 3, 4, 2, 1, 10], [9, 8, 6, 7, 4, 3, 2, 5, 1, 10]}, {[9, 7, 6, 5, 8, 4, 2, 3, 1, 10], [9, 7, 8, 6, 4, 3, 2, 5, 1, 10]}, {[9, 7, 8, 5, 4, 3, 6, 2, 1, 10], [9, 8, 6, 5, 4, 7, 2, 3, 1, 10]}, {[9, 7, 8, 5, 6, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 5, 2, 3, 1, 8]}, {[9, 7, 8, 5, 6, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 2, 3, 1, 6]}, {[9, 7, 8, 6, 4, 5, 3, 10, 2, 1], [10, 9, 7, 5, 6, 4, 2, 3, 1, 8]}, {[9, 7, 8, 6, 5, 3, 4, 10, 2, 1], [10, 9, 6, 7, 5, 4, 2, 3, 1, 8]}, {[9, 7, 8, 6, 5, 4, 10, 2, 3, 1], [10, 8, 9, 6, 5, 4, 2, 3, 1, 7]}, {[9, 7, 8, 6, 5, 4, 10, 3, 1, 2], [9, 10, 8, 6, 5, 4, 2, 3, 1, 7]}, {[9, 7, 8, 6, 10, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 2, 3, 1, 5]}, {[9, 7, 8, 6, 10, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 2, 3, 1, 5]}, {[9, 7, 8, 6, 10, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 2, 3, 1, 5]}, {[9, 7, 8, 6, 10, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 4, 2, 3, 1, 5]}, {[9, 8, 5, 6, 4, 3, 7, 2, 1, 10], [9, 8, 6, 5, 3, 4, 7, 2, 1, 10]}, {[9, 8, 5, 6, 7, 4, 3, 10, 2, 1], [10, 9, 7, 6, 3, 4, 5, 2, 1, 8]}, {[9, 8, 5, 6, 7, 10, 4, 3, 2, 1], [10, 9, 8, 7, 3, 4, 5, 2, 1, 6]}, {[9, 8, 6, 7, 4, 5, 3, 10, 2, 1], [10, 9, 7, 5, 6, 3, 4, 2, 1, 8]}, {[9, 8, 6, 7, 5, 3, 4, 10, 2, 1], [10, 9, 6, 7, 5, 3, 4, 2, 1, 8]}, {[9, 8, 6, 7, 5, 4, 10, 2, 3, 1], [10, 8, 9, 6, 5, 3, 4, 2, 1, 7]}, {[9, 8, 6, 7, 5, 4, 10, 3, 1, 2], [9, 10, 8, 6, 5, 3, 4, 2, 1, 7]}, {[9, 8, 6, 7, 10, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 3, 4, 2, 1, 5]}, {[9, 8, 6, 7, 10, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 3, 4, 2, 1, 5]}, {[9, 8, 6, 7, 10, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 3, 4, 2, 1, 5]}, {[9, 8, 6, 7, 10, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 3, 4, 2, 1, 5]}, {[9, 8, 7, 4, 5, 6, 3, 10, 2, 1], [10, 9, 7, 4, 5, 6, 3, 2, 1, 8]}, {[9, 8, 7, 5, 6, 3, 4, 10, 2, 1], [10, 9, 6, 7, 4, 5, 3, 2, 1, 8]}, {[9, 8, 7, 5, 6, 4, 10, 2, 3, 1], [10, 8, 9, 6, 4, 5, 3, 2, 1, 7]}, {[9, 8, 7, 5, 6, 4, 10, 3, 1, 2], [9, 10, 8, 6, 4, 5, 3, 2, 1, 7]}, {[9, 8, 7, 6, 3, 4, 5, 10, 2, 1], [10, 9, 5, 6, 7, 4, 3, 2, 1, 8]}, {[9, 8, 7, 6, 4, 5, 10, 2, 3, 1], [10, 8, 9, 5, 6, 4, 3, 2, 1, 7]}, {[9, 8, 7, 6, 4, 5, 10, 3, 1, 2], [9, 10, 8, 5, 6, 4, 3, 2, 1, 7]}, {[9, 8, 7, 6, 5, 10, 2, 3, 4, 1], [10, 7, 8, 9, 5, 4, 3, 2, 1, 6]}, {[9, 8, 7, 6, 5, 10, 3, 4, 1, 2], [9, 10, 7, 8, 5, 4, 3, 2, 1, 6]}, {[9, 8, 7, 10, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 3, 2, 1, 4]}, {[9, 8, 7, 10, 5, 6, 3, 4, 2, 1], [10, 9, 7, 8, 5, 6, 3, 2, 1, 4]}, {[9, 8, 7, 10, 5, 6, 4, 2, 3, 1], [10, 8, 9, 7, 5, 6, 3, 2, 1, 4]}, {[9, 8, 7, 10, 5, 6, 4, 3, 1, 2], [9, 10, 8, 7, 5, 6, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 5, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 5, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 4, 5, 3, 1, 2], [9, 10, 8, 6, 7, 5, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 5, 3, 2, 1, 4]}, {[9, 8, 7, 10, 6, 5, 3, 4, 1, 2], [9, 10, 7, 8, 6, 5, 3, 2, 1, 4]}, {[9, 10, 6, 5, 4, 3, 2, 7, 8, 1], [10, 7, 6, 5, 4, 3, 8, 9, 1, 2]}, {[9, 10, 6, 5, 4, 7, 8, 3, 2, 1], [10, 9, 8, 5, 4, 3, 6, 7, 1, 2]}, {[9, 10, 6, 7, 5, 4, 3, 2, 8, 1], [10, 8, 7, 6, 5, 3, 4, 9, 1, 2]}, {[9, 10, 6, 7, 5, 4, 8, 3, 2, 1], [10, 9, 8, 6, 5, 3, 4, 7, 1, 2]}, {[9, 10, 7, 5, 6, 4, 3, 2, 8, 1], [10, 8, 7, 6, 4, 5, 3, 9, 1, 2]}, {[9, 10, 7, 5, 6, 4, 8, 3, 2, 1], [10, 9, 8, 6, 4, 5, 3, 7, 1, 2]}, {[9, 10, 7, 6, 4, 5, 3, 2, 8, 1], [10, 8, 7, 5, 6, 4, 3, 9, 1, 2]}, {[9, 10, 7, 6, 4, 5, 8, 3, 2, 1], [10, 9, 8, 5, 6, 4, 3, 7, 1, 2]}, {[9, 10, 7, 6, 5, 3, 4, 2, 8, 1], [10, 8, 6, 7, 5, 4, 3, 9, 1, 2]}, {[9, 10, 7, 6, 5, 4, 2, 3, 8, 1], [10, 7, 8, 6, 5, 4, 3, 9, 1, 2]}, {[9, 10, 7, 6, 5, 8, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 3, 6, 1, 2]}, {[9, 10, 7, 6, 5, 8, 4, 2, 3, 1], [10, 8, 9, 7, 5, 4, 3, 6, 1, 2]}, {[9, 10, 7, 6, 5, 8, 4, 3, 1, 2], [9, 10, 8, 7, 5, 4, 3, 6, 1, 2]}, {[9, 10, 7, 8, 5, 4, 3, 6, 2, 1], [10, 9, 7, 6, 5, 8, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 5, 3, 4, 1, 2]}, {[9, 10, 8, 5, 4, 3, 6, 7, 2, 1], [10, 9, 6, 5, 4, 7, 8, 3, 1, 2]}, {[9, 10, 8, 5, 6, 4, 3, 7, 2, 1], [10, 9, 7, 6, 4, 5, 8, 3, 1, 2]}, {[9, 10, 8, 6, 4, 5, 3, 7, 2, 1], [10, 9, 7, 5, 6, 4, 8, 3, 1, 2]}, {[9, 10, 8, 6, 5, 3, 4, 7, 2, 1], [10, 9, 6, 7, 5, 4, 8, 3, 1, 2]}, {[9, 10, 8, 6, 5, 4, 7, 2, 3, 1], [10, 8, 9, 6, 5, 4, 7, 3, 1, 2]}, {[9, 10, 8, 6, 7, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 4, 5, 3, 1, 2]}, {[9, 10, 8, 7, 4, 3, 2, 5, 6, 1], [10, 7, 6, 5, 8, 9, 4, 3, 1, 2]}, {[9, 10, 8, 7, 4, 5, 3, 2, 6, 1], [10, 8, 7, 5, 6, 9, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 3, 4, 2, 6, 1], [10, 8, 6, 7, 5, 9, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 4, 2, 3, 6, 1], [10, 7, 8, 6, 5, 9, 4, 3, 1, 2]}, {[10, 6, 5, 4, 7, 8, 9, 3, 2, 1], [10, 9, 8, 4, 3, 2, 5, 6, 7, 1]}, {[10, 6, 7, 5, 4, 3, 2, 8, 9, 1], [10, 7, 6, 5, 4, 2, 3, 8, 9, 1]}, {[10, 6, 7, 5, 4, 8, 9, 3, 2, 1], [10, 9, 8, 5, 4, 2, 3, 6, 7, 1]}, {[10, 6, 7, 8, 5, 4, 3, 2, 9, 1], [10, 8, 7, 6, 5, 2, 3, 4, 9, 1]}, {[10, 6, 7, 8, 5, 4, 9, 3, 2, 1], [10, 9, 8, 6, 5, 2, 3, 4, 7, 1]}, {[10, 7, 5, 6, 4, 3, 2, 8, 9, 1], [10, 7, 6, 5, 3, 4, 2, 8, 9, 1]}, {[10, 7, 5, 6, 4, 8, 9, 3, 2, 1], [10, 9, 8, 5, 3, 4, 2, 6, 7, 1]}, {[10, 7, 6, 4, 5, 8, 9, 3, 2, 1], [10, 9, 8, 4, 5, 3, 2, 6, 7, 1]}, {[10, 7, 6, 5, 8, 9, 3, 4, 2, 1], [10, 9, 7, 8, 4, 3, 2, 5, 6, 1]}, {[10, 7, 6, 5, 8, 9, 4, 2, 3, 1], [10, 8, 9, 7, 4, 3, 2, 5, 6, 1]}, {[10, 7, 8, 5, 6, 4, 3, 2, 9, 1], [10, 8, 7, 6, 4, 5, 2, 3, 9, 1]}, {[10, 7, 8, 5, 6, 4, 9, 3, 2, 1], [10, 9, 8, 6, 4, 5, 2, 3, 7, 1]}, {[10, 7, 8, 6, 4, 5, 3, 2, 9, 1], [10, 8, 7, 5, 6, 4, 2, 3, 9, 1]}, {[10, 7, 8, 6, 4, 5, 9, 3, 2, 1], [10, 9, 8, 5, 6, 4, 2, 3, 7, 1]}, {[10, 7, 8, 6, 5, 3, 4, 2, 9, 1], [10, 8, 6, 7, 5, 4, 2, 3, 9, 1]}, {[10, 7, 8, 6, 5, 9, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 2, 3, 6, 1]}, {[10, 7, 8, 6, 5, 9, 4, 2, 3, 1], [10, 8, 9, 7, 5, 4, 2, 3, 6, 1]}, {[10, 7, 8, 9, 5, 4, 3, 6, 2, 1], [10, 9, 7, 6, 5, 8, 2, 3, 4, 1]}, {[10, 7, 8, 9, 6, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 5, 2, 3, 4, 1]}, {[10, 8, 5, 6, 7, 4, 3, 2, 9, 1], [10, 8, 7, 6, 3, 4, 5, 2, 9, 1]}, {[10, 8, 5, 6, 7, 4, 9, 3, 2, 1], [10, 9, 8, 6, 3, 4, 5, 2, 7, 1]}, {[10, 8, 6, 7, 4, 5, 3, 2, 9, 1], [10, 8, 7, 5, 6, 3, 4, 2, 9, 1]}, {[10, 8, 6, 7, 4, 5, 9, 3, 2, 1], [10, 9, 8, 5, 6, 3, 4, 2, 7, 1]}, {[10, 8, 6, 7, 5, 9, 3, 4, 2, 1], [10, 9, 7, 8, 5, 3, 4, 2, 6, 1]}, {[10, 8, 6, 7, 5, 9, 4, 2, 3, 1], [10, 8, 9, 7, 5, 3, 4, 2, 6, 1]}, {[10, 8, 7, 4, 5, 6, 9, 3, 2, 1], [10, 9, 8, 4, 5, 6, 3, 2, 7, 1]}, {[10, 8, 7, 5, 6, 9, 3, 4, 2, 1], [10, 9, 7, 8, 4, 5, 3, 2, 6, 1]}, {[10, 8, 7, 5, 6, 9, 4, 2, 3, 1], [10, 8, 9, 7, 4, 5, 3, 2, 6, 1]}, {[10, 8, 7, 6, 9, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 4, 3, 2, 5, 1]}, {[10, 8, 7, 6, 9, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 4, 3, 2, 5, 1]}, {[10, 8, 9, 5, 4, 3, 6, 7, 2, 1], [10, 9, 6, 5, 4, 7, 8, 2, 3, 1]}, {[10, 8, 9, 5, 6, 4, 3, 7, 2, 1], [10, 9, 7, 6, 4, 5, 8, 2, 3, 1]}, {[10, 8, 9, 6, 4, 5, 3, 7, 2, 1], [10, 9, 7, 5, 6, 4, 8, 2, 3, 1]}, {[10, 8, 9, 6, 5, 3, 4, 7, 2, 1], [10, 9, 6, 7, 5, 4, 8, 2, 3, 1]}, {[10, 9, 5, 6, 4, 3, 7, 8, 2, 1], [10, 9, 6, 5, 3, 4, 7, 8, 2, 1]}, {[10, 9, 5, 6, 7, 4, 3, 8, 2, 1], [10, 9, 7, 6, 3, 4, 5, 8, 2, 1]}, {[10, 9, 6, 7, 4, 5, 3, 8, 2, 1], [10, 9, 7, 5, 6, 3, 4, 8, 2, 1]}} is given by the following expression /1733 9791 2 235309 3 311 4 4277 5 6 |----- n + ------ n + ------- n + ----- n + ------- n + 3/65536 n \81920 196608 5898240 24576 2949120 7\ n / 11 96367 2 90989 3 33721 4 + 1/5898240 n | 4 + |- --- n - ------ n - ------ n - ------ n / \ 520 960960 524160 240240 11263 5 1497 6 3229 7 8\ - ------ n - ------ n - ------- n - 1/137280 n | C(n) 205920 160160 5765760 / and in Maple input form: (1733/81920*n+9791/196608*n^2+235309/5898240*n^3+311/24576*n^4+4277/2949120*n^5 +3/65536*n^6+1/5898240*n^7)*4^n+(-11/520*n-96367/960960*n^2-90989/524160*n^3-\ 33721/240240*n^4-11263/205920*n^5-1497/160160*n^6-3229/5765760*n^7-1/137280*n^8 )*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 17 16 1/2 15 14 1/2 13 12 Pi m m 241 Pi m 3229 m 35431 Pi m 1497 m --------- - ------ + ------------- - -------- + --------------- - -------- 5898240 137280 5242880 5765760 23592960 160160 1/2 11 10 1/2 9 8 112351 Pi m 11263 m 319279 Pi m 33721 m + ---------------- - --------- + --------------- - -------- 7864320 205920 5898240 240240 1/2 7 6 1/2 5 4 1489207 Pi m 90989 m 202321 Pi m 96367 m + ---------------- - -------- + --------------- - -------- 15728640 524160 2621440 960960 1/2 3 2 15597 Pi m 11 m + -------------- - ----- 655360 520 and in Maple input form: 1/5898240*Pi^(1/2)*m^17-1/137280*m^16+241/5242880*Pi^(1/2)*m^15-3229/5765760*m^ 14+35431/23592960*Pi^(1/2)*m^13-1497/160160*m^12+112351/7864320*Pi^(1/2)*m^11-\ 11263/205920*m^10+319279/5898240*Pi^(1/2)*m^9-33721/240240*m^8+1489207/15728640 *Pi^(1/2)*m^7-90989/524160*m^6+202321/2621440*Pi^(1/2)*m^5-96367/960960*m^4+ 15597/655360*Pi^(1/2)*m^3-11/520*m^2 For the, 18, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[7, 6, 5, 4, 8, 3, 2, 1, 9, 10], [8, 7, 6, 4, 3, 2, 1, 5, 9, 10]}, {[7, 6, 5, 4, 8, 9, 3, 2, 1, 10], [9, 8, 7, 4, 3, 2, 1, 5, 6, 10]}, {[7, 6, 5, 4, 8, 9, 10, 3, 2, 1], [10, 9, 8, 4, 3, 2, 1, 5, 6, 7]}, {[7, 8, 6, 5, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 4, 3, 1, 2, 6, 10]}, {[7, 8, 6, 5, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 4, 3, 1, 2, 6, 7]}, {[7, 8, 9, 6, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 4, 1, 2, 3, 7]}, {[8, 6, 5, 4, 3, 7, 2, 1, 9, 10], [8, 7, 5, 4, 3, 2, 6, 1, 9, 10]}, {[8, 6, 7, 5, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 4, 2, 3, 1, 6, 10]}, {[8, 6, 7, 5, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 4, 2, 3, 1, 6, 7]}, {[8, 7, 5, 6, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 3, 4, 2, 1, 6, 10]}, {[8, 7, 5, 6, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 3, 4, 2, 1, 6, 7]}, {[8, 7, 6, 4, 5, 9, 3, 2, 1, 10], [9, 8, 7, 4, 5, 3, 2, 1, 6, 10]}, {[8, 7, 6, 4, 5, 9, 10, 3, 2, 1], [10, 9, 8, 4, 5, 3, 2, 1, 6, 7]}, {[8, 7, 6, 5, 9, 3, 4, 2, 1, 10], [9, 8, 6, 7, 4, 3, 2, 1, 5, 10]}, {[8, 7, 6, 5, 9, 4, 2, 3, 1, 10], [9, 7, 8, 6, 4, 3, 2, 1, 5, 10]}, {[8, 7, 6, 5, 9, 4, 3, 1, 2, 10], [8, 9, 7, 6, 4, 3, 2, 1, 5, 10]}, {[8, 7, 6, 5, 9, 10, 3, 4, 2, 1], [10, 9, 7, 8, 4, 3, 2, 1, 5, 6]}, {[8, 7, 6, 5, 9, 10, 4, 2, 3, 1], [10, 8, 9, 7, 4, 3, 2, 1, 5, 6]}, {[8, 7, 6, 5, 9, 10, 4, 3, 1, 2], [9, 10, 8, 7, 4, 3, 2, 1, 5, 6]}, {[8, 9, 6, 5, 4, 3, 7, 2, 1, 10], [9, 8, 6, 5, 4, 3, 7, 1, 2, 10]}, {[8, 9, 6, 7, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 3, 4, 1, 2, 7]}, {[8, 9, 7, 5, 4, 3, 2, 6, 1, 10], [9, 7, 6, 5, 4, 8, 3, 1, 2, 10]}, {[8, 9, 7, 5, 6, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 5, 3, 1, 2, 7]}, {[8, 9, 7, 6, 4, 5, 10, 3, 2, 1], [10, 9, 8, 5, 6, 4, 3, 1, 2, 7]}, {[8, 9, 7, 6, 5, 10, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 3, 1, 2, 6]}, {[8, 9, 7, 6, 5, 10, 4, 2, 3, 1], [10, 8, 9, 7, 5, 4, 3, 1, 2, 6]}, {[8, 9, 7, 6, 5, 10, 4, 3, 1, 2], [9, 10, 8, 7, 5, 4, 3, 1, 2, 6]}, {[8, 9, 10, 6, 5, 4, 3, 7, 2, 1], [10, 9, 7, 6, 5, 4, 8, 1, 2, 3]}, {[8, 9, 10, 7, 5, 4, 3, 2, 6, 1], [10, 8, 7, 6, 5, 9, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 4, 3, 2, 1, 5], [9, 8, 7, 6, 10, 5, 4, 1, 2, 3]}, {[9, 6, 5, 4, 3, 7, 8, 2, 1, 10], [9, 8, 5, 4, 3, 2, 6, 7, 1, 10]}, {[9, 6, 7, 5, 4, 3, 8, 2, 1, 10], [9, 8, 6, 5, 4, 2, 3, 7, 1, 10]}, {[9, 6, 7, 8, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 2, 3, 4, 1, 7]}, {[9, 7, 5, 6, 4, 3, 8, 2, 1, 10], [9, 8, 6, 5, 3, 4, 2, 7, 1, 10]}, {[9, 7, 6, 4, 5, 3, 8, 2, 1, 10], [9, 8, 6, 4, 5, 3, 2, 7, 1, 10]}, {[9, 7, 6, 5, 3, 4, 8, 2, 1, 10], [9, 8, 5, 6, 4, 3, 2, 7, 1, 10]}, {[9, 7, 6, 5, 4, 8, 2, 3, 1, 10], [9, 7, 8, 5, 4, 3, 2, 6, 1, 10]}, {[9, 7, 8, 5, 6, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 5, 2, 3, 1, 7]}, {[9, 7, 8, 6, 4, 5, 10, 3, 2, 1], [10, 9, 8, 5, 6, 4, 2, 3, 1, 7]}, {[9, 7, 8, 6, 5, 10, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 2, 3, 1, 6]}, {[9, 7, 8, 6, 5, 10, 4, 2, 3, 1], [10, 8, 9, 7, 5, 4, 2, 3, 1, 6]}, {[9, 7, 8, 6, 5, 10, 4, 3, 1, 2], [9, 10, 8, 7, 5, 4, 2, 3, 1, 6]}, {[9, 8, 5, 6, 7, 4, 10, 3, 2, 1], [10, 9, 8, 6, 3, 4, 5, 2, 1, 7]}, {[9, 8, 6, 7, 4, 5, 10, 3, 2, 1], [10, 9, 8, 5, 6, 3, 4, 2, 1, 7]}, {[9, 8, 6, 7, 5, 10, 3, 4, 2, 1], [10, 9, 7, 8, 5, 3, 4, 2, 1, 6]}, {[9, 8, 6, 7, 5, 10, 4, 2, 3, 1], [10, 8, 9, 7, 5, 3, 4, 2, 1, 6]}, {[9, 8, 6, 7, 5, 10, 4, 3, 1, 2], [9, 10, 8, 7, 5, 3, 4, 2, 1, 6]}, {[9, 8, 7, 4, 5, 6, 10, 3, 2, 1], [10, 9, 8, 4, 5, 6, 3, 2, 1, 7]}, {[9, 8, 7, 5, 6, 10, 3, 4, 2, 1], [10, 9, 7, 8, 4, 5, 3, 2, 1, 6]}, {[9, 8, 7, 5, 6, 10, 4, 2, 3, 1], [10, 8, 9, 7, 4, 5, 3, 2, 1, 6]}, {[9, 8, 7, 5, 6, 10, 4, 3, 1, 2], [9, 10, 8, 7, 4, 5, 3, 2, 1, 6]}, {[9, 8, 7, 6, 10, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 4, 5, 3, 1, 2], [9, 10, 8, 6, 7, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 4, 3, 2, 1, 5]}, {[9, 8, 7, 6, 10, 5, 3, 4, 1, 2], [9, 10, 7, 8, 6, 4, 3, 2, 1, 5]}, {[9, 10, 6, 5, 4, 3, 7, 8, 2, 1], [10, 9, 6, 5, 4, 3, 7, 8, 1, 2]}, {[9, 10, 6, 7, 5, 4, 3, 8, 2, 1], [10, 9, 7, 6, 5, 3, 4, 8, 1, 2]}, {[9, 10, 7, 5, 6, 4, 3, 8, 2, 1], [10, 9, 7, 6, 4, 5, 3, 8, 1, 2]}, {[9, 10, 7, 6, 4, 5, 3, 8, 2, 1], [10, 9, 7, 5, 6, 4, 3, 8, 1, 2]}, {[9, 10, 7, 6, 5, 3, 4, 8, 2, 1], [10, 9, 6, 7, 5, 4, 3, 8, 1, 2]}, {[9, 10, 7, 6, 5, 4, 8, 2, 3, 1], [10, 8, 9, 6, 5, 4, 3, 7, 1, 2]}, {[9, 10, 7, 6, 5, 4, 8, 3, 1, 2], [9, 10, 8, 6, 5, 4, 3, 7, 1, 2]}, {[9, 10, 7, 8, 5, 4, 3, 2, 6, 1], [10, 8, 7, 6, 5, 9, 3, 4, 1, 2]}, {[9, 10, 8, 5, 4, 3, 2, 6, 7, 1], [10, 7, 6, 5, 4, 8, 9, 3, 1, 2]}, {[9, 10, 8, 5, 6, 4, 3, 2, 7, 1], [10, 8, 7, 6, 4, 5, 9, 3, 1, 2]}, {[9, 10, 8, 6, 4, 5, 3, 2, 7, 1], [10, 8, 7, 5, 6, 4, 9, 3, 1, 2]}, {[9, 10, 8, 6, 5, 3, 4, 2, 7, 1], [10, 8, 6, 7, 5, 4, 9, 3, 1, 2]}, {[9, 10, 8, 6, 5, 4, 2, 3, 7, 1], [10, 7, 8, 6, 5, 4, 9, 3, 1, 2]}, {[10, 6, 5, 4, 3, 7, 8, 9, 2, 1], [10, 9, 5, 4, 3, 2, 6, 7, 8, 1]}, {[10, 6, 7, 5, 4, 3, 8, 9, 2, 1], [10, 9, 6, 5, 4, 2, 3, 7, 8, 1]}, {[10, 6, 7, 8, 5, 4, 3, 9, 2, 1], [10, 9, 7, 6, 5, 2, 3, 4, 8, 1]}, {[10, 7, 5, 6, 4, 3, 8, 9, 2, 1], [10, 9, 6, 5, 3, 4, 2, 7, 8, 1]}, {[10, 7, 6, 4, 5, 3, 8, 9, 2, 1], [10, 9, 6, 4, 5, 3, 2, 7, 8, 1]}, {[10, 7, 6, 5, 3, 4, 8, 9, 2, 1], [10, 9, 5, 6, 4, 3, 2, 7, 8, 1]}, {[10, 7, 6, 5, 4, 8, 9, 2, 3, 1], [10, 8, 9, 5, 4, 3, 2, 6, 7, 1]}, {[10, 7, 8, 5, 6, 4, 3, 9, 2, 1], [10, 9, 7, 6, 4, 5, 2, 3, 8, 1]}, {[10, 7, 8, 6, 4, 5, 3, 9, 2, 1], [10, 9, 7, 5, 6, 4, 2, 3, 8, 1]}, {[10, 7, 8, 6, 5, 3, 4, 9, 2, 1], [10, 9, 6, 7, 5, 4, 2, 3, 8, 1]}, {[10, 7, 8, 6, 5, 4, 9, 2, 3, 1], [10, 8, 9, 6, 5, 4, 2, 3, 7, 1]}, {[10, 7, 8, 9, 5, 4, 3, 2, 6, 1], [10, 8, 7, 6, 5, 9, 2, 3, 4, 1]}, {[10, 8, 5, 6, 7, 4, 3, 9, 2, 1], [10, 9, 7, 6, 3, 4, 5, 2, 8, 1]}, {[10, 8, 6, 7, 4, 5, 3, 9, 2, 1], [10, 9, 7, 5, 6, 3, 4, 2, 8, 1]}, {[10, 8, 6, 7, 5, 3, 4, 9, 2, 1], [10, 9, 6, 7, 5, 3, 4, 2, 8, 1]}, {[10, 8, 6, 7, 5, 4, 9, 2, 3, 1], [10, 8, 9, 6, 5, 3, 4, 2, 7, 1]}, {[10, 8, 7, 4, 5, 6, 3, 9, 2, 1], [10, 9, 7, 4, 5, 6, 3, 2, 8, 1]}, {[10, 8, 7, 5, 6, 3, 4, 9, 2, 1], [10, 9, 6, 7, 4, 5, 3, 2, 8, 1]}, {[10, 8, 7, 5, 6, 4, 9, 2, 3, 1], [10, 8, 9, 6, 4, 5, 3, 2, 7, 1]}, {[10, 8, 7, 6, 3, 4, 5, 9, 2, 1], [10, 9, 5, 6, 7, 4, 3, 2, 8, 1]}, {[10, 8, 7, 6, 4, 5, 9, 2, 3, 1], [10, 8, 9, 5, 6, 4, 3, 2, 7, 1]}} is given by the following expression / 81071 59917 2 22279 3 54403 4 30721 5 193 6 |------- n + ------- n + ------ n + ------- n + -------- n + ------- n \3440640 1179648 589824 4718592 23592960 4718592 7\ n / 2831 308467 2 506117 3 1551691 4 + 5/33030144 n | 4 + |- ------ n - ------- n - ------- n - -------- n / \ 120120 2882880 2882880 11531520 72607 5 48623 6 289 7 8\ - ------- n - ------- n - ------ n - 5/768768 n | C(n) 1441440 5765760 576576 / and in Maple input form: (81071/3440640*n+59917/1179648*n^2+22279/589824*n^3+54403/4718592*n^4+30721/ 23592960*n^5+193/4718592*n^6+5/33030144*n^7)*4^n+(-2831/120120*n-308467/2882880 *n^2-506117/2882880*n^3-1551691/11531520*n^4-72607/1441440*n^5-48623/5765760*n^ 6-289/576576*n^7-5/768768*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 17 16 1/2 15 14 1/2 13 12 5 Pi m 5 m 10853 Pi m 289 m 254453 Pi m 48623 m ----------- - ------ + --------------- - ------- + ---------------- - --------- 33030144 768768 264241152 576576 188743680 5765760 1/2 11 10 1/2 9 8 2452609 Pi m 72607 m 1915483 Pi m 1551691 m + ----------------- - --------- + ---------------- - ---------- 188743680 1441440 37748736 11531520 1/2 7 6 1/2 5 4 440179 Pi m 506117 m 8885557 Pi m 308467 m + --------------- - --------- + ---------------- - --------- 4718592 2882880 110100480 2882880 1/2 3 2 243213 Pi m 2831 m + --------------- - ------- 9175040 120120 and in Maple input form: 5/33030144*Pi^(1/2)*m^17-5/768768*m^16+10853/264241152*Pi^(1/2)*m^15-289/576576 *m^14+254453/188743680*Pi^(1/2)*m^13-48623/5765760*m^12+2452609/188743680*Pi^(1 /2)*m^11-72607/1441440*m^10+1915483/37748736*Pi^(1/2)*m^9-1551691/11531520*m^8+ 440179/4718592*Pi^(1/2)*m^7-506117/2882880*m^6+8885557/110100480*Pi^(1/2)*m^5-\ 308467/2882880*m^4+243213/9175040*Pi^(1/2)*m^3-2831/120120*m^2 For the, 19, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[8, 7, 9, 6, 5, 4, 2, 1, 3, 10]}, {[9, 7, 6, 8, 5, 3, 2, 4, 1, 10]}, {[9, 8, 10, 7, 5, 6, 4, 2, 1, 3]}, {[10, 8, 7, 9, 5, 6, 3, 2, 4, 1]}, {[7, 6, 5, 4, 3, 8, 9, 2, 10, 1], [10, 8, 5, 4, 3, 2, 1, 6, 7, 9]}, {[7, 6, 8, 5, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 9, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 2, 1, 3, 4, 6]}, {[7, 8, 6, 5, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 4, 3, 1, 2, 7, 9]}, {[7, 8, 6, 9, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 3, 1, 2, 4, 9]}, {[7, 8, 6, 9, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 3, 1, 2, 4, 6]}, {[8, 6, 5, 7, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 3, 2, 4, 1, 5, 10]}, {[8, 6, 5, 7, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 3, 2, 4, 1, 5, 6]}, {[8, 6, 7, 5, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 4, 2, 3, 1, 7, 9]}, {[8, 6, 7, 9, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 2, 3, 1, 4, 9]}, {[8, 6, 7, 9, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 2, 3, 1, 4, 6]}, {[8, 7, 5, 6, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 3, 4, 2, 1, 7, 9]}, {[8, 7, 6, 4, 5, 3, 9, 2, 10, 1], [10, 8, 6, 4, 5, 3, 2, 1, 7, 9]}, {[8, 7, 6, 5, 3, 4, 9, 2, 10, 1], [10, 8, 5, 6, 4, 3, 2, 1, 7, 9]}, {[8, 7, 6, 5, 4, 9, 2, 1, 3, 10], [8, 7, 9, 5, 4, 3, 2, 1, 6, 10]}, {[8, 7, 6, 5, 4, 9, 2, 3, 10, 1], [10, 7, 8, 5, 4, 3, 2, 1, 6, 9]}, {[8, 7, 6, 5, 4, 9, 3, 10, 1, 2], [9, 10, 7, 5, 4, 3, 2, 1, 6, 8]}, {[8, 7, 6, 5, 4, 9, 10, 2, 1, 3], [9, 8, 10, 5, 4, 3, 2, 1, 6, 7]}, {[8, 7, 9, 5, 4, 6, 3, 2, 1, 10], [9, 8, 7, 5, 4, 6, 2, 1, 3, 10]}, {[8, 7, 9, 5, 6, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 5, 2, 1, 3, 9]}, {[8, 7, 9, 5, 6, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 2, 1, 3, 6]}, {[8, 7, 9, 6, 4, 3, 5, 2, 1, 10], [9, 8, 6, 5, 7, 4, 2, 1, 3, 10]}, {[8, 7, 9, 6, 4, 5, 3, 2, 10, 1], [10, 8, 7, 5, 6, 4, 2, 1, 3, 9]}, {[8, 7, 9, 6, 5, 3, 2, 4, 1, 10], [9, 7, 6, 8, 5, 4, 2, 1, 3, 10]}, {[8, 7, 9, 6, 5, 3, 4, 2, 10, 1], [10, 8, 6, 7, 5, 4, 2, 1, 3, 9]}, {[8, 7, 9, 6, 5, 4, 2, 3, 10, 1], [10, 7, 8, 6, 5, 4, 2, 1, 3, 9]}, {[8, 7, 9, 6, 5, 4, 3, 10, 1, 2], [9, 10, 7, 6, 5, 4, 2, 1, 3, 8]}, {[8, 7, 9, 6, 10, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 2, 1, 3, 5]}, {[8, 7, 9, 6, 10, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 2, 1, 3, 5]}, {[8, 7, 9, 6, 10, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 2, 1, 3, 5]}, {[8, 7, 9, 6, 10, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 4, 2, 1, 3, 5]}, {[8, 7, 9, 10, 5, 4, 3, 2, 1, 6], [9, 8, 7, 6, 5, 10, 2, 1, 3, 4]}, {[8, 7, 9, 10, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 2, 1, 3, 4]}, {[8, 7, 9, 10, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 2, 1, 3, 4]}, {[8, 7, 9, 10, 6, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 5, 2, 1, 3, 4]}, {[8, 7, 9, 10, 6, 5, 4, 2, 1, 3], [9, 8, 10, 7, 6, 5, 2, 1, 3, 4]}, {[8, 9, 6, 5, 4, 3, 2, 7, 10, 1], [10, 7, 6, 5, 4, 3, 8, 1, 2, 9]}, {[8, 9, 6, 5, 7, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 3, 5, 1, 2, 9]}, {[8, 9, 6, 5, 7, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 3, 5, 1, 2, 6]}, {[8, 9, 7, 5, 4, 6, 3, 2, 10, 1], [10, 8, 7, 5, 4, 6, 3, 1, 2, 9]}, {[8, 9, 7, 6, 4, 3, 5, 2, 10, 1], [10, 8, 6, 5, 7, 4, 3, 1, 2, 9]}, {[8, 9, 7, 6, 5, 3, 2, 4, 10, 1], [10, 7, 6, 8, 5, 4, 3, 1, 2, 9]}, {[8, 9, 7, 6, 5, 4, 10, 2, 1, 3], [9, 8, 10, 6, 5, 4, 3, 1, 2, 7]}, {[8, 9, 7, 10, 5, 4, 3, 2, 1, 6], [9, 8, 7, 6, 5, 10, 3, 1, 2, 4]}, {[8, 9, 7, 10, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 3, 1, 2, 4]}, {[8, 9, 7, 10, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 3, 1, 2, 4]}, {[8, 9, 7, 10, 6, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 5, 3, 1, 2, 4]}, {[8, 9, 7, 10, 6, 5, 4, 2, 1, 3], [9, 8, 10, 7, 6, 5, 3, 1, 2, 4]}, {[9, 6, 5, 4, 3, 2, 7, 8, 10, 1], [10, 6, 5, 4, 3, 2, 7, 8, 1, 9]}, {[9, 6, 5, 7, 4, 8, 3, 2, 1, 10], [9, 8, 7, 5, 3, 2, 4, 6, 1, 10]}, {[9, 6, 5, 7, 8, 4, 3, 2, 10, 1], [10, 8, 7, 6, 3, 2, 4, 5, 1, 9]}, {[9, 6, 5, 7, 8, 10, 4, 3, 2, 1], [10, 9, 8, 7, 3, 2, 4, 5, 1, 6]}, {[9, 6, 7, 5, 4, 3, 2, 8, 10, 1], [10, 7, 6, 5, 4, 2, 3, 8, 1, 9]}, {[9, 6, 7, 5, 8, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 2, 3, 5, 1, 9]}, {[9, 6, 7, 5, 8, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 2, 3, 5, 1, 6]}, {[9, 7, 5, 4, 6, 8, 3, 2, 1, 10], [9, 8, 7, 4, 3, 5, 2, 6, 1, 10]}, {[9, 7, 5, 6, 4, 3, 2, 8, 10, 1], [10, 7, 6, 5, 3, 4, 2, 8, 1, 9]}, {[9, 7, 5, 6, 8, 4, 3, 2, 10, 1], [10, 8, 7, 6, 3, 4, 2, 5, 1, 9]}, {[9, 7, 5, 6, 8, 10, 4, 3, 2, 1], [10, 9, 8, 7, 3, 4, 2, 5, 1, 6]}, {[9, 7, 6, 4, 5, 3, 2, 8, 10, 1], [10, 7, 6, 4, 5, 3, 2, 8, 1, 9]}, {[9, 7, 6, 5, 3, 4, 2, 8, 10, 1], [10, 7, 5, 6, 4, 3, 2, 8, 1, 9]}, {[9, 7, 6, 5, 4, 2, 3, 8, 10, 1], [10, 6, 7, 5, 4, 3, 2, 8, 1, 9]}, {[9, 7, 6, 5, 4, 3, 8, 10, 1, 2], [9, 10, 6, 5, 4, 3, 2, 7, 1, 8]}, {[9, 7, 6, 8, 4, 3, 5, 2, 1, 10], [9, 8, 6, 5, 7, 3, 2, 4, 1, 10]}, {[9, 7, 6, 8, 4, 5, 3, 2, 10, 1], [10, 8, 7, 5, 6, 3, 2, 4, 1, 9]}, {[9, 7, 6, 8, 5, 3, 4, 2, 10, 1], [10, 8, 6, 7, 5, 3, 2, 4, 1, 9]}, {[9, 7, 6, 8, 5, 4, 2, 3, 10, 1], [10, 7, 8, 6, 5, 3, 2, 4, 1, 9]}, {[9, 7, 6, 8, 5, 4, 3, 10, 1, 2], [9, 10, 7, 6, 5, 3, 2, 4, 1, 8]}, {[9, 7, 6, 8, 10, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 3, 2, 4, 1, 5]}, {[9, 7, 6, 8, 10, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 3, 2, 4, 1, 5]}, {[9, 7, 6, 8, 10, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 3, 2, 4, 1, 5]}, {[9, 7, 6, 8, 10, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 3, 2, 4, 1, 5]}, {[9, 7, 8, 5, 4, 6, 3, 2, 10, 1], [10, 8, 7, 5, 4, 6, 2, 3, 1, 9]}, {[9, 7, 8, 6, 4, 3, 5, 2, 10, 1], [10, 8, 6, 5, 7, 4, 2, 3, 1, 9]}, {[9, 7, 8, 6, 5, 3, 2, 4, 10, 1], [10, 7, 6, 8, 5, 4, 2, 3, 1, 9]}, {[9, 7, 8, 6, 5, 4, 10, 2, 1, 3], [9, 8, 10, 6, 5, 4, 2, 3, 1, 7]}, {[9, 7, 8, 10, 5, 4, 3, 2, 1, 6], [9, 8, 7, 6, 5, 10, 2, 3, 1, 4]}, {[9, 7, 8, 10, 5, 4, 6, 3, 2, 1], [10, 9, 8, 6, 5, 7, 2, 3, 1, 4]}, {[9, 7, 8, 10, 6, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 5, 2, 3, 1, 4]}, {[9, 7, 8, 10, 6, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 5, 2, 3, 1, 4]}, {[9, 7, 8, 10, 6, 5, 4, 2, 1, 3], [9, 8, 10, 7, 6, 5, 2, 3, 1, 4]}, {[9, 8, 5, 4, 6, 3, 7, 2, 1, 10], [9, 8, 6, 4, 3, 5, 7, 2, 1, 10]}, {[9, 8, 5, 4, 6, 7, 3, 2, 10, 1], [10, 8, 7, 4, 3, 5, 6, 2, 1, 9]}, {[9, 8, 5, 6, 4, 7, 3, 2, 10, 1], [10, 8, 7, 5, 3, 4, 6, 2, 1, 9]}, {[9, 8, 6, 4, 5, 7, 3, 2, 10, 1], [10, 8, 7, 4, 5, 3, 6, 2, 1, 9]}, {[9, 8, 6, 5, 7, 3, 4, 2, 10, 1], [10, 8, 6, 7, 4, 3, 5, 2, 1, 9]}, {[9, 8, 6, 5, 7, 4, 2, 3, 10, 1], [10, 7, 8, 6, 4, 3, 5, 2, 1, 9]}, {[9, 8, 6, 5, 7, 4, 3, 10, 1, 2], [9, 10, 7, 6, 4, 3, 5, 2, 1, 8]}, {[9, 8, 6, 7, 4, 3, 5, 2, 10, 1], [10, 8, 6, 5, 7, 3, 4, 2, 1, 9]}, {[9, 8, 6, 7, 5, 3, 2, 4, 10, 1], [10, 7, 6, 8, 5, 3, 4, 2, 1, 9]}, {[9, 8, 6, 7, 5, 4, 10, 2, 1, 3], [9, 8, 10, 6, 5, 3, 4, 2, 1, 7]}, {[9, 8, 7, 4, 3, 5, 6, 2, 10, 1], [10, 8, 5, 4, 6, 7, 3, 2, 1, 9]}, {[9, 8, 7, 4, 5, 3, 6, 2, 10, 1], [10, 8, 6, 4, 5, 7, 3, 2, 1, 9]}, {[9, 8, 7, 5, 3, 4, 6, 2, 10, 1], [10, 8, 5, 6, 4, 7, 3, 2, 1, 9]}, {[9, 8, 7, 5, 4, 6, 2, 3, 10, 1], [10, 7, 8, 5, 4, 6, 3, 2, 1, 9]}, {[9, 8, 7, 5, 4, 6, 3, 10, 1, 2], [9, 10, 7, 5, 4, 6, 3, 2, 1, 8]}, {[9, 8, 7, 5, 6, 3, 2, 4, 10, 1], [10, 7, 6, 8, 4, 5, 3, 2, 1, 9]}, {[9, 8, 7, 5, 6, 4, 10, 2, 1, 3], [9, 8, 10, 6, 4, 5, 3, 2, 1, 7]}, {[9, 8, 7, 6, 3, 2, 4, 5, 10, 1], [10, 6, 5, 7, 8, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 3, 4, 2, 5, 10, 1], [10, 7, 5, 6, 8, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 4, 2, 3, 5, 10, 1], [10, 6, 7, 5, 8, 4, 3, 2, 1, 9]}, {[9, 8, 7, 6, 4, 3, 5, 10, 1, 2], [9, 10, 6, 5, 7, 4, 3, 2, 1, 8]}, {[9, 8, 7, 6, 4, 5, 10, 2, 1, 3], [9, 8, 10, 5, 6, 4, 3, 2, 1, 7]}, {[9, 8, 10, 5, 4, 6, 7, 3, 2, 1], [10, 9, 8, 5, 4, 6, 7, 2, 1, 3]}, {[9, 8, 10, 5, 6, 4, 7, 3, 2, 1], [10, 9, 8, 6, 4, 5, 7, 2, 1, 3]}, {[9, 8, 10, 6, 4, 5, 7, 3, 2, 1], [10, 9, 8, 5, 6, 4, 7, 2, 1, 3]}, {[9, 8, 10, 6, 5, 7, 3, 4, 2, 1], [10, 9, 7, 8, 5, 4, 6, 2, 1, 3]}, {[9, 8, 10, 6, 5, 7, 4, 2, 3, 1], [10, 8, 9, 7, 5, 4, 6, 2, 1, 3]}, {[9, 8, 10, 6, 5, 7, 4, 3, 1, 2], [9, 10, 8, 7, 5, 4, 6, 2, 1, 3]}, {[9, 8, 10, 6, 7, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 4, 5, 2, 1, 3]}, {[9, 8, 10, 6, 7, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 4, 5, 2, 1, 3]}, {[9, 8, 10, 6, 7, 5, 4, 2, 1, 3], [9, 8, 10, 7, 6, 4, 5, 2, 1, 3]}, {[9, 8, 10, 7, 4, 3, 5, 6, 2, 1], [10, 9, 6, 5, 7, 8, 4, 2, 1, 3]}, {[9, 8, 10, 7, 4, 5, 3, 6, 2, 1], [10, 9, 7, 5, 6, 8, 4, 2, 1, 3]}, {[9, 8, 10, 7, 5, 3, 4, 6, 2, 1], [10, 9, 6, 7, 5, 8, 4, 2, 1, 3]}, {[9, 8, 10, 7, 5, 4, 6, 2, 3, 1], [10, 8, 9, 6, 5, 7, 4, 2, 1, 3]}, {[9, 8, 10, 7, 5, 4, 6, 3, 1, 2], [9, 10, 8, 6, 5, 7, 4, 2, 1, 3]}, {[9, 8, 10, 7, 5, 6, 3, 2, 4, 1], [10, 8, 7, 9, 5, 6, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 3, 2, 4, 5, 1], [10, 7, 6, 8, 9, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 3, 4, 2, 5, 1], [10, 8, 6, 7, 9, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 4, 2, 3, 5, 1], [10, 7, 8, 6, 9, 5, 4, 2, 1, 3]}, {[9, 8, 10, 7, 6, 4, 3, 5, 1, 2], [9, 10, 7, 6, 8, 5, 4, 2, 1, 3]}, {[9, 10, 6, 5, 7, 4, 8, 3, 2, 1], [10, 9, 8, 6, 4, 3, 5, 7, 1, 2]}, {[9, 10, 7, 5, 4, 6, 8, 3, 2, 1], [10, 9, 8, 5, 4, 6, 3, 7, 1, 2]}, {[9, 10, 7, 6, 8, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 4, 3, 5, 1, 2]}, {[9, 10, 7, 6, 8, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 4, 3, 5, 1, 2]}, {[9, 10, 8, 5, 4, 6, 3, 7, 2, 1], [10, 9, 7, 5, 4, 6, 8, 3, 1, 2]}, {[9, 10, 8, 6, 4, 3, 5, 7, 2, 1], [10, 9, 6, 5, 7, 4, 8, 3, 1, 2]}, {[9, 10, 8, 6, 5, 7, 3, 2, 4, 1], [10, 8, 7, 9, 5, 4, 6, 3, 1, 2]}, {[9, 10, 8, 7, 4, 3, 5, 2, 6, 1], [10, 8, 6, 5, 7, 9, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 3, 2, 4, 6, 1], [10, 7, 6, 8, 5, 9, 4, 3, 1, 2]}, {[10, 6, 5, 7, 4, 8, 9, 3, 2, 1], [10, 9, 8, 5, 3, 2, 4, 6, 7, 1]}, {[10, 6, 5, 7, 8, 4, 9, 3, 2, 1], [10, 9, 8, 6, 3, 2, 4, 5, 7, 1]}, {[10, 6, 7, 5, 8, 4, 9, 3, 2, 1], [10, 9, 8, 6, 4, 2, 3, 5, 7, 1]}, {[10, 7, 5, 4, 6, 8, 9, 3, 2, 1], [10, 9, 8, 4, 3, 5, 2, 6, 7, 1]}, {[10, 7, 5, 6, 8, 4, 9, 3, 2, 1], [10, 9, 8, 6, 3, 4, 2, 5, 7, 1]}, {[10, 7, 6, 8, 4, 5, 9, 3, 2, 1], [10, 9, 8, 5, 6, 3, 2, 4, 7, 1]}, {[10, 7, 6, 8, 5, 9, 3, 4, 2, 1], [10, 9, 7, 8, 5, 3, 2, 4, 6, 1]}, {[10, 7, 6, 8, 5, 9, 4, 2, 3, 1], [10, 8, 9, 7, 5, 3, 2, 4, 6, 1]}, {[10, 7, 6, 8, 9, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 3, 2, 4, 5, 1]}, {[10, 7, 6, 8, 9, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 3, 2, 4, 5, 1]}, {[10, 7, 8, 5, 4, 6, 9, 3, 2, 1], [10, 9, 8, 5, 4, 6, 2, 3, 7, 1]}, {[10, 7, 8, 6, 9, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 4, 2, 3, 5, 1]}, {[10, 7, 8, 6, 9, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 4, 2, 3, 5, 1]}, {[10, 8, 5, 4, 6, 7, 9, 3, 2, 1], [10, 9, 8, 4, 3, 5, 6, 2, 7, 1]}, {[10, 8, 5, 6, 4, 7, 9, 3, 2, 1], [10, 9, 8, 5, 3, 4, 6, 2, 7, 1]}, {[10, 8, 6, 4, 5, 7, 9, 3, 2, 1], [10, 9, 8, 4, 5, 3, 6, 2, 7, 1]}, {[10, 8, 6, 5, 7, 9, 3, 4, 2, 1], [10, 9, 7, 8, 4, 3, 5, 2, 6, 1]}, {[10, 8, 6, 5, 7, 9, 4, 2, 3, 1], [10, 8, 9, 7, 4, 3, 5, 2, 6, 1]}, {[10, 8, 6, 7, 9, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 3, 4, 2, 5, 1]}, {[10, 8, 6, 7, 9, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 3, 4, 2, 5, 1]}, {[10, 8, 7, 9, 4, 3, 5, 6, 2, 1], [10, 9, 6, 5, 7, 8, 3, 2, 4, 1]}, {[10, 8, 7, 9, 4, 5, 3, 6, 2, 1], [10, 9, 7, 5, 6, 8, 3, 2, 4, 1]}, {[10, 8, 7, 9, 5, 3, 4, 6, 2, 1], [10, 9, 6, 7, 5, 8, 3, 2, 4, 1]}, {[10, 8, 7, 9, 5, 4, 6, 2, 3, 1], [10, 8, 9, 6, 5, 7, 3, 2, 4, 1]}, {[10, 8, 9, 5, 4, 6, 3, 7, 2, 1], [10, 9, 7, 5, 4, 6, 8, 2, 3, 1]}, {[10, 8, 9, 6, 4, 3, 5, 7, 2, 1], [10, 9, 6, 5, 7, 4, 8, 2, 3, 1]}, {[10, 9, 5, 4, 6, 3, 7, 8, 2, 1], [10, 9, 6, 4, 3, 5, 7, 8, 2, 1]}, {[10, 9, 5, 4, 6, 7, 3, 8, 2, 1], [10, 9, 7, 4, 3, 5, 6, 8, 2, 1]}, {[10, 9, 5, 6, 4, 7, 3, 8, 2, 1], [10, 9, 7, 5, 3, 4, 6, 8, 2, 1]}, {[10, 9, 6, 4, 5, 7, 3, 8, 2, 1], [10, 9, 7, 4, 5, 3, 6, 8, 2, 1]}, {[10, 9, 6, 5, 7, 3, 4, 8, 2, 1], [10, 9, 6, 7, 4, 3, 5, 8, 2, 1]}, { [7, 6, 5, 4, 3, 8, 2, 9, 1, 10], [7, 6, 5, 4, 3, 8, 2, 9, 10, 1], [9, 7, 5, 4, 3, 2, 1, 6, 8, 10], [10, 7, 5, 4, 3, 2, 1, 6, 8, 9]}, { [7, 6, 8, 5, 4, 3, 2, 9, 1, 10], [7, 6, 8, 5, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 4, 2, 1, 3, 8, 10], [10, 7, 6, 5, 4, 2, 1, 3, 8, 9]}, { [8, 6, 5, 4, 3, 2, 7, 9, 1, 10], [8, 6, 5, 4, 3, 2, 7, 9, 10, 1], [9, 6, 5, 4, 3, 2, 7, 1, 8, 10], [10, 6, 5, 4, 3, 2, 7, 1, 8, 9]}, { [8, 6, 5, 7, 4, 3, 2, 9, 1, 10], [8, 6, 5, 7, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 3, 2, 4, 1, 8, 10], [10, 7, 6, 5, 3, 2, 4, 1, 8, 9]}, { [8, 7, 5, 4, 6, 3, 2, 9, 1, 10], [8, 7, 5, 4, 6, 3, 2, 9, 10, 1], [9, 7, 6, 4, 3, 5, 2, 1, 8, 10], [10, 7, 6, 4, 3, 5, 2, 1, 8, 9]}, { [8, 7, 6, 4, 3, 5, 2, 9, 1, 10], [8, 7, 6, 4, 3, 5, 2, 9, 10, 1], [9, 7, 5, 4, 6, 3, 2, 1, 8, 10], [10, 7, 5, 4, 6, 3, 2, 1, 8, 9]}, { [8, 7, 6, 5, 3, 2, 4, 9, 1, 10], [8, 7, 6, 5, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 4, 3, 2, 1, 8, 10], [10, 6, 5, 7, 4, 3, 2, 1, 8, 9]}} is given by the following expression / 57 1501 2 1261 3 1115 4 4243 5 23 6 |- ----- n - ------ n + ------- n + ------ n + -------- n + ------- n \ 81920 983040 2949120 786432 11796480 1310720 7\ n / 2293 2 100 3 881 4 + 1/11796480 n | 4 + |1/1430 n + ------ n + ----- n - ------ n / \ 720720 27027 617760 18251 5 7577 6 773 7 8\ - ------- n - ------- n - ------- n - 1/308880 n | C(n) 4324320 4324320 4324320 / and in Maple input form: (-57/81920*n-1501/983040*n^2+1261/2949120*n^3+1115/786432*n^4+4243/11796480*n^5 +23/1310720*n^6+1/11796480*n^7)*4^n+(1/1430*n+2293/720720*n^2+100/27027*n^3-881 /617760*n^4-18251/4324320*n^5-7577/4324320*n^6-773/4324320*n^7-1/308880*n^8)*C( n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 17 16 1/2 15 14 1/2 13 12 Pi m m 37 Pi m 773 m 35807 Pi m 7577 m --------- - ------ + ------------ - ------- + --------------- - -------- 11796480 308880 2097152 4324320 94371840 4324320 1/2 11 10 1/2 9 8 1/2 7 57329 Pi m 18251 m 190877 Pi m 881 m 1645 Pi m + --------------- - --------- + --------------- - ------ - ------------- 31457280 4324320 94371840 617760 1572864 6 1/2 5 4 1/2 3 2 100 m 6327 Pi m 2293 m 513 Pi m m + ------ - ------------- + ------- - ------------ + ---- 27027 2621440 720720 655360 1430 and in Maple input form: 1/11796480*Pi^(1/2)*m^17-1/308880*m^16+37/2097152*Pi^(1/2)*m^15-773/4324320*m^ 14+35807/94371840*Pi^(1/2)*m^13-7577/4324320*m^12+57329/31457280*Pi^(1/2)*m^11-\ 18251/4324320*m^10+190877/94371840*Pi^(1/2)*m^9-881/617760*m^8-1645/1572864*Pi^ (1/2)*m^7+100/27027*m^6-6327/2621440*Pi^(1/2)*m^5+2293/720720*m^4-513/655360*Pi ^(1/2)*m^3+1/1430*m^2 For the, 20, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[7, 6, 5, 4, 8, 3, 9, 2, 1, 10], [9, 8, 6, 4, 3, 2, 1, 5, 7, 10]}, {[7, 6, 5, 4, 8, 3, 9, 10, 2, 1], [10, 9, 6, 4, 3, 2, 1, 5, 7, 8]}, {[7, 6, 5, 4, 8, 9, 3, 2, 10, 1], [10, 8, 7, 4, 3, 2, 1, 5, 6, 9]}, {[7, 6, 5, 4, 8, 9, 3, 10, 2, 1], [10, 9, 7, 4, 3, 2, 1, 5, 6, 8]}, {[7, 6, 5, 8, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 3, 2, 1, 4, 6, 10]}, {[7, 6, 5, 8, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 3, 2, 1, 4, 6, 7]}, {[7, 6, 5, 8, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 3, 2, 1, 4, 5, 9]}, {[7, 6, 5, 8, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 3, 2, 1, 4, 5, 7]}, {[7, 6, 8, 5, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 4, 2, 1, 3, 7, 10]}, {[7, 6, 8, 5, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 4, 2, 1, 3, 7, 8]}, {[7, 6, 8, 5, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 4, 2, 1, 3, 6, 10]}, {[7, 6, 8, 5, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 4, 2, 1, 3, 6, 7]}, {[7, 6, 8, 9, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 2, 1, 3, 4, 8]}, {[7, 6, 8, 9, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 2, 1, 3, 4, 7]}, {[7, 8, 6, 5, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 4, 3, 1, 2, 6, 9]}, {[7, 8, 6, 5, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 4, 3, 1, 2, 6, 8]}, {[7, 8, 6, 5, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 3, 1, 2, 5, 9]}, {[7, 8, 6, 5, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 3, 1, 2, 5, 7]}, {[7, 8, 6, 9, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 3, 1, 2, 4, 8]}, {[7, 8, 6, 9, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 3, 1, 2, 4, 7]}, {[8, 6, 5, 4, 3, 7, 9, 2, 1, 10], [9, 8, 5, 4, 3, 2, 6, 1, 7, 10]}, {[8, 6, 5, 4, 3, 7, 9, 10, 2, 1], [10, 9, 5, 4, 3, 2, 6, 1, 7, 8]}, {[8, 6, 5, 4, 7, 9, 3, 2, 1, 10], [9, 8, 7, 4, 3, 2, 5, 1, 6, 10]}, {[8, 6, 5, 4, 7, 9, 10, 3, 2, 1], [10, 9, 8, 4, 3, 2, 5, 1, 6, 7]}, {[8, 6, 5, 7, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 3, 2, 4, 1, 7, 10]}, {[8, 6, 5, 7, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 3, 2, 4, 1, 7, 8]}, {[8, 6, 5, 7, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 3, 2, 4, 1, 6, 10]}, {[8, 6, 5, 7, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 3, 2, 4, 1, 6, 7]}, {[8, 6, 7, 5, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 4, 2, 3, 1, 6, 9]}, {[8, 6, 7, 5, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 4, 2, 3, 1, 6, 8]}, {[8, 6, 7, 5, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 2, 3, 1, 5, 9]}, {[8, 6, 7, 5, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 2, 3, 1, 5, 7]}, {[8, 6, 7, 9, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 2, 3, 1, 4, 8]}, {[8, 6, 7, 9, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 2, 3, 1, 4, 7]}, {[8, 7, 5, 4, 6, 3, 9, 2, 1, 10], [9, 8, 6, 4, 3, 5, 2, 1, 7, 10]}, {[8, 7, 5, 4, 6, 3, 9, 10, 2, 1], [10, 9, 6, 4, 3, 5, 2, 1, 7, 8]}, {[8, 7, 5, 4, 6, 9, 3, 2, 1, 10], [9, 8, 7, 4, 3, 5, 2, 1, 6, 10]}, {[8, 7, 5, 4, 6, 9, 10, 3, 2, 1], [10, 9, 8, 4, 3, 5, 2, 1, 6, 7]}, {[8, 7, 5, 6, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 3, 4, 2, 1, 6, 9]}, {[8, 7, 5, 6, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 3, 4, 2, 1, 6, 8]}, {[8, 7, 5, 6, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 3, 4, 2, 1, 5, 9]}, {[8, 7, 5, 6, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 3, 4, 2, 1, 5, 7]}, {[8, 7, 6, 4, 3, 5, 9, 2, 1, 10], [9, 8, 5, 4, 6, 3, 2, 1, 7, 10]}, {[8, 7, 6, 4, 3, 5, 9, 10, 2, 1], [10, 9, 5, 4, 6, 3, 2, 1, 7, 8]}, {[8, 7, 6, 4, 5, 9, 3, 2, 10, 1], [10, 8, 7, 4, 5, 3, 2, 1, 6, 9]}, {[8, 7, 6, 4, 5, 9, 3, 10, 2, 1], [10, 9, 7, 4, 5, 3, 2, 1, 6, 8]}, {[8, 7, 6, 5, 9, 3, 2, 1, 4, 10], [8, 7, 6, 9, 4, 3, 2, 1, 5, 10]}, {[8, 7, 6, 5, 9, 3, 2, 4, 1, 10], [9, 7, 6, 8, 4, 3, 2, 1, 5, 10]}, {[8, 7, 6, 5, 9, 3, 4, 2, 10, 1], [10, 8, 6, 7, 4, 3, 2, 1, 5, 9]}, {[8, 7, 6, 5, 9, 3, 4, 10, 2, 1], [10, 9, 6, 7, 4, 3, 2, 1, 5, 8]}, {[8, 7, 6, 5, 9, 4, 2, 1, 3, 10], [8, 7, 9, 6, 4, 3, 2, 1, 5, 10]}, {[8, 7, 6, 5, 9, 4, 2, 3, 10, 1], [10, 7, 8, 6, 4, 3, 2, 1, 5, 9]}, {[8, 7, 6, 5, 9, 4, 3, 10, 1, 2], [9, 10, 7, 6, 4, 3, 2, 1, 5, 8]}, {[8, 7, 6, 5, 9, 4, 10, 2, 3, 1], [10, 8, 9, 6, 4, 3, 2, 1, 5, 7]}, {[8, 7, 6, 5, 9, 4, 10, 3, 1, 2], [9, 10, 8, 6, 4, 3, 2, 1, 5, 7]}, {[8, 7, 6, 5, 9, 10, 3, 2, 1, 4], [9, 8, 7, 10, 4, 3, 2, 1, 5, 6]}, {[8, 7, 6, 5, 9, 10, 3, 2, 4, 1], [10, 8, 7, 9, 4, 3, 2, 1, 5, 6]}, {[8, 7, 6, 5, 9, 10, 4, 2, 1, 3], [9, 8, 10, 7, 4, 3, 2, 1, 5, 6]}, {[8, 7, 6, 9, 4, 3, 5, 2, 1, 10], 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7, 8, 6, 9, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 4, 2, 3, 5, 1]}, {[10, 8, 5, 4, 3, 6, 7, 9, 2, 1], [10, 9, 5, 4, 3, 6, 7, 2, 8, 1]}, {[10, 8, 5, 4, 6, 7, 3, 2, 9, 1], [10, 8, 7, 4, 3, 5, 6, 2, 9, 1]}, {[10, 8, 5, 4, 6, 7, 3, 9, 2, 1], [10, 9, 7, 4, 3, 5, 6, 2, 8, 1]}, {[10, 8, 5, 6, 4, 3, 7, 9, 2, 1], [10, 9, 6, 5, 3, 4, 7, 2, 8, 1]}, {[10, 8, 5, 6, 4, 7, 3, 2, 9, 1], [10, 8, 7, 5, 3, 4, 6, 2, 9, 1]}, {[10, 8, 5, 6, 4, 7, 3, 9, 2, 1], [10, 9, 7, 5, 3, 4, 6, 2, 8, 1]}, {[10, 8, 6, 4, 5, 3, 7, 9, 2, 1], [10, 9, 6, 4, 5, 3, 7, 2, 8, 1]}, {[10, 8, 6, 4, 5, 7, 3, 2, 9, 1], [10, 8, 7, 4, 5, 3, 6, 2, 9, 1]}, {[10, 8, 6, 4, 5, 7, 3, 9, 2, 1], [10, 9, 7, 4, 5, 3, 6, 2, 8, 1]}, {[10, 8, 6, 5, 3, 4, 7, 9, 2, 1], [10, 9, 5, 6, 4, 3, 7, 2, 8, 1]}, {[10, 8, 6, 5, 4, 7, 9, 2, 3, 1], [10, 8, 9, 5, 4, 3, 6, 2, 7, 1]}, {[10, 8, 6, 5, 7, 3, 4, 2, 9, 1], [10, 8, 6, 7, 4, 3, 5, 2, 9, 1]}, {[10, 8, 6, 5, 7, 3, 4, 9, 2, 1], [10, 9, 6, 7, 4, 3, 5, 2, 8, 1]}, {[10, 8, 6, 5, 7, 4, 9, 2, 3, 1], [10, 8, 9, 6, 4, 3, 5, 2, 7, 1]}, {[10, 8, 6, 7, 4, 3, 5, 9, 2, 1], [10, 9, 6, 5, 7, 3, 4, 2, 8, 1]}, {[10, 8, 6, 7, 5, 9, 3, 2, 4, 1], [10, 8, 7, 9, 5, 3, 4, 2, 6, 1]}, {[10, 8, 6, 7, 9, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 3, 4, 2, 5, 1]}, {[10, 8, 7, 4, 3, 5, 6, 9, 2, 1], [10, 9, 5, 4, 6, 7, 3, 2, 8, 1]}, {[10, 8, 7, 4, 5, 3, 6, 9, 2, 1], [10, 9, 6, 4, 5, 7, 3, 2, 8, 1]}, {[10, 8, 7, 5, 3, 4, 6, 9, 2, 1], [10, 9, 5, 6, 4, 7, 3, 2, 8, 1]}, {[10, 8, 7, 5, 4, 6, 9, 2, 3, 1], [10, 8, 9, 5, 4, 6, 3, 2, 7, 1]}, {[10, 8, 7, 5, 6, 9, 3, 2, 4, 1], [10, 8, 7, 9, 4, 5, 3, 2, 6, 1]}, { [7, 6, 5, 4, 8, 3, 2, 9, 1, 10], [7, 6, 5, 4, 8, 3, 2, 9, 10, 1], [9, 7, 6, 4, 3, 2, 1, 5, 8, 10], [10, 7, 6, 4, 3, 2, 1, 5, 8, 9]}, { [7, 6, 5, 8, 4, 3, 2, 9, 1, 10], [7, 6, 5, 8, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 3, 2, 1, 4, 8, 10], [10, 7, 6, 5, 3, 2, 1, 4, 8, 9]}, { [8, 6, 5, 4, 3, 7, 2, 9, 1, 10], [8, 6, 5, 4, 3, 7, 2, 9, 10, 1], [9, 7, 5, 4, 3, 2, 6, 1, 8, 10], [10, 7, 5, 4, 3, 2, 6, 1, 8, 9]}, { [8, 6, 5, 4, 7, 3, 2, 9, 1, 10], [8, 6, 5, 4, 7, 3, 2, 9, 10, 1], [9, 7, 6, 4, 3, 2, 5, 1, 8, 10], [10, 7, 6, 4, 3, 2, 5, 1, 8, 9]}, { [8, 7, 5, 4, 3, 2, 6, 9, 1, 10], [8, 7, 5, 4, 3, 2, 6, 9, 10, 1], [9, 6, 5, 4, 3, 7, 2, 1, 8, 10], [10, 6, 5, 4, 3, 7, 2, 1, 8, 9]}, { [8, 7, 5, 4, 3, 6, 2, 9, 1, 10], [8, 7, 5, 4, 3, 6, 2, 9, 10, 1], [9, 7, 5, 4, 3, 6, 2, 1, 8, 10], [10, 7, 5, 4, 3, 6, 2, 1, 8, 9]}, { [8, 7, 6, 4, 3, 2, 5, 9, 1, 10], [8, 7, 6, 4, 3, 2, 5, 9, 10, 1], [9, 6, 5, 4, 7, 3, 2, 1, 8, 10], [10, 6, 5, 4, 7, 3, 2, 1, 8, 9]}} is given by the following expression / 2347 3961 2 661 3 3067 4 3233 5 149 6 |- ------- n - ------- n + ------ n + ------- n + -------- n + -------- n \ 1720320 2949120 589824 2359296 11796480 11796480 7\ n / 41 3313 2 137 3 2753 4 + 1/16515072 n | 4 + |----- n + ------ n + ----- n - ------ n / \30030 720720 45045 864864 6163 5 6103 6 7 8\ - ------- n - ------- n - 3/22880 n - 1/432432 n | C(n) 1441440 4324320 / and in Maple input form: (-2347/1720320*n-3961/2949120*n^2+661/589824*n^3+3067/2359296*n^4+3233/11796480 *n^5+149/11796480*n^6+1/16515072*n^7)*4^n+(41/30030*n+3313/720720*n^2+137/45045 *n^3-2753/864864*n^4-6163/1441440*n^5-6103/4324320*n^6-3/22880*n^7-1/432432*n^8 )*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 17 16 1/2 15 14 1/2 13 12 Pi m m 8389 Pi m 3 m 5441 Pi m 6103 m --------- - ------ + -------------- - ----- + -------------- - -------- 16515072 432432 660602880 22880 18874368 4324320 1/2 11 10 1/2 9 8 1/2 7 151777 Pi m 6163 m 48755 Pi m 2753 m 1943 Pi m + ---------------- - -------- + -------------- - ------- - ------------- 94371840 1441440 18874368 864864 23592960 6 1/2 5 4 1/2 3 2 137 m 31657 Pi m 3313 m 7041 Pi m 41 m + ------ - -------------- + ------- - ------------- + ----- 45045 11010048 720720 4587520 30030 and in Maple input form: 1/16515072*Pi^(1/2)*m^17-1/432432*m^16+8389/660602880*Pi^(1/2)*m^15-3/22880*m^ 14+5441/18874368*Pi^(1/2)*m^13-6103/4324320*m^12+151777/94371840*Pi^(1/2)*m^11-\ 6163/1441440*m^10+48755/18874368*Pi^(1/2)*m^9-2753/864864*m^8-1943/23592960*Pi^ (1/2)*m^7+137/45045*m^6-31657/11010048*Pi^(1/2)*m^5+3313/720720*m^4-7041/ 4587520*Pi^(1/2)*m^3+41/30030*m^2 For the, 21, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[8, 7, 6, 9, 5, 3, 2, 1, 4, 10]}, {[9, 7, 5, 4, 3, 6, 2, 8, 1, 10]}, {[9, 8, 7, 10, 5, 6, 3, 2, 1, 4]}, {[10, 7, 5, 4, 3, 6, 2, 8, 9, 1]}, {[10, 8, 5, 4, 3, 6, 7, 2, 9, 1]}, {[10, 8, 6, 4, 5, 3, 7, 2, 9, 1]}, {[7, 6, 5, 8, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 3, 2, 1, 4, 7, 10]}, {[7, 6, 5, 8, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 3, 2, 1, 4, 7, 8]}, {[7, 6, 5, 8, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 3, 2, 1, 4, 5, 8]}, {[7, 8, 6, 5, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 3, 1, 2, 5, 8]}, {[8, 6, 5, 4, 7, 3, 9, 2, 1, 10], [9, 8, 6, 4, 3, 2, 5, 1, 7, 10]}, {[8, 6, 5, 4, 7, 3, 9, 10, 2, 1], [10, 9, 6, 4, 3, 2, 5, 1, 7, 8]}, {[8, 6, 7, 5, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 2, 3, 1, 5, 8]}, {[8, 7, 5, 4, 3, 6, 9, 2, 1, 10], [9, 8, 5, 4, 3, 6, 2, 1, 7, 10]}, {[8, 7, 5, 4, 3, 6, 9, 10, 2, 1], [10, 9, 5, 4, 3, 6, 2, 1, 7, 8]}, {[8, 7, 5, 6, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 3, 4, 2, 1, 5, 8]}, {[8, 7, 6, 9, 4, 3, 2, 5, 1, 10], [9, 7, 6, 5, 8, 3, 2, 1, 4, 10]}, {[8, 7, 6, 9, 4, 5, 3, 10, 2, 1], [10, 9, 7, 5, 6, 3, 2, 1, 4, 8]}, {[8, 7, 6, 9, 5, 3, 4, 10, 2, 1], [10, 9, 6, 7, 5, 3, 2, 1, 4, 8]}, {[8, 7, 6, 9, 5, 4, 10, 2, 3, 1], [10, 8, 9, 6, 5, 3, 2, 1, 4, 7]}, {[8, 7, 6, 9, 5, 4, 10, 3, 1, 2], [9, 10, 8, 6, 5, 3, 2, 1, 4, 7]}, {[8, 7, 6, 9, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 3, 2, 1, 4, 5]}, {[8, 7, 6, 9, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 3, 2, 1, 4, 5]}, {[8, 9, 6, 5, 4, 7, 3, 10, 2, 1], [10, 9, 7, 5, 4, 3, 6, 1, 2, 8]}, {[8, 9, 7, 5, 4, 3, 6, 10, 2, 1], [10, 9, 6, 5, 4, 7, 3, 1, 2, 8]}, {[8, 9, 7, 6, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 4, 3, 1, 2, 5]}, {[8, 9, 7, 6, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 4, 3, 1, 2, 5]}, {[9, 6, 5, 4, 7, 3, 2, 8, 1, 10], [9, 7, 6, 4, 3, 2, 5, 8, 1, 10]}, {[9, 6, 5, 4, 7, 8, 3, 10, 2, 1], [10, 9, 7, 4, 3, 2, 5, 6, 1, 8]}, {[9, 6, 7, 5, 4, 8, 3, 10, 2, 1], [10, 9, 7, 5, 4, 2, 3, 6, 1, 8]}, {[9, 7, 5, 6, 4, 8, 3, 10, 2, 1], [10, 9, 7, 5, 3, 4, 2, 6, 1, 8]}, {[9, 7, 6, 4, 5, 8, 3, 10, 2, 1], [10, 9, 7, 4, 5, 3, 2, 6, 1, 8]}, {[9, 7, 6, 5, 8, 3, 4, 10, 2, 1], [10, 9, 6, 7, 4, 3, 2, 5, 1, 8]}, {[9, 7, 6, 5, 8, 4, 10, 2, 3, 1], [10, 8, 9, 6, 4, 3, 2, 5, 1, 7]}, {[9, 7, 6, 5, 8, 4, 10, 3, 1, 2], [9, 10, 8, 6, 4, 3, 2, 5, 1, 7]}, {[9, 7, 8, 5, 4, 3, 6, 10, 2, 1], [10, 9, 6, 5, 4, 7, 2, 3, 1, 8]}, {[9, 7, 8, 6, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 4, 2, 3, 1, 5]}, {[9, 7, 8, 6, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 4, 2, 3, 1, 5]}, {[9, 8, 5, 4, 3, 6, 7, 10, 2, 1], [10, 9, 5, 4, 3, 6, 7, 2, 1, 8]}, {[9, 8, 5, 6, 4, 3, 7, 10, 2, 1], [10, 9, 6, 5, 3, 4, 7, 2, 1, 8]}, {[9, 8, 6, 4, 5, 3, 7, 10, 2, 1], [10, 9, 6, 4, 5, 3, 7, 2, 1, 8]}, {[9, 8, 6, 5, 3, 4, 7, 10, 2, 1], [10, 9, 5, 6, 4, 3, 7, 2, 1, 8]}, {[9, 8, 6, 5, 4, 7, 10, 2, 3, 1], [10, 8, 9, 5, 4, 3, 6, 2, 1, 7]}, {[9, 8, 6, 5, 4, 7, 10, 3, 1, 2], [9, 10, 8, 5, 4, 3, 6, 2, 1, 7]}, {[9, 8, 6, 7, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 3, 4, 2, 1, 5]}, {[9, 8, 6, 7, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 3, 4, 2, 1, 5]}, {[9, 8, 7, 10, 4, 3, 2, 5, 6, 1], [10, 7, 6, 5, 8, 9, 3, 2, 1, 4]}, {[9, 8, 7, 10, 4, 5, 3, 2, 6, 1], [10, 8, 7, 5, 6, 9, 3, 2, 1, 4]}, {[9, 8, 7, 10, 5, 3, 4, 2, 6, 1], [10, 8, 6, 7, 5, 9, 3, 2, 1, 4]}, {[9, 8, 7, 10, 5, 4, 2, 3, 6, 1], [10, 7, 8, 6, 5, 9, 3, 2, 1, 4]}, {[9, 8, 7, 10, 5, 4, 3, 6, 1, 2], [9, 10, 7, 6, 5, 8, 3, 2, 1, 4]}, {[9, 10, 6, 5, 4, 7, 3, 2, 8, 1], [10, 8, 7, 5, 4, 3, 6, 9, 1, 2]}, {[9, 10, 7, 5, 4, 3, 6, 2, 8, 1], [10, 8, 6, 5, 4, 7, 3, 9, 1, 2]}, {[9, 10, 7, 6, 4, 3, 2, 5, 8, 1], [10, 7, 6, 5, 8, 4, 3, 9, 1, 2]}, {[10, 6, 5, 4, 7, 3, 2, 8, 9, 1], [10, 7, 6, 4, 3, 2, 5, 8, 9, 1]}, {[10, 6, 5, 4, 7, 8, 3, 2, 9, 1], [10, 8, 7, 4, 3, 2, 5, 6, 9, 1]}, {[10, 6, 7, 5, 4, 8, 3, 2, 9, 1], [10, 8, 7, 5, 4, 2, 3, 6, 9, 1]}, {[10, 7, 5, 6, 4, 8, 3, 2, 9, 1], [10, 8, 7, 5, 3, 4, 2, 6, 9, 1]}, {[10, 7, 6, 4, 5, 8, 3, 2, 9, 1], [10, 8, 7, 4, 5, 3, 2, 6, 9, 1]}, {[10, 7, 6, 5, 8, 3, 4, 2, 9, 1], [10, 8, 6, 7, 4, 3, 2, 5, 9, 1]}, {[10, 7, 6, 5, 8, 4, 2, 3, 9, 1], [10, 7, 8, 6, 4, 3, 2, 5, 9, 1]}, {[10, 7, 8, 5, 4, 3, 6, 2, 9, 1], [10, 8, 6, 5, 4, 7, 2, 3, 9, 1]}, {[10, 8, 5, 6, 4, 3, 7, 2, 9, 1], [10, 8, 6, 5, 3, 4, 7, 2, 9, 1]}} is given by the following expression / 487 41 2 4327 3 61 4 341 5 6 |- ------ n - ----- n + ------- n + ----- n + ------- n + 1/98304 n \ 286720 32768 2949120 49152 1474560 7\ n / 17 3823 2 733 3 4391 4 + 1/20643840 n | 4 + |----- n + ------ n + ------ n - ------- n / \10010 720720 270270 1081080 1163 5 2683 6 29 7 8\ - ------ n - ------- n - ------ n - 1/540540 n | C(n) 270270 2162160 270270 / and in Maple input form: (-487/286720*n-41/32768*n^2+4327/2949120*n^3+61/49152*n^4+341/1474560*n^5+1/ 98304*n^6+1/20643840*n^7)*4^n+(17/10010*n+3823/720720*n^2+733/270270*n^3-4391/ 1081080*n^4-1163/270270*n^5-2683/2162160*n^6-29/270270*n^7-1/540540*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 17 16 1/2 15 14 1/2 13 12 Pi m m 563 Pi m 29 m 2863 Pi m 2683 m --------- - ------ + ------------- - ------ + -------------- - -------- 20643840 540540 55050240 270270 11796480 2162160 1/2 11 10 1/2 9 8 1/2 7 5903 Pi m 1163 m 16889 Pi m 4391 m 1047 Pi m + -------------- - -------- + -------------- - ------- + ------------- 3932160 270270 5898240 1081080 2621440 6 1/2 5 4 1/2 3 2 733 m 28499 Pi m 3823 m 4383 Pi m 17 m + ------ - -------------- + ------- - ------------- + ----- 270270 9175040 720720 2293760 10010 and in Maple input form: 1/20643840*Pi^(1/2)*m^17-1/540540*m^16+563/55050240*Pi^(1/2)*m^15-29/270270*m^ 14+2863/11796480*Pi^(1/2)*m^13-2683/2162160*m^12+5903/3932160*Pi^(1/2)*m^11-\ 1163/270270*m^10+16889/5898240*Pi^(1/2)*m^9-4391/1081080*m^8+1047/2621440*Pi^(1 /2)*m^7+733/270270*m^6-28499/9175040*Pi^(1/2)*m^5+3823/720720*m^4-4383/2293760* Pi^(1/2)*m^3+17/10010*m^2 For the, 22, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[7, 6, 5, 4, 8, 3, 9, 2, 10, 1], [10, 8, 6, 4, 3, 2, 1, 5, 7, 9]}, {[7, 6, 8, 5, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 4, 2, 1, 3, 7, 9]}, {[7, 6, 8, 5, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 2, 1, 3, 5, 9]}, {[7, 6, 8, 5, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 2, 1, 3, 5, 7]}, {[8, 6, 5, 4, 3, 7, 9, 2, 10, 1], [10, 8, 5, 4, 3, 2, 6, 1, 7, 9]}, {[8, 6, 5, 7, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 3, 2, 4, 1, 7, 9]}, {[8, 6, 5, 7, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 3, 2, 4, 1, 5, 9]}, {[8, 6, 5, 7, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 3, 2, 4, 1, 5, 7]}, {[8, 7, 5, 4, 6, 3, 9, 2, 10, 1], [10, 8, 6, 4, 3, 5, 2, 1, 7, 9]}, {[8, 7, 6, 4, 3, 5, 9, 2, 10, 1], [10, 8, 5, 4, 6, 3, 2, 1, 7, 9]}, {[8, 7, 6, 5, 9, 3, 2, 4, 10, 1], [10, 7, 6, 8, 4, 3, 2, 1, 5, 9]}, {[8, 7, 6, 5, 9, 4, 10, 2, 1, 3], [9, 8, 10, 6, 4, 3, 2, 1, 5, 7]}, {[8, 7, 9, 5, 4, 3, 2, 6, 10, 1], [10, 7, 6, 5, 4, 8, 2, 1, 3, 9]}, {[8, 7, 9, 5, 4, 6, 3, 2, 10, 1], [10, 8, 7, 5, 4, 6, 2, 1, 3, 9]}, {[8, 7, 9, 5, 4, 6, 10, 3, 2, 1], [10, 9, 8, 5, 4, 6, 2, 1, 3, 7]}, {[8, 7, 9, 6, 4, 3, 5, 2, 10, 1], [10, 8, 6, 5, 7, 4, 2, 1, 3, 9]}, {[8, 7, 9, 6, 5, 3, 2, 4, 10, 1], [10, 7, 6, 8, 5, 4, 2, 1, 3, 9]}, {[8, 7, 9, 6, 5, 4, 10, 2, 1, 3], [9, 8, 10, 6, 5, 4, 2, 1, 3, 7]}, {[8, 7, 9, 6, 10, 4, 3, 2, 1, 5], [9, 8, 7, 6, 10, 4, 2, 1, 3, 5]}, {[8, 7, 9, 6, 10, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 4, 2, 1, 3, 5]}, {[8, 7, 9, 6, 10, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 4, 2, 1, 3, 5]}, {[8, 7, 9, 6, 10, 5, 4, 2, 1, 3], [9, 8, 10, 7, 6, 4, 2, 1, 3, 5]}, {[9, 6, 5, 4, 3, 7, 2, 8, 10, 1], [10, 7, 5, 4, 3, 2, 6, 8, 1, 9]}, {[9, 6, 5, 7, 4, 3, 2, 8, 10, 1], [10, 7, 6, 5, 3, 2, 4, 8, 1, 9]}, {[9, 6, 5, 7, 4, 8, 3, 2, 10, 1], [10, 8, 7, 5, 3, 2, 4, 6, 1, 9]}, {[9, 6, 5, 7, 4, 8, 10, 3, 2, 1], [10, 9, 8, 5, 3, 2, 4, 6, 1, 7]}, {[9, 7, 5, 4, 3, 2, 6, 8, 10, 1], [10, 6, 5, 4, 3, 7, 2, 8, 1, 9]}, {[9, 7, 5, 4, 6, 3, 2, 8, 10, 1], [10, 7, 6, 4, 3, 5, 2, 8, 1, 9]}, {[9, 7, 5, 4, 6, 8, 3, 2, 10, 1], [10, 8, 7, 4, 3, 5, 2, 6, 1, 9]}, {[9, 7, 5, 4, 6, 8, 10, 3, 2, 1], [10, 9, 8, 4, 3, 5, 2, 6, 1, 7]}, {[9, 7, 6, 4, 3, 5, 2, 8, 10, 1], [10, 7, 5, 4, 6, 3, 2, 8, 1, 9]}, {[9, 7, 6, 5, 3, 2, 4, 8, 10, 1], [10, 6, 5, 7, 4, 3, 2, 8, 1, 9]}, {[9, 7, 6, 5, 4, 8, 10, 2, 1, 3], [9, 8, 10, 5, 4, 3, 2, 6, 1, 7]}, {[9, 7, 6, 8, 4, 3, 5, 2, 10, 1], [10, 8, 6, 5, 7, 3, 2, 4, 1, 9]}, {[9, 7, 6, 8, 5, 3, 2, 4, 10, 1], [10, 7, 6, 8, 5, 3, 2, 4, 1, 9]}, {[9, 7, 6, 8, 5, 4, 10, 2, 1, 3], [9, 8, 10, 6, 5, 3, 2, 4, 1, 7]}, {[9, 7, 6, 8, 10, 4, 3, 2, 1, 5], [9, 8, 7, 6, 10, 3, 2, 4, 1, 5]}, {[9, 7, 6, 8, 10, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 3, 2, 4, 1, 5]}, {[9, 7, 6, 8, 10, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 3, 2, 4, 1, 5]}, {[9, 7, 6, 8, 10, 5, 4, 2, 1, 3], [9, 8, 10, 7, 6, 3, 2, 4, 1, 5]}, {[9, 8, 5, 4, 6, 3, 7, 2, 10, 1], [10, 8, 6, 4, 3, 5, 7, 2, 1, 9]}, {[9, 8, 6, 4, 3, 5, 7, 2, 10, 1], [10, 8, 5, 4, 6, 3, 7, 2, 1, 9]}, {[9, 8, 6, 5, 7, 3, 2, 4, 10, 1], [10, 7, 6, 8, 4, 3, 5, 2, 1, 9]}, {[9, 8, 6, 5, 7, 4, 10, 2, 1, 3], [9, 8, 10, 6, 4, 3, 5, 2, 1, 7]}, {[9, 8, 7, 4, 3, 5, 2, 6, 10, 1], [10, 7, 5, 4, 6, 8, 3, 2, 1, 9]}, {[9, 8, 7, 5, 3, 2, 4, 6, 10, 1], [10, 6, 5, 7, 4, 8, 3, 2, 1, 9]}, {[9, 8, 7, 5, 4, 6, 10, 2, 1, 3], [9, 8, 10, 5, 4, 6, 3, 2, 1, 7]}, {[9, 8, 10, 5, 4, 6, 3, 7, 2, 1], [10, 9, 7, 5, 4, 6, 8, 2, 1, 3]}, {[9, 8, 10, 6, 4, 3, 5, 7, 2, 1], [10, 9, 6, 5, 7, 4, 8, 2, 1, 3]}, {[9, 8, 10, 6, 5, 7, 3, 2, 4, 1], [10, 8, 7, 9, 5, 4, 6, 2, 1, 3]}, {[9, 8, 10, 6, 5, 7, 4, 2, 1, 3], [9, 8, 10, 7, 5, 4, 6, 2, 1, 3]}, {[9, 8, 10, 7, 4, 3, 5, 2, 6, 1], [10, 8, 6, 5, 7, 9, 4, 2, 1, 3]}, {[9, 8, 10, 7, 5, 3, 2, 4, 6, 1], [10, 7, 6, 8, 5, 9, 4, 2, 1, 3]}, {[10, 6, 5, 7, 4, 8, 3, 9, 2, 1], [10, 9, 7, 5, 3, 2, 4, 6, 8, 1]}, {[10, 7, 5, 4, 6, 8, 3, 9, 2, 1], [10, 9, 7, 4, 3, 5, 2, 6, 8, 1]}, {[10, 7, 6, 8, 4, 3, 5, 9, 2, 1], [10, 9, 6, 5, 7, 3, 2, 4, 8, 1]}, {[10, 7, 6, 8, 5, 9, 3, 2, 4, 1], [10, 8, 7, 9, 5, 3, 2, 4, 6, 1]}, {[10, 8, 5, 4, 6, 3, 7, 9, 2, 1], [10, 9, 6, 4, 3, 5, 7, 2, 8, 1]}, {[10, 8, 6, 4, 3, 5, 7, 9, 2, 1], [10, 9, 5, 4, 6, 3, 7, 2, 8, 1]}, {[10, 8, 6, 5, 7, 9, 3, 2, 4, 1], [10, 8, 7, 9, 4, 3, 5, 2, 6, 1]}} is given by the following expression / 481 739 2 353 3 109 4 1241 5 109 6 |------- n + ------- n - ------- n - ------- n + -------- n + -------- n \3440640 5898240 1179648 4718592 23592960 23592960 7\ n / 347 2 25 3 22081 4 + 1/33030144 n | 4 + |-2/15015 n - ------ n - ------ n + -------- n / \ 720720 384384 34594560 17 5 6 31 7 8\ + ----- n - 7/44928 n - ------ n - 1/988416 n | C(n) 72072 823680 / and in Maple input form: (481/3440640*n+739/5898240*n^2-353/1179648*n^3-109/4718592*n^4+1241/23592960*n^ 5+109/23592960*n^6+1/33030144*n^7)*4^n+(-2/15015*n-347/720720*n^2-25/384384*n^3 +22081/34594560*n^4+17/72072*n^5-7/44928*n^6-31/823680*n^7-1/988416*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 17 16 1/2 15 14 1/2 13 12 Pi m m 6149 Pi m 31 m 10909 Pi m 7 m --------- - ------ + -------------- - ------ + --------------- - ----- 33030144 988416 1321205760 823680 188743680 44928 1/2 11 10 1/2 9 8 1/2 7 6809 Pi m 17 m 12277 Pi m 22081 m 9973 Pi m + -------------- + ------ - -------------- + -------- - ------------- 188743680 72072 37748736 34594560 47185920 6 1/2 5 4 1/2 3 2 25 m 30911 Pi m 347 m 1443 Pi m 2 m - ------ + -------------- - ------ + ------------- - ----- 384384 110100480 720720 9175040 15015 and in Maple input form: 1/33030144*Pi^(1/2)*m^17-1/988416*m^16+6149/1321205760*Pi^(1/2)*m^15-31/823680* m^14+10909/188743680*Pi^(1/2)*m^13-7/44928*m^12+6809/188743680*Pi^(1/2)*m^11+17 /72072*m^10-12277/37748736*Pi^(1/2)*m^9+22081/34594560*m^8-9973/47185920*Pi^(1/ 2)*m^7-25/384384*m^6+30911/110100480*Pi^(1/2)*m^5-347/720720*m^4+1443/9175040* Pi^(1/2)*m^3-2/15015*m^2 For the, 23, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[9, 8, 10, 6, 5, 4, 7, 2, 1, 3]}, {[10, 7, 6, 8, 5, 3, 2, 4, 9, 1]}, {[7, 6, 5, 8, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 3, 2, 1, 4, 7, 9]}, {[7, 6, 5, 8, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 3, 2, 1, 4, 6, 9]}, {[7, 6, 5, 8, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 3, 2, 1, 4, 6, 8]}, {[7, 6, 8, 5, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 4, 2, 1, 3, 6, 9]}, {[7, 6, 8, 5, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 4, 2, 1, 3, 6, 8]}, {[7, 6, 8, 5, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 2, 1, 3, 5, 8]}, {[8, 6, 5, 4, 7, 3, 9, 2, 10, 1], [10, 8, 6, 4, 3, 2, 5, 1, 7, 9]}, {[8, 6, 5, 4, 7, 9, 3, 2, 10, 1], [10, 8, 7, 4, 3, 2, 5, 1, 6, 9]}, {[8, 6, 5, 4, 7, 9, 3, 10, 2, 1], [10, 9, 7, 4, 3, 2, 5, 1, 6, 8]}, {[8, 6, 5, 7, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 3, 2, 4, 1, 6, 9]}, {[8, 6, 5, 7, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 3, 2, 4, 1, 6, 8]}, {[8, 6, 5, 7, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 3, 2, 4, 1, 5, 8]}, {[8, 7, 5, 4, 3, 6, 9, 2, 10, 1], [10, 8, 5, 4, 3, 6, 2, 1, 7, 9]}, {[8, 7, 5, 4, 6, 9, 3, 2, 10, 1], [10, 8, 7, 4, 3, 5, 2, 1, 6, 9]}, {[8, 7, 5, 4, 6, 9, 3, 10, 2, 1], [10, 9, 7, 4, 3, 5, 2, 1, 6, 8]}, {[8, 7, 6, 9, 4, 3, 2, 5, 10, 1], [10, 7, 6, 5, 8, 3, 2, 1, 4, 9]}, {[8, 7, 6, 9, 4, 3, 5, 2, 10, 1], [10, 8, 6, 5, 7, 3, 2, 1, 4, 9]}, {[8, 7, 6, 9, 4, 3, 5, 10, 2, 1], [10, 9, 6, 5, 7, 3, 2, 1, 4, 8]}, {[8, 7, 6, 9, 5, 3, 2, 4, 10, 1], [10, 7, 6, 8, 5, 3, 2, 1, 4, 9]}, {[8, 7, 6, 9, 5, 4, 10, 2, 1, 3], [9, 8, 10, 6, 5, 3, 2, 1, 4, 7]}, {[8, 7, 6, 9, 5, 10, 3, 2, 1, 4], [9, 8, 7, 10, 5, 3, 2, 1, 4, 6]}, {[8, 7, 6, 9, 5, 10, 3, 2, 4, 1], [10, 8, 7, 9, 5, 3, 2, 1, 4, 6]}, {[8, 7, 6, 9, 5, 10, 4, 2, 1, 3], [9, 8, 10, 7, 5, 3, 2, 1, 4, 6]}, {[8, 7, 9, 5, 4, 3, 6, 2, 10, 1], [10, 8, 6, 5, 4, 7, 2, 1, 3, 9]}, {[8, 7, 9, 5, 4, 3, 6, 10, 2, 1], [10, 9, 6, 5, 4, 7, 2, 1, 3, 8]}, {[8, 7, 9, 5, 4, 6, 3, 10, 2, 1], [10, 9, 7, 5, 4, 6, 2, 1, 3, 8]}, {[8, 7, 9, 6, 4, 3, 2, 5, 10, 1], [10, 7, 6, 5, 8, 4, 2, 1, 3, 9]}, {[8, 7, 9, 6, 4, 3, 5, 10, 2, 1], [10, 9, 6, 5, 7, 4, 2, 1, 3, 8]}, {[8, 7, 9, 6, 5, 10, 3, 2, 1, 4], [9, 8, 7, 10, 5, 4, 2, 1, 3, 6]}, {[8, 7, 9, 6, 5, 10, 3, 2, 4, 1], [10, 8, 7, 9, 5, 4, 2, 1, 3, 6]}, {[8, 7, 9, 6, 5, 10, 4, 2, 1, 3], [9, 8, 10, 7, 5, 4, 2, 1, 3, 6]}, {[8, 7, 9, 6, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 4, 2, 1, 3, 5]}, {[8, 7, 9, 6, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 4, 2, 1, 3, 5]}, {[9, 6, 5, 4, 7, 3, 2, 8, 10, 1], [10, 7, 6, 4, 3, 2, 5, 8, 1, 9]}, {[9, 6, 5, 4, 7, 3, 8, 2, 10, 1], [10, 8, 6, 4, 3, 2, 5, 7, 1, 9]}, {[9, 6, 5, 4, 7, 3, 8, 10, 2, 1], [10, 9, 6, 4, 3, 2, 5, 7, 1, 8]}, {[9, 6, 5, 7, 4, 3, 8, 2, 10, 1], [10, 8, 6, 5, 3, 2, 4, 7, 1, 9]}, {[9, 6, 5, 7, 4, 3, 8, 10, 2, 1], [10, 9, 6, 5, 3, 2, 4, 7, 1, 8]}, {[9, 6, 5, 7, 4, 8, 3, 10, 2, 1], [10, 9, 7, 5, 3, 2, 4, 6, 1, 8]}, {[9, 7, 5, 4, 3, 6, 2, 8, 10, 1], [10, 7, 5, 4, 3, 6, 2, 8, 1, 9]}, {[9, 7, 5, 4, 3, 6, 8, 2, 10, 1], [10, 8, 5, 4, 3, 6, 2, 7, 1, 9]}, {[9, 7, 5, 4, 3, 6, 8, 10, 2, 1], [10, 9, 5, 4, 3, 6, 2, 7, 1, 8]}, {[9, 7, 5, 4, 6, 3, 8, 2, 10, 1], [10, 8, 6, 4, 3, 5, 2, 7, 1, 9]}, {[9, 7, 5, 4, 6, 3, 8, 10, 2, 1], [10, 9, 6, 4, 3, 5, 2, 7, 1, 8]}, {[9, 7, 5, 4, 6, 8, 3, 10, 2, 1], [10, 9, 7, 4, 3, 5, 2, 6, 1, 8]}, {[9, 7, 6, 4, 3, 2, 5, 8, 10, 1], [10, 6, 5, 4, 7, 3, 2, 8, 1, 9]}, {[9, 7, 6, 4, 3, 5, 8, 2, 10, 1], [10, 8, 5, 4, 6, 3, 2, 7, 1, 9]}, {[9, 7, 6, 4, 3, 5, 8, 10, 2, 1], [10, 9, 5, 4, 6, 3, 2, 7, 1, 8]}, {[9, 7, 6, 5, 8, 3, 2, 4, 10, 1], [10, 7, 6, 8, 4, 3, 2, 5, 1, 9]}, {[9, 7, 6, 5, 8, 4, 10, 2, 1, 3], [9, 8, 10, 6, 4, 3, 2, 5, 1, 7]}, {[9, 7, 6, 5, 8, 10, 3, 2, 1, 4], [9, 8, 7, 10, 4, 3, 2, 5, 1, 6]}, {[9, 7, 6, 5, 8, 10, 3, 2, 4, 1], [10, 8, 7, 9, 4, 3, 2, 5, 1, 6]}, {[9, 7, 6, 5, 8, 10, 4, 2, 1, 3], [9, 8, 10, 7, 4, 3, 2, 5, 1, 6]}, {[9, 7, 6, 8, 4, 3, 2, 5, 10, 1], [10, 7, 6, 5, 8, 3, 2, 4, 1, 9]}, {[9, 7, 6, 8, 4, 3, 5, 10, 2, 1], [10, 9, 6, 5, 7, 3, 2, 4, 1, 8]}, {[9, 7, 6, 8, 5, 10, 3, 2, 1, 4], [9, 8, 7, 10, 5, 3, 2, 4, 1, 6]}, {[9, 7, 6, 8, 5, 10, 3, 2, 4, 1], [10, 8, 7, 9, 5, 3, 2, 4, 1, 6]}, {[9, 7, 6, 8, 5, 10, 4, 2, 1, 3], [9, 8, 10, 7, 5, 3, 2, 4, 1, 6]}, {[9, 7, 6, 8, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 3, 2, 4, 1, 5]}, {[9, 7, 6, 8, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 3, 2, 4, 1, 5]}, {[9, 8, 5, 4, 3, 6, 2, 7, 10, 1], [10, 7, 5, 4, 3, 6, 8, 2, 1, 9]}, {[9, 8, 5, 4, 6, 3, 2, 7, 10, 1], [10, 7, 6, 4, 3, 5, 8, 2, 1, 9]}, {[9, 8, 5, 4, 6, 3, 7, 10, 2, 1], [10, 9, 6, 4, 3, 5, 7, 2, 1, 8]}, {[9, 8, 6, 4, 3, 2, 5, 7, 10, 1], [10, 6, 5, 4, 7, 3, 8, 2, 1, 9]}, {[9, 8, 6, 4, 3, 5, 2, 7, 10, 1], [10, 7, 5, 4, 6, 3, 8, 2, 1, 9]}, {[9, 8, 6, 4, 3, 5, 7, 10, 2, 1], [10, 9, 5, 4, 6, 3, 7, 2, 1, 8]}, {[9, 8, 6, 5, 3, 2, 4, 7, 10, 1], [10, 6, 5, 7, 4, 3, 8, 2, 1, 9]}, {[9, 8, 6, 5, 4, 7, 10, 2, 1, 3], [9, 8, 10, 5, 4, 3, 6, 2, 1, 7]}, {[9, 8, 6, 5, 7, 10, 3, 2, 1, 4], [9, 8, 7, 10, 4, 3, 5, 2, 1, 6]}, {[9, 8, 6, 5, 7, 10, 3, 2, 4, 1], [10, 8, 7, 9, 4, 3, 5, 2, 1, 6]}, {[9, 8, 6, 5, 7, 10, 4, 2, 1, 3], [9, 8, 10, 7, 4, 3, 5, 2, 1, 6]}, {[9, 8, 7, 10, 4, 3, 5, 2, 6, 1], [10, 8, 6, 5, 7, 9, 3, 2, 1, 4]}, {[9, 8, 7, 10, 5, 3, 2, 4, 6, 1], [10, 7, 6, 8, 5, 9, 3, 2, 1, 4]}, {[9, 8, 7, 10, 5, 4, 6, 2, 1, 3], [9, 8, 10, 6, 5, 7, 3, 2, 1, 4]}, {[9, 8, 10, 5, 4, 3, 6, 2, 7, 1], [10, 8, 6, 5, 4, 7, 9, 2, 1, 3]}, {[9, 8, 10, 5, 4, 6, 3, 2, 7, 1], [10, 8, 7, 5, 4, 6, 9, 2, 1, 3]}, {[9, 8, 10, 6, 4, 3, 2, 5, 7, 1], [10, 7, 6, 5, 8, 4, 9, 2, 1, 3]}, {[9, 8, 10, 6, 4, 3, 5, 2, 7, 1], [10, 8, 6, 5, 7, 4, 9, 2, 1, 3]}, {[9, 8, 10, 6, 5, 3, 2, 4, 7, 1], [10, 7, 6, 8, 5, 4, 9, 2, 1, 3]}, {[10, 6, 5, 4, 7, 3, 8, 2, 9, 1], [10, 8, 6, 4, 3, 2, 5, 7, 9, 1]}, {[10, 6, 5, 7, 4, 3, 8, 2, 9, 1], [10, 8, 6, 5, 3, 2, 4, 7, 9, 1]}, {[10, 6, 5, 7, 4, 8, 3, 2, 9, 1], [10, 8, 7, 5, 3, 2, 4, 6, 9, 1]}, {[10, 7, 5, 4, 3, 6, 8, 2, 9, 1], [10, 8, 5, 4, 3, 6, 2, 7, 9, 1]}, {[10, 7, 5, 4, 6, 3, 8, 2, 9, 1], [10, 8, 6, 4, 3, 5, 2, 7, 9, 1]}, {[10, 7, 5, 4, 6, 8, 3, 2, 9, 1], [10, 8, 7, 4, 3, 5, 2, 6, 9, 1]}, {[10, 7, 6, 4, 3, 5, 8, 2, 9, 1], [10, 8, 5, 4, 6, 3, 2, 7, 9, 1]}, {[10, 7, 6, 5, 8, 3, 2, 4, 9, 1], [10, 7, 6, 8, 4, 3, 2, 5, 9, 1]}, {[10, 7, 6, 8, 4, 3, 5, 2, 9, 1], [10, 8, 6, 5, 7, 3, 2, 4, 9, 1]}, {[10, 8, 5, 4, 6, 3, 7, 2, 9, 1], [10, 8, 6, 4, 3, 5, 7, 2, 9, 1]}} is given by the following expression / 443 61 2 1793 3 4 137 5 11 6 |------- n - ------- n - ------- n + 5/294912 n + ------- n + ------- n \1720320 2949120 5898240 2949120 2949120 7\ n / 31 1711 2 3013 3 6491 4 + 1/41287680 n | 4 + |- ------ n - ------- n + -------- n + ------- n / \ 120120 2882880 17297280 8648640 199 5 193 6 7 8\ + ------- n - ------- n - 7/224640 n - 1/1235520 n | C(n) 1729728 1235520 / and in Maple input form: (443/1720320*n-61/2949120*n^2-1793/5898240*n^3+5/294912*n^4+137/2949120*n^5+11/ 2949120*n^6+1/41287680*n^7)*4^n+(-31/120120*n-1711/2882880*n^2+3013/17297280*n^ 3+6491/8648640*n^4+199/1729728*n^5-193/1235520*n^6-7/224640*n^7-1/1235520*n^8)* C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 17 16 1/2 15 14 1/2 13 12 Pi m m 1241 Pi m 7 m 239 Pi m 193 m --------- - ------- + -------------- - ------ + ------------- - ------- 41287680 1235520 330301440 224640 4718592 1235520 1/2 11 10 1/2 9 8 1/2 7 1633 Pi m 199 m 3361 Pi m 6491 m 17113 Pi m + -------------- + ------- - ------------- + ------- - -------------- 23592960 1729728 11796480 8648640 47185920 6 1/2 5 4 1/2 3 2 3013 m 2579 Pi m 1711 m 1329 Pi m 31 m + -------- + ------------- - ------- + ------------- - ------ 17297280 11010048 2882880 4587520 120120 and in Maple input form: 1/41287680*Pi^(1/2)*m^17-1/1235520*m^16+1241/330301440*Pi^(1/2)*m^15-7/224640*m ^14+239/4718592*Pi^(1/2)*m^13-193/1235520*m^12+1633/23592960*Pi^(1/2)*m^11+199/ 1729728*m^10-3361/11796480*Pi^(1/2)*m^9+6491/8648640*m^8-17113/47185920*Pi^(1/2 )*m^7+3013/17297280*m^6+2579/11010048*Pi^(1/2)*m^5-1711/2882880*m^4+1329/ 4587520*Pi^(1/2)*m^3-31/120120*m^2 For the, 24, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[6, 5, 4, 3, 2, 1, 7, 8, 9, 10]}, {[7, 8, 6, 5, 4, 3, 1, 2, 9, 10]}, {[8, 6, 7, 5, 4, 2, 3, 1, 9, 10]}, {[8, 7, 5, 6, 3, 4, 2, 1, 9, 10]}, {[8, 9, 10, 7, 6, 5, 4, 1, 2, 3]}, {[9, 10, 7, 8, 6, 5, 3, 4, 1, 2]}, {[9, 10, 8, 6, 7, 4, 5, 3, 1, 2]}, {[10, 7, 8, 9, 6, 5, 2, 3, 4, 1]}, {[10, 8, 9, 6, 7, 4, 5, 2, 3, 1]}, {[10, 9, 6, 7, 8, 3, 4, 5, 2, 1]}, {[6, 7, 5, 4, 3, 2, 1, 8, 9, 10], [7, 6, 5, 4, 3, 1, 2, 8, 9, 10]}, {[6, 7, 8, 5, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 4, 1, 2, 3, 9, 10]}, {[6, 7, 8, 9, 5, 4, 3, 2, 1, 10], [9, 8, 7, 6, 5, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 10, 5, 4, 3, 2, 1], [10, 9, 8, 7, 6, 1, 2, 3, 4, 5]}, {[7, 5, 6, 4, 3, 2, 1, 8, 9, 10], [7, 6, 5, 4, 2, 3, 1, 8, 9, 10]}, {[7, 6, 4, 5, 3, 2, 1, 8, 9, 10], [7, 6, 5, 3, 4, 2, 1, 8, 9, 10]}, {[7, 8, 5, 6, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 3, 4, 1, 2, 9, 10]}, {[7, 8, 6, 4, 5, 3, 2, 1, 9, 10], [8, 7, 6, 4, 5, 3, 1, 2, 9, 10]}, {[7, 8, 6, 5, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 4, 3, 1, 2, 9, 10]}, {[7, 8, 6, 5, 4, 2, 3, 1, 9, 10], [8, 6, 7, 5, 4, 3, 1, 2, 9, 10]}, {[7, 8, 9, 5, 6, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 5, 1, 2, 3, 10]}, {[7, 8, 9, 6, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 4, 1, 2, 3, 10]}, {[7, 8, 9, 6, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 4, 1, 2, 3, 10]}, {[7, 8, 9, 6, 5, 4, 2, 3, 1, 10], [9, 7, 8, 6, 5, 4, 1, 2, 3, 10]}, {[7, 8, 9, 6, 5, 4, 3, 1, 2, 10], [8, 9, 7, 6, 5, 4, 1, 2, 3, 10]}, {[7, 8, 9, 10, 5, 6, 4, 3, 2, 1], [10, 9, 8, 7, 5, 6, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 5, 1, 2, 3, 4]}, {[8, 5, 6, 7, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 2, 3, 4, 1, 9, 10]}, {[8, 6, 7, 4, 5, 3, 2, 1, 9, 10], [8, 7, 6, 4, 5, 2, 3, 1, 9, 10]}, {[8, 6, 7, 5, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 4, 2, 3, 1, 9, 10]}, {[8, 7, 4, 5, 6, 3, 2, 1, 9, 10], [8, 7, 6, 3, 4, 5, 2, 1, 9, 10]}, {[8, 9, 5, 6, 7, 4, 3, 2, 1, 10], [9, 8, 7, 6, 3, 4, 5, 1, 2, 10]}, {[8, 9, 6, 7, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 3, 4, 1, 2, 10]}, {[8, 9, 6, 7, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 3, 4, 1, 2, 10]}, {[8, 9, 6, 7, 5, 4, 2, 3, 1, 10], [9, 7, 8, 6, 5, 3, 4, 1, 2, 10]}, {[8, 9, 6, 7, 5, 4, 3, 1, 2, 10], [8, 9, 7, 6, 5, 3, 4, 1, 2, 10]}, {[8, 9, 7, 4, 5, 6, 3, 2, 1, 10], [9, 8, 7, 4, 5, 6, 3, 1, 2, 10]}, {[8, 9, 7, 5, 6, 3, 4, 2, 1, 10], [9, 8, 6, 7, 4, 5, 3, 1, 2, 10]}, {[8, 9, 7, 5, 6, 4, 2, 3, 1, 10], [9, 7, 8, 6, 4, 5, 3, 1, 2, 10]}, {[8, 9, 7, 5, 6, 4, 3, 1, 2, 10], [8, 9, 7, 6, 4, 5, 3, 1, 2, 10]}, {[8, 9, 7, 6, 3, 4, 5, 2, 1, 10], [9, 8, 5, 6, 7, 4, 3, 1, 2, 10]}, {[8, 9, 7, 6, 4, 5, 2, 3, 1, 10], [9, 7, 8, 5, 6, 4, 3, 1, 2, 10]}, {[8, 9, 7, 6, 5, 2, 3, 4, 1, 10], [9, 6, 7, 8, 5, 4, 3, 1, 2, 10]}, {[8, 9, 10, 5, 6, 7, 4, 3, 2, 1], [10, 9, 8, 7, 4, 5, 6, 1, 2, 3]}, {[8, 9, 10, 6, 7, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 4, 5, 1, 2, 3]}, {[8, 9, 10, 7, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 4, 1, 2, 3]}, {[8, 9, 10, 7, 5, 6, 3, 4, 2, 1], [10, 9, 7, 8, 5, 6, 4, 1, 2, 3]}, {[8, 9, 10, 7, 5, 6, 4, 2, 3, 1], [10, 8, 9, 7, 5, 6, 4, 1, 2, 3]}, {[8, 9, 10, 7, 5, 6, 4, 3, 1, 2], [9, 10, 8, 7, 5, 6, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 4, 5, 3, 1, 2], [9, 10, 8, 6, 7, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 5, 3, 4, 1, 2], [9, 10, 7, 8, 6, 5, 4, 1, 2, 3]}, {[9, 5, 6, 7, 8, 4, 3, 2, 1, 10], [9, 8, 7, 6, 2, 3, 4, 5, 1, 10]}, {[9, 6, 7, 8, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 2, 3, 4, 1, 10]}, {[9, 6, 7, 8, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 2, 3, 4, 1, 10]}, {[9, 6, 7, 8, 5, 4, 2, 3, 1, 10], [9, 7, 8, 6, 5, 2, 3, 4, 1, 10]}, {[9, 7, 8, 4, 5, 6, 3, 2, 1, 10], [9, 8, 7, 4, 5, 6, 2, 3, 1, 10]}, {[9, 7, 8, 5, 6, 3, 4, 2, 1, 10], [9, 8, 6, 7, 4, 5, 2, 3, 1, 10]}, {[9, 7, 8, 5, 6, 4, 2, 3, 1, 10], [9, 7, 8, 6, 4, 5, 2, 3, 1, 10]}, {[9, 7, 8, 6, 3, 4, 5, 2, 1, 10], [9, 8, 5, 6, 7, 4, 2, 3, 1, 10]}, {[9, 8, 4, 5, 6, 7, 3, 2, 1, 10], [9, 8, 7, 3, 4, 5, 6, 2, 1, 10]}, {[9, 8, 5, 6, 7, 3, 4, 2, 1, 10], [9, 8, 6, 7, 3, 4, 5, 2, 1, 10]}, {[9, 10, 5, 6, 7, 8, 4, 3, 2, 1], [10, 9, 8, 7, 3, 4, 5, 6, 1, 2]}, {[9, 10, 6, 7, 8, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 3, 4, 5, 1, 2]}, {[9, 10, 6, 7, 8, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 3, 4, 5, 1, 2]}, {[9, 10, 6, 7, 8, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 3, 4, 5, 1, 2]}, {[9, 10, 6, 7, 8, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 3, 4, 5, 1, 2]}, {[9, 10, 7, 8, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 3, 4, 1, 2]}, {[9, 10, 7, 8, 5, 6, 3, 4, 2, 1], [10, 9, 7, 8, 5, 6, 3, 4, 1, 2]}, {[9, 10, 7, 8, 5, 6, 4, 2, 3, 1], [10, 8, 9, 7, 5, 6, 3, 4, 1, 2]}, {[9, 10, 7, 8, 5, 6, 4, 3, 1, 2], [9, 10, 8, 7, 5, 6, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 5, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 5, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 4, 5, 3, 1, 2], [9, 10, 8, 6, 7, 5, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 5, 3, 4, 1, 2]}, {[9, 10, 8, 4, 5, 6, 7, 3, 2, 1], [10, 9, 8, 4, 5, 6, 7, 3, 1, 2]}, {[9, 10, 8, 5, 6, 7, 3, 4, 2, 1], [10, 9, 7, 8, 4, 5, 6, 3, 1, 2]}, {[9, 10, 8, 5, 6, 7, 4, 2, 3, 1], [10, 8, 9, 7, 4, 5, 6, 3, 1, 2]}, {[9, 10, 8, 5, 6, 7, 4, 3, 1, 2], [9, 10, 8, 7, 4, 5, 6, 3, 1, 2]}, {[9, 10, 8, 6, 7, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 4, 5, 3, 1, 2]}, {[9, 10, 8, 6, 7, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 4, 5, 3, 1, 2]}, {[9, 10, 8, 6, 7, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 4, 5, 3, 1, 2]}, {[9, 10, 8, 7, 3, 4, 5, 6, 2, 1], [10, 9, 5, 6, 7, 8, 4, 3, 1, 2]}, {[9, 10, 8, 7, 4, 5, 6, 2, 3, 1], [10, 8, 9, 5, 6, 7, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 6, 2, 3, 4, 1], [10, 7, 8, 9, 5, 6, 4, 3, 1, 2]}, {[9, 10, 8, 7, 6, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 5, 4, 3, 1, 2]}, {[10, 5, 6, 7, 8, 9, 4, 3, 2, 1], [10, 9, 8, 7, 2, 3, 4, 5, 6, 1]}, {[10, 6, 7, 8, 9, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 2, 3, 4, 5, 1]}, {[10, 6, 7, 8, 9, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 2, 3, 4, 5, 1]}, {[10, 6, 7, 8, 9, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 2, 3, 4, 5, 1]}, {[10, 7, 8, 9, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 2, 3, 4, 1]}, {[10, 7, 8, 9, 5, 6, 3, 4, 2, 1], [10, 9, 7, 8, 5, 6, 2, 3, 4, 1]}, {[10, 7, 8, 9, 5, 6, 4, 2, 3, 1], [10, 8, 9, 7, 5, 6, 2, 3, 4, 1]}, {[10, 7, 8, 9, 6, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 5, 2, 3, 4, 1]}, {[10, 7, 8, 9, 6, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 5, 2, 3, 4, 1]}, {[10, 8, 9, 4, 5, 6, 7, 3, 2, 1], [10, 9, 8, 4, 5, 6, 7, 2, 3, 1]}, {[10, 8, 9, 5, 6, 7, 3, 4, 2, 1], [10, 9, 7, 8, 4, 5, 6, 2, 3, 1]}, {[10, 8, 9, 5, 6, 7, 4, 2, 3, 1], [10, 8, 9, 7, 4, 5, 6, 2, 3, 1]}, {[10, 8, 9, 6, 7, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 4, 5, 2, 3, 1]}, {[10, 8, 9, 7, 3, 4, 5, 6, 2, 1], [10, 9, 5, 6, 7, 8, 4, 2, 3, 1]}, {[10, 9, 4, 5, 6, 7, 8, 3, 2, 1], [10, 9, 8, 3, 4, 5, 6, 7, 2, 1]}, {[10, 9, 5, 6, 7, 8, 3, 4, 2, 1], [10, 9, 7, 8, 3, 4, 5, 6, 2, 1]}} is given by the following expression / 30059 34885 2 26091 3 11987 4 623 5 6\ |- 1/2 - ----- n - ----- n - ----- n - ------ n - ------ n - 7/196608 n | \ 24576 32768 65536 196608 196608 / n / 1741427 1338841 2 32339513 3 14148499 4 371617 5 4 + |1/2 + ------- n + ------- n + -------- n + -------- n + ------- n \ 720720 308880 8648640 8648640 1081080 5813 6 941 7 8\ + ------ n + ------- n + 1/411840 n | C(n) 196560 1235520 / and in Maple input form: (-1/2-30059/24576*n-34885/32768*n^2-26091/65536*n^3-11987/196608*n^4-623/196608 *n^5-7/196608*n^6)*4^n+(1/2+1741427/720720*n+1338841/308880*n^2+32339513/ 8648640*n^3+14148499/8648640*n^4+371617/1081080*n^5+5813/196560*n^6+941/1235520 *n^7+1/411840*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 16 1/2 15 14 1/2 13 12 1/2 11 m 7 Pi m 941 m 5047 Pi m 5813 m 101503 Pi m ------ - ----------- + ------- - -------------- + -------- - ---------------- 411840 196608 1235520 1572864 196560 1572864 10 1/2 9 8 1/2 7 371617 m 244689 Pi m 14148499 m 792979 Pi m + ---------- - --------------- + ----------- - --------------- 1081080 524288 8648640 524288 6 1/2 5 4 1/2 3 32339513 m 1903783 Pi m 1338841 m 122945 Pi m + ----------- - ---------------- + ---------- - --------------- 8648640 786432 308880 65536 2 1/2 1741427 m 9 Pi m + ---------- - --------- + 1/2 720720 16 and in Maple input form: 1/411840*m^16-7/196608*Pi^(1/2)*m^15+941/1235520*m^14-5047/1572864*Pi^(1/2)*m^ 13+5813/196560*m^12-101503/1572864*Pi^(1/2)*m^11+371617/1081080*m^10-244689/ 524288*Pi^(1/2)*m^9+14148499/8648640*m^8-792979/524288*Pi^(1/2)*m^7+32339513/ 8648640*m^6-1903783/786432*Pi^(1/2)*m^5+1338841/308880*m^4-122945/65536*Pi^(1/2 )*m^3+1741427/720720*m^2-9/16*Pi^(1/2)*m+1/2 For the, 25, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[7, 6, 4, 3, 5, 2, 1, 8, 9, 10]}, {[8, 7, 4, 3, 5, 6, 2, 1, 9, 10]}, {[8, 9, 7, 5, 4, 6, 3, 1, 2, 10]}, {[9, 7, 8, 5, 4, 6, 2, 3, 1, 10]}, {[9, 8, 4, 3, 5, 6, 7, 2, 1, 10]}, {[9, 8, 5, 6, 3, 4, 7, 2, 1, 10]}, {[9, 10, 8, 5, 4, 6, 7, 3, 1, 2]}, {[10, 8, 9, 5, 4, 6, 7, 2, 3, 1]}, {[10, 9, 4, 3, 5, 6, 7, 8, 2, 1]}, {[10, 9, 5, 6, 3, 4, 7, 8, 2, 1]}, {[6, 5, 4, 3, 2, 7, 1, 8, 9, 10], [7, 5, 4, 3, 2, 1, 6, 8, 9, 10]}, {[6, 5, 4, 3, 2, 7, 8, 1, 9, 10], [8, 5, 4, 3, 2, 1, 6, 7, 9, 10]}, {[6, 5, 7, 4, 3, 2, 1, 8, 9, 10], [7, 6, 5, 4, 2, 1, 3, 8, 9, 10]}, {[6, 5, 7, 8, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 2, 1, 3, 4, 9, 10]}, {[6, 5, 7, 8, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 2, 1, 3, 4, 5, 10]}, {[6, 5, 7, 8, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 2, 1, 3, 4, 5, 6]}, {[6, 7, 5, 4, 3, 2, 8, 1, 9, 10], [8, 6, 5, 4, 3, 1, 2, 7, 9, 10]}, {[6, 7, 5, 8, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 3, 1, 2, 4, 9, 10]}, {[6, 7, 5, 8, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 3, 1, 2, 4, 5, 10]}, {[6, 7, 5, 8, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 3, 1, 2, 4, 5, 6]}, {[6, 7, 8, 5, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 4, 1, 2, 3, 5, 10]}, {[6, 7, 8, 5, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 4, 1, 2, 3, 5, 6]}, {[6, 7, 8, 9, 5, 4, 3, 2, 10, 1], [10, 8, 7, 6, 5, 1, 2, 3, 4, 9]}, {[6, 7, 8, 9, 5, 10, 4, 3, 2, 1], [10, 9, 8, 7, 5, 1, 2, 3, 4, 6]}, {[7, 5, 4, 6, 3, 2, 1, 8, 9, 10], [7, 6, 5, 3, 2, 4, 1, 8, 9, 10]}, {[7, 5, 6, 4, 3, 2, 8, 1, 9, 10], [8, 6, 5, 4, 2, 3, 1, 7, 9, 10]}, {[7, 5, 6, 8, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 2, 3, 1, 4, 9, 10]}, {[7, 5, 6, 8, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 2, 3, 1, 4, 5, 10]}, {[7, 5, 6, 8, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 2, 3, 1, 4, 5, 6]}, {[7, 6, 4, 5, 3, 2, 8, 1, 9, 10], [8, 6, 5, 3, 4, 2, 1, 7, 9, 10]}, {[7, 6, 5, 3, 4, 2, 8, 1, 9, 10], [8, 6, 4, 5, 3, 2, 1, 7, 9, 10]}, {[7, 6, 5, 4, 2, 3, 8, 1, 9, 10], [8, 5, 6, 4, 3, 2, 1, 7, 9, 10]}, {[7, 6, 5, 4, 3, 8, 1, 2, 9, 10], [7, 8, 5, 4, 3, 2, 1, 6, 9, 10]}, {[7, 6, 5, 4, 3, 8, 9, 1, 2, 10], [8, 9, 5, 4, 3, 2, 1, 6, 7, 10]}, {[7, 6, 5, 4, 3, 8, 9, 10, 1, 2], [9, 10, 5, 4, 3, 2, 1, 6, 7, 8]}, {[7, 6, 8, 4, 5, 3, 2, 1, 9, 10], [8, 7, 6, 4, 5, 2, 1, 3, 9, 10]}, {[7, 6, 8, 5, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 4, 2, 1, 3, 9, 10]}, {[7, 6, 8, 5, 4, 2, 3, 1, 9, 10], [8, 6, 7, 5, 4, 2, 1, 3, 9, 10]}, {[7, 6, 8, 5, 4, 3, 1, 2, 9, 10], [7, 8, 6, 5, 4, 2, 1, 3, 9, 10]}, {[7, 6, 8, 9, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 5, 4, 2, 3, 1, 10], [9, 7, 8, 6, 5, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 5, 4, 3, 1, 2, 10], [8, 9, 7, 6, 5, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 10, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 2, 1, 3, 4, 5]}, {[7, 6, 8, 9, 10, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 2, 1, 3, 4, 5]}, {[7, 6, 8, 9, 10, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 2, 1, 3, 4, 5]}, {[7, 6, 8, 9, 10, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 2, 1, 3, 4, 5]}, {[7, 8, 5, 4, 6, 3, 2, 1, 9, 10], [8, 7, 6, 4, 3, 5, 1, 2, 9, 10]}, {[7, 8, 5, 6, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 3, 4, 1, 2, 5, 10]}, {[7, 8, 5, 6, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 3, 4, 1, 2, 5, 6]}, {[7, 8, 6, 4, 3, 5, 2, 1, 9, 10], [8, 7, 5, 4, 6, 3, 1, 2, 9, 10]}, {[7, 8, 6, 5, 3, 2, 4, 1, 9, 10], [8, 6, 5, 7, 4, 3, 1, 2, 9, 10]}, {[7, 8, 6, 5, 4, 3, 9, 1, 2, 10], [8, 9, 6, 5, 4, 3, 1, 2, 7, 10]}, {[7, 8, 6, 5, 4, 3, 9, 10, 1, 2], [9, 10, 6, 5, 4, 3, 1, 2, 7, 8]}, {[7, 8, 6, 9, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 3, 1, 2, 4, 10]}, {[7, 8, 6, 9, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 3, 1, 2, 4, 10]}, {[7, 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7, 4, 8, 3, 1, 2]}, {[9, 10, 8, 6, 4, 5, 7, 2, 3, 1], [10, 8, 9, 5, 6, 4, 7, 3, 1, 2]}, {[9, 10, 8, 6, 5, 7, 2, 3, 4, 1], [10, 7, 8, 9, 5, 4, 6, 3, 1, 2]}, {[9, 10, 8, 6, 7, 3, 2, 4, 5, 1], [10, 7, 6, 8, 9, 4, 5, 3, 1, 2]}, {[9, 10, 8, 6, 7, 3, 4, 2, 5, 1], [10, 8, 6, 7, 9, 4, 5, 3, 1, 2]}, {[9, 10, 8, 6, 7, 4, 2, 3, 5, 1], [10, 7, 8, 6, 9, 4, 5, 3, 1, 2]}, {[9, 10, 8, 7, 3, 2, 4, 5, 6, 1], [10, 6, 5, 7, 8, 9, 4, 3, 1, 2]}, {[9, 10, 8, 7, 3, 4, 2, 5, 6, 1], [10, 7, 5, 6, 8, 9, 4, 3, 1, 2]}, {[9, 10, 8, 7, 3, 4, 5, 2, 6, 1], [10, 8, 5, 6, 7, 9, 4, 3, 1, 2]}, {[9, 10, 8, 7, 4, 2, 3, 5, 6, 1], [10, 6, 7, 5, 8, 9, 4, 3, 1, 2]}, {[9, 10, 8, 7, 4, 5, 2, 3, 6, 1], [10, 7, 8, 5, 6, 9, 4, 3, 1, 2]}, {[9, 10, 8, 7, 5, 2, 3, 4, 6, 1], [10, 6, 7, 8, 5, 9, 4, 3, 1, 2]}, {[10, 5, 4, 6, 7, 8, 9, 3, 2, 1], [10, 9, 8, 3, 2, 4, 5, 6, 7, 1]}, {[10, 5, 6, 4, 7, 8, 9, 3, 2, 1], [10, 9, 8, 4, 2, 3, 5, 6, 7, 1]}, {[10, 5, 6, 7, 4, 8, 9, 3, 2, 1], [10, 9, 8, 5, 2, 3, 4, 6, 7, 1]}, {[10, 5, 6, 7, 8, 4, 9, 3, 2, 1], [10, 9, 8, 6, 2, 3, 4, 5, 7, 1]}, {[10, 6, 4, 5, 7, 8, 9, 3, 2, 1], [10, 9, 8, 3, 4, 2, 5, 6, 7, 1]}, {[10, 6, 5, 7, 8, 9, 3, 4, 2, 1], [10, 9, 7, 8, 3, 2, 4, 5, 6, 1]}, {[10, 6, 5, 7, 8, 9, 4, 2, 3, 1], [10, 8, 9, 7, 3, 2, 4, 5, 6, 1]}, {[10, 6, 7, 4, 5, 8, 9, 3, 2, 1], [10, 9, 8, 4, 5, 2, 3, 6, 7, 1]}, {[10, 6, 7, 5, 8, 9, 3, 4, 2, 1], [10, 9, 7, 8, 4, 2, 3, 5, 6, 1]}, {[10, 6, 7, 5, 8, 9, 4, 2, 3, 1], [10, 8, 9, 7, 4, 2, 3, 5, 6, 1]}, {[10, 6, 7, 8, 4, 5, 9, 3, 2, 1], [10, 9, 8, 5, 6, 2, 3, 4, 7, 1]}, {[10, 6, 7, 8, 5, 9, 3, 4, 2, 1], [10, 9, 7, 8, 5, 2, 3, 4, 6, 1]}, {[10, 6, 7, 8, 5, 9, 4, 2, 3, 1], [10, 8, 9, 7, 5, 2, 3, 4, 6, 1]}, {[10, 6, 7, 8, 9, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 2, 3, 4, 5, 1]}, {[10, 6, 7, 8, 9, 5, 3, 2, 4, 1], [10, 8, 7, 9, 6, 2, 3, 4, 5, 1]}, {[10, 7, 4, 5, 6, 8, 9, 3, 2, 1], [10, 9, 8, 3, 4, 5, 2, 6, 7, 1]}, {[10, 7, 5, 6, 8, 9, 3, 4, 2, 1], [10, 9, 7, 8, 3, 4, 2, 5, 6, 1]}, {[10, 7, 5, 6, 8, 9, 4, 2, 3, 1], [10, 8, 9, 7, 3, 4, 2, 5, 6, 1]}, {[10, 7, 6, 8, 9, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 3, 2, 4, 5, 1]}, {[10, 7, 6, 8, 9, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 3, 2, 4, 5, 1]}, {[10, 7, 6, 8, 9, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 3, 2, 4, 5, 1]}, {[10, 7, 8, 4, 5, 6, 9, 3, 2, 1], [10, 9, 8, 4, 5, 6, 2, 3, 7, 1]}, {[10, 7, 8, 5, 6, 9, 3, 4, 2, 1], [10, 9, 7, 8, 4, 5, 2, 3, 6, 1]}, {[10, 7, 8, 5, 6, 9, 4, 2, 3, 1], [10, 8, 9, 7, 4, 5, 2, 3, 6, 1]}, {[10, 7, 8, 6, 9, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 4, 2, 3, 5, 1]}, {[10, 7, 8, 6, 9, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 4, 2, 3, 5, 1]}, {[10, 7, 8, 6, 9, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 4, 2, 3, 5, 1]}, {[10, 7, 8, 9, 4, 3, 5, 6, 2, 1], [10, 9, 6, 5, 7, 8, 2, 3, 4, 1]}, {[10, 7, 8, 9, 4, 5, 3, 6, 2, 1], [10, 9, 7, 5, 6, 8, 2, 3, 4, 1]}, {[10, 7, 8, 9, 5, 3, 4, 6, 2, 1], [10, 9, 6, 7, 5, 8, 2, 3, 4, 1]}, {[10, 7, 8, 9, 5, 4, 6, 2, 3, 1], [10, 8, 9, 6, 5, 7, 2, 3, 4, 1]}, {[10, 7, 8, 9, 5, 6, 3, 2, 4, 1], [10, 8, 7, 9, 5, 6, 2, 3, 4, 1]}, {[10, 7, 8, 9, 6, 3, 4, 2, 5, 1], [10, 8, 6, 7, 9, 5, 2, 3, 4, 1]}, {[10, 8, 4, 5, 6, 7, 9, 3, 2, 1], [10, 9, 8, 3, 4, 5, 6, 2, 7, 1]}, {[10, 8, 5, 6, 7, 9, 3, 4, 2, 1], [10, 9, 7, 8, 3, 4, 5, 2, 6, 1]}, {[10, 8, 5, 6, 7, 9, 4, 2, 3, 1], [10, 8, 9, 7, 3, 4, 5, 2, 6, 1]}, {[10, 8, 6, 7, 9, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 3, 4, 2, 5, 1]}, {[10, 8, 6, 7, 9, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 3, 4, 2, 5, 1]}, {[10, 8, 7, 9, 3, 4, 5, 6, 2, 1], [10, 9, 5, 6, 7, 8, 3, 2, 4, 1]}, {[10, 8, 7, 9, 4, 5, 6, 2, 3, 1], [10, 8, 9, 5, 6, 7, 3, 2, 4, 1]}, {[10, 8, 9, 4, 3, 5, 6, 7, 2, 1], [10, 9, 5, 4, 6, 7, 8, 2, 3, 1]}, {[10, 8, 9, 4, 5, 3, 6, 7, 2, 1], [10, 9, 6, 4, 5, 7, 8, 2, 3, 1]}, {[10, 8, 9, 4, 5, 6, 3, 7, 2, 1], [10, 9, 7, 4, 5, 6, 8, 2, 3, 1]}, {[10, 8, 9, 5, 3, 4, 6, 7, 2, 1], [10, 9, 5, 6, 4, 7, 8, 2, 3, 1]}, {[10, 8, 9, 5, 6, 3, 4, 7, 2, 1], [10, 9, 6, 7, 4, 5, 8, 2, 3, 1]}, {[10, 8, 9, 5, 6, 4, 7, 2, 3, 1], [10, 8, 9, 6, 4, 5, 7, 2, 3, 1]}, {[10, 8, 9, 6, 3, 4, 5, 7, 2, 1], [10, 9, 5, 6, 7, 4, 8, 2, 3, 1]}, {[10, 9, 4, 5, 3, 6, 7, 8, 2, 1], [10, 9, 5, 3, 4, 6, 7, 8, 2, 1]}, {[10, 9, 4, 5, 6, 3, 7, 8, 2, 1], [10, 9, 6, 3, 4, 5, 7, 8, 2, 1]}, {[10, 9, 4, 5, 6, 7, 3, 8, 2, 1], [10, 9, 7, 3, 4, 5, 6, 8, 2, 1]}, {[10, 9, 5, 6, 7, 3, 4, 8, 2, 1], [10, 9, 6, 7, 3, 4, 5, 8, 2, 1]}, { [6, 5, 4, 3, 2, 7, 8, 9, 1, 10], [6, 5, 4, 3, 2, 7, 8, 9, 10, 1], [9, 5, 4, 3, 2, 1, 6, 7, 8, 10], [10, 5, 4, 3, 2, 1, 6, 7, 8, 9]}, { [6, 7, 5, 4, 3, 2, 8, 9, 1, 10], [6, 7, 5, 4, 3, 2, 8, 9, 10, 1], [9, 6, 5, 4, 3, 1, 2, 7, 8, 10], [10, 6, 5, 4, 3, 1, 2, 7, 8, 9]}, { [6, 7, 8, 5, 4, 3, 2, 9, 1, 10], [6, 7, 8, 5, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 4, 1, 2, 3, 8, 10], [10, 7, 6, 5, 4, 1, 2, 3, 8, 9]}, { [7, 5, 6, 4, 3, 2, 8, 9, 1, 10], [7, 5, 6, 4, 3, 2, 8, 9, 10, 1], [9, 6, 5, 4, 2, 3, 1, 7, 8, 10], [10, 6, 5, 4, 2, 3, 1, 7, 8, 9]}, { [7, 6, 4, 5, 3, 2, 8, 9, 1, 10], [7, 6, 4, 5, 3, 2, 8, 9, 10, 1], [9, 6, 5, 3, 4, 2, 1, 7, 8, 10], [10, 6, 5, 3, 4, 2, 1, 7, 8, 9]}, { [7, 6, 5, 3, 4, 2, 8, 9, 1, 10], [7, 6, 5, 3, 4, 2, 8, 9, 10, 1], [9, 6, 4, 5, 3, 2, 1, 7, 8, 10], [10, 6, 4, 5, 3, 2, 1, 7, 8, 9]}, { [7, 6, 5, 4, 2, 3, 8, 9, 1, 10], [7, 6, 5, 4, 2, 3, 8, 9, 10, 1], [9, 5, 6, 4, 3, 2, 1, 7, 8, 10], [10, 5, 6, 4, 3, 2, 1, 7, 8, 9]}, { [7, 8, 5, 6, 4, 3, 2, 9, 1, 10], [7, 8, 5, 6, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 3, 4, 1, 2, 8, 10], [10, 7, 6, 5, 3, 4, 1, 2, 8, 9]}, { [7, 8, 6, 4, 5, 3, 2, 9, 1, 10], [7, 8, 6, 4, 5, 3, 2, 9, 10, 1], [9, 7, 6, 4, 5, 3, 1, 2, 8, 10], [10, 7, 6, 4, 5, 3, 1, 2, 8, 9]}, { [7, 8, 6, 5, 3, 4, 2, 9, 1, 10], [7, 8, 6, 5, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 4, 3, 1, 2, 8, 10], [10, 7, 5, 6, 4, 3, 1, 2, 8, 9]}, { [7, 8, 6, 5, 4, 2, 3, 9, 1, 10], [7, 8, 6, 5, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 4, 3, 1, 2, 8, 10], [10, 6, 7, 5, 4, 3, 1, 2, 8, 9]}, { [8, 5, 6, 7, 4, 3, 2, 9, 1, 10], [8, 5, 6, 7, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 2, 3, 4, 1, 8, 10], [10, 7, 6, 5, 2, 3, 4, 1, 8, 9]}, { [8, 6, 7, 4, 5, 3, 2, 9, 1, 10], [8, 6, 7, 4, 5, 3, 2, 9, 10, 1], [9, 7, 6, 4, 5, 2, 3, 1, 8, 10], [10, 7, 6, 4, 5, 2, 3, 1, 8, 9]}, { [8, 6, 7, 5, 3, 4, 2, 9, 1, 10], [8, 6, 7, 5, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 4, 2, 3, 1, 8, 10], [10, 7, 5, 6, 4, 2, 3, 1, 8, 9]}, { [8, 6, 7, 5, 4, 2, 3, 9, 1, 10], [8, 6, 7, 5, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 4, 2, 3, 1, 8, 10], [10, 6, 7, 5, 4, 2, 3, 1, 8, 9]}, { [8, 7, 4, 5, 6, 3, 2, 9, 1, 10], [8, 7, 4, 5, 6, 3, 2, 9, 10, 1], [9, 7, 6, 3, 4, 5, 2, 1, 8, 10], [10, 7, 6, 3, 4, 5, 2, 1, 8, 9]}, { [8, 7, 5, 6, 3, 4, 2, 9, 1, 10], [8, 7, 5, 6, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 3, 4, 2, 1, 8, 10], [10, 7, 5, 6, 3, 4, 2, 1, 8, 9]}, { [8, 7, 5, 6, 4, 2, 3, 9, 1, 10], [8, 7, 5, 6, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 3, 4, 2, 1, 8, 10], [10, 6, 7, 5, 3, 4, 2, 1, 8, 9]}, { [8, 7, 6, 3, 4, 5, 2, 9, 1, 10], [8, 7, 6, 3, 4, 5, 2, 9, 10, 1], [9, 7, 4, 5, 6, 3, 2, 1, 8, 10], [10, 7, 4, 5, 6, 3, 2, 1, 8, 9]}, { [8, 7, 6, 4, 5, 2, 3, 9, 1, 10], [8, 7, 6, 4, 5, 2, 3, 9, 10, 1], [9, 6, 7, 4, 5, 3, 2, 1, 8, 10], [10, 6, 7, 4, 5, 3, 2, 1, 8, 9]}, { [8, 7, 6, 5, 2, 3, 4, 9, 1, 10], [8, 7, 6, 5, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 4, 3, 2, 1, 8, 10], [10, 5, 6, 7, 4, 3, 2, 1, 8, 9]}} is given by the following expression / 1847 17319 2 5117 3 1287 4 479 5 6\ n |- ----- n - ------ n - ------ n - ------ n - ------ n - 7/655360 n | 4 + \ 81920 327680 131072 131072 655360 / /129 61489 2 3130637 3 148661 4 200021 5 5053 6 |---- n + ------ n + -------- n + ------- n + ------- n + ------ n \5720 576576 17297280 1081080 4324320 864864 3503 7 8\ + -------- n + 1/1235520 n | C(n) 17297280 / and in Maple input form: (-1847/81920*n-17319/327680*n^2-5117/131072*n^3-1287/131072*n^4-479/655360*n^5-\ 7/655360*n^6)*4^n+(129/5720*n+61489/576576*n^2+3130637/17297280*n^3+148661/ 1081080*n^4+200021/4324320*n^5+5053/864864*n^6+3503/17297280*n^7+1/1235520*n^8) *C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 16 1/2 15 14 1/2 13 12 1/2 11 m 7 Pi m 3503 m 779 Pi m 5053 m 55791 Pi m ------- - ----------- + -------- - ------------- + -------- - --------------- 1235520 655360 17297280 1048576 864864 5242880 10 1/2 9 8 1/2 7 6 200021 m 52519 Pi m 148661 m 507369 Pi m 3130637 m + ---------- - -------------- + --------- - --------------- + ---------- 4324320 1048576 1081080 5242880 17297280 1/2 5 4 1/2 3 2 42995 Pi m 61489 m 16623 Pi m 129 m - -------------- + -------- - -------------- + ------ 524288 576576 655360 5720 and in Maple input form: 1/1235520*m^16-7/655360*Pi^(1/2)*m^15+3503/17297280*m^14-779/1048576*Pi^(1/2)*m ^13+5053/864864*m^12-55791/5242880*Pi^(1/2)*m^11+200021/4324320*m^10-52519/ 1048576*Pi^(1/2)*m^9+148661/1081080*m^8-507369/5242880*Pi^(1/2)*m^7+3130637/ 17297280*m^6-42995/524288*Pi^(1/2)*m^5+61489/576576*m^4-16623/655360*Pi^(1/2)*m ^3+129/5720*m^2 For the, 26, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[7, 5, 4, 3, 2, 6, 1, 8, 9, 10]}, {[8, 5, 4, 3, 2, 6, 7, 1, 9, 10]}, {[8, 9, 6, 5, 4, 3, 7, 1, 2, 10]}, {[9, 5, 4, 3, 2, 6, 7, 8, 1, 10]}, {[9, 6, 7, 5, 4, 2, 3, 8, 1, 10]}, {[9, 7, 5, 6, 3, 4, 2, 8, 1, 10]}, {[9, 10, 6, 5, 4, 3, 7, 8, 1, 2]}, {[10, 5, 4, 3, 2, 6, 7, 8, 9, 1]}, {[10, 6, 7, 5, 4, 2, 3, 8, 9, 1]}, {[10, 7, 5, 6, 3, 4, 2, 8, 9, 1]}, {[6, 5, 4, 3, 7, 2, 1, 8, 9, 10], [7, 6, 4, 3, 2, 1, 5, 8, 9, 10]}, {[6, 5, 4, 3, 7, 8, 2, 1, 9, 10], [8, 7, 4, 3, 2, 1, 5, 6, 9, 10]}, {[6, 5, 4, 3, 7, 8, 9, 2, 1, 10], [9, 8, 4, 3, 2, 1, 5, 6, 7, 10]}, {[6, 5, 4, 3, 7, 8, 9, 10, 2, 1], [10, 9, 4, 3, 2, 1, 5, 6, 7, 8]}, {[6, 5, 4, 7, 3, 2, 1, 8, 9, 10], [7, 6, 5, 3, 2, 1, 4, 8, 9, 10]}, {[6, 5, 4, 7, 8, 3, 2, 1, 9, 10], [8, 7, 6, 3, 2, 1, 4, 5, 9, 10]}, {[6, 5, 4, 7, 8, 9, 3, 2, 1, 10], [9, 8, 7, 3, 2, 1, 4, 5, 6, 10]}, {[6, 5, 4, 7, 8, 9, 10, 3, 2, 1], [10, 9, 8, 3, 2, 1, 4, 5, 6, 7]}, {[6, 7, 5, 4, 3, 8, 2, 1, 9, 10], [8, 7, 5, 4, 3, 1, 2, 6, 9, 10]}, {[6, 7, 5, 4, 3, 8, 9, 2, 1, 10], [9, 8, 5, 4, 3, 1, 2, 6, 7, 10]}, {[6, 7, 5, 4, 3, 8, 9, 10, 2, 1], [10, 9, 5, 4, 3, 1, 2, 6, 7, 8]}, {[6, 7, 5, 4, 8, 3, 2, 1, 9, 10], [8, 7, 6, 4, 3, 1, 2, 5, 9, 10]}, {[6, 7, 5, 4, 8, 9, 3, 2, 1, 10], [9, 8, 7, 4, 3, 1, 2, 5, 6, 10]}, {[6, 7, 5, 4, 8, 9, 10, 3, 2, 1], [10, 9, 8, 4, 3, 1, 2, 5, 6, 7]}, {[6, 7, 8, 5, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 4, 1, 2, 3, 7, 10]}, {[6, 7, 8, 5, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 4, 1, 2, 3, 7, 8]}, {[6, 7, 8, 5, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 4, 1, 2, 3, 6, 10]}, {[6, 7, 8, 5, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 4, 1, 2, 3, 6, 7]}, {[6, 7, 8, 9, 5, 4, 3, 10, 2, 1], [10, 9, 7, 6, 5, 1, 2, 3, 4, 8]}, {[6, 7, 8, 9, 5, 4, 10, 3, 2, 1], [10, 9, 8, 6, 5, 1, 2, 3, 4, 7]}, {[7, 5, 4, 3, 6, 2, 1, 8, 9, 10], [7, 6, 4, 3, 2, 5, 1, 8, 9, 10]}, {[7, 5, 6, 4, 3, 8, 2, 1, 9, 10], [8, 7, 5, 4, 2, 3, 1, 6, 9, 10]}, {[7, 5, 6, 4, 3, 8, 9, 2, 1, 10], [9, 8, 5, 4, 2, 3, 1, 6, 7, 10]}, {[7, 5, 6, 4, 3, 8, 9, 10, 2, 1], [10, 9, 5, 4, 2, 3, 1, 6, 7, 8]}, {[7, 5, 6, 4, 8, 3, 2, 1, 9, 10], [8, 7, 6, 4, 2, 3, 1, 5, 9, 10]}, {[7, 5, 6, 4, 8, 9, 3, 2, 1, 10], [9, 8, 7, 4, 2, 3, 1, 5, 6, 10]}, {[7, 5, 6, 4, 8, 9, 10, 3, 2, 1], [10, 9, 8, 4, 2, 3, 1, 5, 6, 7]}, {[7, 6, 4, 5, 3, 8, 2, 1, 9, 10], [8, 7, 5, 3, 4, 2, 1, 6, 9, 10]}, {[7, 6, 4, 5, 3, 8, 9, 2, 1, 10], [9, 8, 5, 3, 4, 2, 1, 6, 7, 10]}, {[7, 6, 4, 5, 3, 8, 9, 10, 2, 1], [10, 9, 5, 3, 4, 2, 1, 6, 7, 8]}, {[7, 6, 4, 5, 8, 3, 2, 1, 9, 10], [8, 7, 6, 3, 4, 2, 1, 5, 9, 10]}, {[7, 6, 4, 5, 8, 9, 3, 2, 1, 10], [9, 8, 7, 3, 4, 2, 1, 5, 6, 10]}, {[7, 6, 4, 5, 8, 9, 10, 3, 2, 1], [10, 9, 8, 3, 4, 2, 1, 5, 6, 7]}, {[7, 6, 5, 3, 4, 8, 2, 1, 9, 10], [8, 7, 4, 5, 3, 2, 1, 6, 9, 10]}, {[7, 6, 5, 3, 4, 8, 9, 2, 1, 10], [9, 8, 4, 5, 3, 2, 1, 6, 7, 10]}, {[7, 6, 5, 3, 4, 8, 9, 10, 2, 1], [10, 9, 4, 5, 3, 2, 1, 6, 7, 8]}, {[7, 6, 5, 4, 8, 2, 3, 1, 9, 10], [8, 6, 7, 4, 3, 2, 1, 5, 9, 10]}, {[7, 6, 5, 4, 8, 3, 1, 2, 9, 10], [7, 8, 6, 4, 3, 2, 1, 5, 9, 10]}, {[7, 6, 5, 4, 8, 9, 2, 3, 1, 10], [9, 7, 8, 4, 3, 2, 1, 5, 6, 10]}, {[7, 6, 5, 4, 8, 9, 3, 1, 2, 10], [8, 9, 7, 4, 3, 2, 1, 5, 6, 10]}, {[7, 6, 5, 4, 8, 9, 10, 2, 3, 1], [10, 8, 9, 4, 3, 2, 1, 5, 6, 7]}, {[7, 6, 5, 4, 8, 9, 10, 3, 1, 2], [9, 10, 8, 4, 3, 2, 1, 5, 6, 7]}, {[7, 6, 5, 8, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 3, 2, 1, 4, 9, 10]}, {[7, 6, 5, 8, 4, 2, 3, 1, 9, 10], [8, 6, 7, 5, 3, 2, 1, 4, 9, 10]}, {[7, 6, 5, 8, 4, 3, 1, 2, 9, 10], [7, 8, 6, 5, 3, 2, 1, 4, 9, 10]}, {[7, 6, 5, 8, 9, 3, 4, 2, 1, 10], [9, 8, 6, 7, 3, 2, 1, 4, 5, 10]}, {[7, 6, 5, 8, 9, 4, 2, 3, 1, 10], [9, 7, 8, 6, 3, 2, 1, 4, 5, 10]}, {[7, 6, 5, 8, 9, 4, 3, 1, 2, 10], [8, 9, 7, 6, 3, 2, 1, 4, 5, 10]}, {[7, 6, 5, 8, 9, 10, 3, 4, 2, 1], [10, 9, 7, 8, 3, 2, 1, 4, 5, 6]}, {[7, 6, 5, 8, 9, 10, 4, 2, 3, 1], [10, 8, 9, 7, 3, 2, 1, 4, 5, 6]}, {[7, 6, 5, 8, 9, 10, 4, 3, 1, 2], [9, 10, 8, 7, 3, 2, 1, 4, 5, 6]}, {[7, 8, 5, 4, 3, 2, 6, 1, 9, 10], [8, 6, 5, 4, 3, 7, 1, 2, 9, 10]}, {[7, 8, 5, 4, 3, 6, 2, 1, 9, 10], [8, 7, 5, 4, 3, 6, 1, 2, 9, 10]}, {[7, 8, 5, 6, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 3, 4, 1, 2, 7, 10]}, {[7, 8, 5, 6, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 3, 4, 1, 2, 7, 8]}, {[7, 8, 5, 6, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 3, 4, 1, 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8, 1], [10, 7, 5, 6, 4, 3, 8, 9, 1, 2]}, {[9, 10, 6, 5, 3, 4, 7, 8, 2, 1], [10, 9, 5, 6, 4, 3, 7, 8, 1, 2]}, {[9, 10, 6, 5, 4, 2, 3, 7, 8, 1], [10, 6, 7, 5, 4, 3, 8, 9, 1, 2]}, {[9, 10, 6, 5, 4, 7, 8, 2, 3, 1], [10, 8, 9, 5, 4, 3, 6, 7, 1, 2]}, {[9, 10, 6, 5, 4, 7, 8, 3, 1, 2], [9, 10, 8, 5, 4, 3, 6, 7, 1, 2]}, {[9, 10, 6, 7, 4, 5, 3, 2, 8, 1], [10, 8, 7, 5, 6, 3, 4, 9, 1, 2]}, {[9, 10, 6, 7, 4, 5, 3, 8, 2, 1], [10, 9, 7, 5, 6, 3, 4, 8, 1, 2]}, {[9, 10, 6, 7, 5, 3, 4, 2, 8, 1], [10, 8, 6, 7, 5, 3, 4, 9, 1, 2]}, {[9, 10, 6, 7, 5, 3, 4, 8, 2, 1], [10, 9, 6, 7, 5, 3, 4, 8, 1, 2]}, {[9, 10, 6, 7, 5, 4, 2, 3, 8, 1], [10, 7, 8, 6, 5, 3, 4, 9, 1, 2]}, {[9, 10, 6, 7, 5, 4, 3, 8, 1, 2], [9, 10, 7, 6, 5, 3, 4, 8, 1, 2]}, {[9, 10, 6, 7, 5, 4, 8, 2, 3, 1], [10, 8, 9, 6, 5, 3, 4, 7, 1, 2]}, {[9, 10, 6, 7, 5, 4, 8, 3, 1, 2], [9, 10, 8, 6, 5, 3, 4, 7, 1, 2]}, {[9, 10, 6, 7, 8, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 3, 4, 5, 1, 2]}, {[9, 10, 7, 4, 5, 6, 3, 2, 8, 1], [10, 8, 7, 4, 5, 6, 3, 9, 1, 2]}, {[9, 10, 7, 4, 5, 6, 3, 8, 2, 1], [10, 9, 7, 4, 5, 6, 3, 8, 1, 2]}, {[9, 10, 7, 5, 6, 3, 4, 2, 8, 1], [10, 8, 6, 7, 4, 5, 3, 9, 1, 2]}, {[9, 10, 7, 5, 6, 3, 4, 8, 2, 1], [10, 9, 6, 7, 4, 5, 3, 8, 1, 2]}, {[9, 10, 7, 5, 6, 4, 2, 3, 8, 1], [10, 7, 8, 6, 4, 5, 3, 9, 1, 2]}, {[9, 10, 7, 5, 6, 4, 3, 8, 1, 2], [9, 10, 7, 6, 4, 5, 3, 8, 1, 2]}, {[9, 10, 7, 5, 6, 4, 8, 2, 3, 1], [10, 8, 9, 6, 4, 5, 3, 7, 1, 2]}, {[9, 10, 7, 5, 6, 4, 8, 3, 1, 2], [9, 10, 8, 6, 4, 5, 3, 7, 1, 2]}, {[9, 10, 7, 6, 3, 4, 5, 2, 8, 1], [10, 8, 5, 6, 7, 4, 3, 9, 1, 2]}, {[9, 10, 7, 6, 3, 4, 5, 8, 2, 1], [10, 9, 5, 6, 7, 4, 3, 8, 1, 2]}, {[9, 10, 7, 6, 4, 5, 2, 3, 8, 1], [10, 7, 8, 5, 6, 4, 3, 9, 1, 2]}, {[9, 10, 7, 6, 4, 5, 8, 2, 3, 1], [10, 8, 9, 5, 6, 4, 3, 7, 1, 2]}, {[9, 10, 7, 6, 4, 5, 8, 3, 1, 2], [9, 10, 8, 5, 6, 4, 3, 7, 1, 2]}, {[9, 10, 7, 6, 5, 2, 3, 4, 8, 1], [10, 6, 7, 8, 5, 4, 3, 9, 1, 2]}, {[9, 10, 7, 6, 5, 8, 2, 3, 4, 1], [10, 7, 8, 9, 5, 4, 3, 6, 1, 2]}, {[9, 10, 7, 6, 5, 8, 3, 4, 1, 2], [9, 10, 7, 8, 5, 4, 3, 6, 1, 2]}, {[9, 10, 7, 8, 4, 3, 2, 5, 6, 1], [10, 7, 6, 5, 8, 9, 3, 4, 1, 2]}, {[9, 10, 7, 8, 4, 5, 3, 2, 6, 1], [10, 8, 7, 5, 6, 9, 3, 4, 1, 2]}, {[9, 10, 7, 8, 5, 3, 4, 2, 6, 1], [10, 8, 6, 7, 5, 9, 3, 4, 1, 2]}, {[9, 10, 7, 8, 5, 4, 2, 3, 6, 1], [10, 7, 8, 6, 5, 9, 3, 4, 1, 2]}, {[9, 10, 8, 4, 3, 2, 5, 6, 7, 1], [10, 6, 5, 4, 7, 8, 9, 3, 1, 2]}, {[9, 10, 8, 4, 5, 3, 2, 6, 7, 1], [10, 7, 6, 4, 5, 8, 9, 3, 1, 2]}, {[9, 10, 8, 4, 5, 6, 3, 2, 7, 1], [10, 8, 7, 4, 5, 6, 9, 3, 1, 2]}, {[9, 10, 8, 5, 3, 4, 2, 6, 7, 1], [10, 7, 5, 6, 4, 8, 9, 3, 1, 2]}, {[9, 10, 8, 5, 4, 2, 3, 6, 7, 1], [10, 6, 7, 5, 4, 8, 9, 3, 1, 2]}, {[9, 10, 8, 5, 6, 3, 4, 2, 7, 1], [10, 8, 6, 7, 4, 5, 9, 3, 1, 2]}, {[9, 10, 8, 5, 6, 4, 2, 3, 7, 1], [10, 7, 8, 6, 4, 5, 9, 3, 1, 2]}, {[9, 10, 8, 6, 3, 4, 5, 2, 7, 1], [10, 8, 5, 6, 7, 4, 9, 3, 1, 2]}, {[9, 10, 8, 6, 4, 5, 2, 3, 7, 1], [10, 7, 8, 5, 6, 4, 9, 3, 1, 2]}, {[9, 10, 8, 6, 5, 2, 3, 4, 7, 1], [10, 6, 7, 8, 5, 4, 9, 3, 1, 2]}, {[10, 5, 4, 3, 6, 7, 8, 9, 2, 1], [10, 9, 4, 3, 2, 5, 6, 7, 8, 1]}, {[10, 5, 6, 4, 3, 2, 7, 8, 9, 1], [10, 6, 5, 4, 2, 3, 7, 8, 9, 1]}, {[10, 5, 6, 4, 3, 7, 8, 9, 2, 1], [10, 9, 5, 4, 2, 3, 6, 7, 8, 1]}, {[10, 5, 6, 7, 4, 3, 2, 8, 9, 1], [10, 7, 6, 5, 2, 3, 4, 8, 9, 1]}, {[10, 5, 6, 7, 4, 3, 8, 9, 2, 1], [10, 9, 6, 5, 2, 3, 4, 7, 8, 1]}, {[10, 5, 6, 7, 8, 4, 3, 2, 9, 1], [10, 8, 7, 6, 2, 3, 4, 5, 9, 1]}, {[10, 5, 6, 7, 8, 4, 3, 9, 2, 1], [10, 9, 7, 6, 2, 3, 4, 5, 8, 1]}, {[10, 6, 4, 5, 3, 2, 7, 8, 9, 1], [10, 6, 5, 3, 4, 2, 7, 8, 9, 1]}, {[10, 6, 4, 5, 3, 7, 8, 9, 2, 1], [10, 9, 5, 3, 4, 2, 6, 7, 8, 1]}, {[10, 6, 5, 3, 4, 7, 8, 9, 2, 1], [10, 9, 4, 5, 3, 2, 6, 7, 8, 1]}, {[10, 6, 5, 4, 7, 8, 9, 2, 3, 1], [10, 8, 9, 4, 3, 2, 5, 6, 7, 1]}, {[10, 6, 7, 4, 5, 3, 2, 8, 9, 1], [10, 7, 6, 4, 5, 2, 3, 8, 9, 1]}, {[10, 6, 7, 4, 5, 3, 8, 9, 2, 1], [10, 9, 6, 4, 5, 2, 3, 7, 8, 1]}, {[10, 6, 7, 5, 3, 4, 2, 8, 9, 1], [10, 7, 5, 6, 4, 2, 3, 8, 9, 1]}, {[10, 6, 7, 5, 3, 4, 8, 9, 2, 1], [10, 9, 5, 6, 4, 2, 3, 7, 8, 1]}, {[10, 6, 7, 5, 4, 8, 9, 2, 3, 1], [10, 8, 9, 5, 4, 2, 3, 6, 7, 1]}, {[10, 6, 7, 8, 4, 5, 3, 2, 9, 1], [10, 8, 7, 5, 6, 2, 3, 4, 9, 1]}, {[10, 6, 7, 8, 4, 5, 3, 9, 2, 1], [10, 9, 7, 5, 6, 2, 3, 4, 8, 1]}, {[10, 6, 7, 8, 5, 3, 4, 2, 9, 1], [10, 8, 6, 7, 5, 2, 3, 4, 9, 1]}, {[10, 6, 7, 8, 5, 3, 4, 9, 2, 1], [10, 9, 6, 7, 5, 2, 3, 4, 8, 1]}, {[10, 6, 7, 8, 5, 4, 2, 3, 9, 1], [10, 7, 8, 6, 5, 2, 3, 4, 9, 1]}, {[10, 6, 7, 8, 5, 4, 9, 2, 3, 1], [10, 8, 9, 6, 5, 2, 3, 4, 7, 1]}, {[10, 6, 7, 8, 9, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 2, 3, 4, 5, 1]}, {[10, 7, 4, 5, 6, 3, 2, 8, 9, 1], [10, 7, 6, 3, 4, 5, 2, 8, 9, 1]}, {[10, 7, 4, 5, 6, 3, 8, 9, 2, 1], [10, 9, 6, 3, 4, 5, 2, 7, 8, 1]}, {[10, 7, 5, 6, 3, 4, 8, 9, 2, 1], [10, 9, 5, 6, 3, 4, 2, 7, 8, 1]}, {[10, 7, 5, 6, 4, 8, 9, 2, 3, 1], [10, 8, 9, 5, 3, 4, 2, 6, 7, 1]}, {[10, 7, 6, 3, 4, 5, 8, 9, 2, 1], [10, 9, 4, 5, 6, 3, 2, 7, 8, 1]}, {[10, 7, 6, 4, 5, 8, 9, 2, 3, 1], [10, 8, 9, 4, 5, 3, 2, 6, 7, 1]}, {[10, 7, 6, 5, 8, 9, 2, 3, 4, 1], [10, 7, 8, 9, 4, 3, 2, 5, 6, 1]}, {[10, 7, 8, 4, 5, 6, 3, 2, 9, 1], [10, 8, 7, 4, 5, 6, 2, 3, 9, 1]}, {[10, 7, 8, 4, 5, 6, 3, 9, 2, 1], [10, 9, 7, 4, 5, 6, 2, 3, 8, 1]}, {[10, 7, 8, 5, 6, 3, 4, 2, 9, 1], [10, 8, 6, 7, 4, 5, 2, 3, 9, 1]}, {[10, 7, 8, 5, 6, 3, 4, 9, 2, 1], [10, 9, 6, 7, 4, 5, 2, 3, 8, 1]}, {[10, 7, 8, 5, 6, 4, 2, 3, 9, 1], [10, 7, 8, 6, 4, 5, 2, 3, 9, 1]}, {[10, 7, 8, 5, 6, 4, 9, 2, 3, 1], [10, 8, 9, 6, 4, 5, 2, 3, 7, 1]}, {[10, 7, 8, 6, 3, 4, 5, 2, 9, 1], [10, 8, 5, 6, 7, 4, 2, 3, 9, 1]}, {[10, 7, 8, 6, 3, 4, 5, 9, 2, 1], [10, 9, 5, 6, 7, 4, 2, 3, 8, 1]}, {[10, 7, 8, 6, 4, 5, 9, 2, 3, 1], [10, 8, 9, 5, 6, 4, 2, 3, 7, 1]}, {[10, 7, 8, 6, 5, 9, 2, 3, 4, 1], [10, 7, 8, 9, 5, 4, 2, 3, 6, 1]}, {[10, 7, 8, 9, 4, 5, 3, 2, 6, 1], [10, 8, 7, 5, 6, 9, 2, 3, 4, 1]}, {[10, 7, 8, 9, 5, 3, 4, 2, 6, 1], [10, 8, 6, 7, 5, 9, 2, 3, 4, 1]}, {[10, 8, 4, 5, 6, 7, 3, 2, 9, 1], [10, 8, 7, 3, 4, 5, 6, 2, 9, 1]}, {[10, 8, 4, 5, 6, 7, 3, 9, 2, 1], [10, 9, 7, 3, 4, 5, 6, 2, 8, 1]}, {[10, 8, 5, 6, 7, 3, 4, 2, 9, 1], [10, 8, 6, 7, 3, 4, 5, 2, 9, 1]}, {[10, 8, 5, 6, 7, 3, 4, 9, 2, 1], [10, 9, 6, 7, 3, 4, 5, 2, 8, 1]}, {[10, 8, 5, 6, 7, 4, 9, 2, 3, 1], [10, 8, 9, 6, 3, 4, 5, 2, 7, 1]}, {[10, 8, 6, 7, 3, 4, 5, 9, 2, 1], [10, 9, 5, 6, 7, 3, 4, 2, 8, 1]}, {[10, 8, 6, 7, 4, 5, 9, 2, 3, 1], [10, 8, 9, 5, 6, 3, 4, 2, 7, 1]}, {[10, 8, 7, 3, 4, 5, 6, 9, 2, 1], [10, 9, 4, 5, 6, 7, 3, 2, 8, 1]}, {[10, 8, 7, 4, 5, 6, 9, 2, 3, 1], [10, 8, 9, 4, 5, 6, 3, 2, 7, 1]}} is given by the following expression / 2277 3601 2 4471 3 997 4 349 5 6\ n / |- ----- n - ----- n - ------ n - ------ n - ------ n - 1/131072 n | 4 + | \ 81920 65536 131072 131072 655360 / \ 159 116537 2 1065217 3 537829 4 8963 5 107 6 ---- n + ------ n + ------- n + ------- n + ------ n + ----- n 5720 960960 5765760 4324320 240240 24570 839 7 8\ + ------- n + 1/1729728 n | C(n) 5765760 / and in Maple input form: (-2277/81920*n-3601/65536*n^2-4471/131072*n^3-997/131072*n^4-349/655360*n^5-1/ 131072*n^6)*4^n+(159/5720*n+116537/960960*n^2+1065217/5765760*n^3+537829/ 4324320*n^4+8963/240240*n^5+107/24570*n^6+839/5765760*n^7+1/1729728*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 16 1/2 15 14 1/2 13 12 1/2 11 m Pi m 839 m 2837 Pi m 107 m 43021 Pi m ------- - --------- + ------- - -------------- + ------- - --------------- 1729728 131072 5765760 5242880 24570 5242880 10 1/2 9 8 1/2 7 6 8963 m 44741 Pi m 537829 m 97855 Pi m 1065217 m + -------- - -------------- + --------- - -------------- + ---------- 240240 1048576 4324320 1048576 5765760 1/2 5 4 1/2 3 2 234909 Pi m 116537 m 20493 Pi m 159 m - --------------- + --------- - -------------- + ------ 2621440 960960 655360 5720 and in Maple input form: 1/1729728*m^16-1/131072*Pi^(1/2)*m^15+839/5765760*m^14-2837/5242880*Pi^(1/2)*m^ 13+107/24570*m^12-43021/5242880*Pi^(1/2)*m^11+8963/240240*m^10-44741/1048576*Pi ^(1/2)*m^9+537829/4324320*m^8-97855/1048576*Pi^(1/2)*m^7+1065217/5765760*m^6-\ 234909/2621440*Pi^(1/2)*m^5+116537/960960*m^4-20493/655360*Pi^(1/2)*m^3+159/ 5720*m^2 For the, 27, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[7, 6, 8, 5, 4, 2, 1, 3, 9, 10]}, {[8, 6, 5, 7, 3, 2, 4, 1, 9, 10]}, {[8, 7, 9, 10, 6, 5, 2, 1, 3, 4]}, {[8, 9, 7, 10, 6, 5, 3, 1, 2, 4]}, {[9, 7, 8, 10, 6, 5, 2, 3, 1, 4]}, {[9, 8, 10, 6, 7, 4, 5, 2, 1, 3]}, {[9, 10, 7, 6, 8, 4, 3, 5, 1, 2]}, {[10, 7, 6, 8, 9, 3, 2, 4, 5, 1]}, {[10, 7, 8, 6, 9, 4, 2, 3, 5, 1]}, {[10, 8, 6, 7, 9, 3, 4, 2, 5, 1]}, {[6, 5, 4, 3, 7, 2, 8, 1, 9, 10], [8, 6, 4, 3, 2, 1, 5, 7, 9, 10]}, {[6, 5, 4, 3, 7, 8, 9, 2, 10, 1], [10, 8, 4, 3, 2, 1, 5, 6, 7, 9]}, {[6, 5, 7, 4, 3, 2, 8, 1, 9, 10], [8, 6, 5, 4, 2, 1, 3, 7, 9, 10]}, {[6, 5, 7, 4, 8, 3, 2, 1, 9, 10], [8, 7, 6, 4, 2, 1, 3, 5, 9, 10]}, {[6, 5, 7, 4, 8, 9, 3, 2, 1, 10], [9, 8, 7, 4, 2, 1, 3, 5, 6, 10]}, {[6, 5, 7, 4, 8, 9, 10, 3, 2, 1], [10, 9, 8, 4, 2, 1, 3, 5, 6, 7]}, {[6, 5, 7, 8, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 2, 1, 3, 4, 6, 10]}, {[6, 5, 7, 8, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 2, 1, 3, 4, 6, 7]}, {[6, 5, 7, 8, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 2, 1, 3, 4, 5, 9]}, {[6, 5, 7, 8, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 2, 1, 3, 4, 5, 7]}, {[6, 7, 5, 4, 3, 8, 9, 2, 10, 1], [10, 8, 5, 4, 3, 1, 2, 6, 7, 9]}, {[6, 7, 5, 8, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 3, 1, 2, 4, 6, 10]}, {[6, 7, 5, 8, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 3, 1, 2, 4, 6, 7]}, {[6, 7, 5, 8, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 3, 1, 2, 4, 5, 9]}, {[6, 7, 5, 8, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 3, 1, 2, 4, 5, 7]}, {[6, 7, 8, 5, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 4, 1, 2, 3, 7, 9]}, {[6, 7, 8, 5, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 4, 1, 2, 3, 5, 9]}, {[6, 7, 8, 5, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 4, 1, 2, 3, 5, 7]}, {[7, 5, 4, 3, 2, 6, 8, 1, 9, 10], [8, 5, 4, 3, 2, 6, 1, 7, 9, 10]}, {[7, 5, 4, 6, 3, 2, 8, 1, 9, 10], [8, 6, 5, 3, 2, 4, 1, 7, 9, 10]}, {[7, 5, 4, 6, 8, 3, 2, 1, 9, 10], [8, 7, 6, 3, 2, 4, 1, 5, 9, 10]}, {[7, 5, 4, 6, 8, 9, 3, 2, 1, 10], [9, 8, 7, 3, 2, 4, 1, 5, 6, 10]}, {[7, 5, 4, 6, 8, 9, 10, 3, 2, 1], [10, 9, 8, 3, 2, 4, 1, 5, 6, 7]}, {[7, 5, 6, 4, 3, 8, 9, 2, 10, 1], [10, 8, 5, 4, 2, 3, 1, 6, 7, 9]}, {[7, 5, 6, 8, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 2, 3, 1, 4, 6, 10]}, {[7, 5, 6, 8, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 2, 3, 1, 4, 6, 7]}, {[7, 5, 6, 8, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 2, 3, 1, 4, 5, 9]}, {[7, 5, 6, 8, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 2, 3, 1, 4, 5, 7]}, {[7, 6, 4, 3, 5, 2, 8, 1, 9, 10], [8, 6, 4, 3, 5, 2, 1, 7, 9, 10]}, {[7, 6, 4, 5, 3, 8, 9, 2, 10, 1], [10, 8, 5, 3, 4, 2, 1, 6, 7, 9]}, {[7, 6, 5, 3, 2, 4, 8, 1, 9, 10], [8, 5, 4, 6, 3, 2, 1, 7, 9, 10]}, {[7, 6, 5, 3, 4, 8, 9, 2, 10, 1], [10, 8, 4, 5, 3, 2, 1, 6, 7, 9]}, {[7, 6, 5, 4, 8, 2, 1, 3, 9, 10], [7, 6, 8, 4, 3, 2, 1, 5, 9, 10]}, {[7, 6, 5, 4, 8, 3, 9, 1, 2, 10], [8, 9, 6, 4, 3, 2, 1, 5, 7, 10]}, {[7, 6, 5, 4, 8, 3, 9, 10, 1, 2], [9, 10, 6, 4, 3, 2, 1, 5, 7, 8]}, {[7, 6, 5, 4, 8, 9, 2, 1, 3, 10], [8, 7, 9, 4, 3, 2, 1, 5, 6, 10]}, {[7, 6, 5, 4, 8, 9, 2, 3, 10, 1], [10, 7, 8, 4, 3, 2, 1, 5, 6, 9]}, {[7, 6, 5, 4, 8, 9, 3, 10, 1, 2], [9, 10, 7, 4, 3, 2, 1, 5, 6, 8]}, {[7, 6, 5, 4, 8, 9, 10, 2, 1, 3], [9, 8, 10, 4, 3, 2, 1, 5, 6, 7]}, {[7, 6, 8, 4, 3, 5, 2, 1, 9, 10], [8, 7, 5, 4, 6, 2, 1, 3, 9, 10]}, {[7, 6, 8, 4, 5, 9, 3, 2, 1, 10], [9, 8, 7, 4, 5, 2, 1, 3, 6, 10]}, {[7, 6, 8, 4, 5, 9, 10, 3, 2, 1], [10, 9, 8, 4, 5, 2, 1, 3, 6, 7]}, {[7, 6, 8, 5, 3, 2, 4, 1, 9, 10], [8, 6, 5, 7, 4, 2, 1, 3, 9, 10]}, {[7, 6, 8, 5, 4, 3, 9, 1, 2, 10], [8, 9, 6, 5, 4, 2, 1, 3, 7, 10]}, {[7, 6, 8, 5, 4, 3, 9, 10, 1, 2], [9, 10, 6, 5, 4, 2, 1, 3, 7, 8]}, {[7, 6, 8, 5, 9, 3, 4, 2, 1, 10], [9, 8, 6, 7, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 4, 2, 3, 1, 10], [9, 7, 8, 6, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 4, 3, 1, 2, 10], [8, 9, 7, 6, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 10, 3, 4, 2, 1], [10, 9, 7, 8, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 5, 9, 10, 4, 2, 3, 1], [10, 8, 9, 7, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 5, 9, 10, 4, 3, 1, 2], [9, 10, 8, 7, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 9, 4, 3, 2, 1, 5, 10], [8, 7, 6, 5, 9, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 4, 3, 5, 2, 1, 10], [9, 8, 6, 5, 7, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 4, 5, 3, 2, 10, 1], [10, 8, 7, 5, 6, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 4, 5, 10, 3, 2, 1], [10, 9, 8, 5, 6, 2, 1, 3, 4, 7]}, {[7, 6, 8, 9, 5, 3, 2, 4, 1, 10], [9, 7, 6, 8, 5, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 5, 3, 4, 2, 10, 1], [10, 8, 6, 7, 5, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 5, 4, 2, 1, 3, 10], [8, 7, 9, 6, 5, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 5, 4, 2, 3, 10, 1], [10, 7, 8, 6, 5, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 5, 4, 3, 10, 1, 2], [9, 10, 7, 6, 5, 2, 1, 3, 4, 8]}, {[7, 6, 8, 9, 5, 10, 3, 4, 2, 1], [10, 9, 7, 8, 5, 2, 1, 3, 4, 6]}, {[7, 6, 8, 9, 5, 10, 4, 2, 3, 1], [10, 8, 9, 7, 5, 2, 1, 3, 4, 6]}, {[7, 6, 8, 9, 5, 10, 4, 3, 1, 2], [9, 10, 8, 7, 5, 2, 1, 3, 4, 6]}, {[7, 6, 8, 9, 10, 4, 3, 2, 1, 5], [9, 8, 7, 6, 10, 2, 1, 3, 4, 5]}, {[7, 6, 8, 9, 10, 4, 3, 5, 2, 1], [10, 9, 7, 6, 8, 2, 1, 3, 4, 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[10, 8, 6, 7, 9, 4, 3, 5, 1, 2]}, {[9, 10, 7, 6, 8, 4, 2, 3, 5, 1], [10, 7, 8, 6, 9, 4, 3, 5, 1, 2]}, {[9, 10, 7, 8, 4, 3, 5, 2, 6, 1], [10, 8, 6, 5, 7, 9, 3, 4, 1, 2]}, {[9, 10, 7, 8, 5, 3, 2, 4, 6, 1], [10, 7, 6, 8, 5, 9, 3, 4, 1, 2]}, {[9, 10, 8, 4, 3, 5, 2, 6, 7, 1], [10, 7, 5, 4, 6, 8, 9, 3, 1, 2]}, {[9, 10, 8, 4, 3, 5, 6, 2, 7, 1], [10, 8, 5, 4, 6, 7, 9, 3, 1, 2]}, {[9, 10, 8, 4, 5, 3, 6, 2, 7, 1], [10, 8, 6, 4, 5, 7, 9, 3, 1, 2]}, {[9, 10, 8, 5, 3, 2, 4, 6, 7, 1], [10, 6, 5, 7, 4, 8, 9, 3, 1, 2]}, {[9, 10, 8, 5, 3, 4, 6, 2, 7, 1], [10, 8, 5, 6, 4, 7, 9, 3, 1, 2]}, {[9, 10, 8, 5, 4, 6, 2, 3, 7, 1], [10, 7, 8, 5, 4, 6, 9, 3, 1, 2]}, {[9, 10, 8, 5, 6, 3, 2, 4, 7, 1], [10, 7, 6, 8, 4, 5, 9, 3, 1, 2]}, {[9, 10, 8, 6, 3, 2, 4, 5, 7, 1], [10, 6, 5, 7, 8, 4, 9, 3, 1, 2]}, {[9, 10, 8, 6, 3, 4, 2, 5, 7, 1], [10, 7, 5, 6, 8, 4, 9, 3, 1, 2]}, {[9, 10, 8, 6, 4, 2, 3, 5, 7, 1], [10, 6, 7, 5, 8, 4, 9, 3, 1, 2]}, {[10, 5, 4, 6, 3, 7, 8, 9, 2, 1], [10, 9, 5, 3, 2, 4, 6, 7, 8, 1]}, {[10, 5, 4, 6, 7, 3, 8, 9, 2, 1], [10, 9, 6, 3, 2, 4, 5, 7, 8, 1]}, {[10, 5, 4, 6, 7, 8, 3, 9, 2, 1], [10, 9, 7, 3, 2, 4, 5, 6, 8, 1]}, {[10, 5, 6, 4, 7, 3, 8, 9, 2, 1], [10, 9, 6, 4, 2, 3, 5, 7, 8, 1]}, {[10, 5, 6, 4, 7, 8, 3, 9, 2, 1], [10, 9, 7, 4, 2, 3, 5, 6, 8, 1]}, {[10, 5, 6, 7, 4, 8, 3, 9, 2, 1], [10, 9, 7, 5, 2, 3, 4, 6, 8, 1]}, {[10, 6, 4, 3, 5, 7, 8, 9, 2, 1], [10, 9, 4, 3, 5, 2, 6, 7, 8, 1]}, {[10, 6, 4, 5, 7, 3, 8, 9, 2, 1], [10, 9, 6, 3, 4, 2, 5, 7, 8, 1]}, {[10, 6, 4, 5, 7, 8, 3, 9, 2, 1], [10, 9, 7, 3, 4, 2, 5, 6, 8, 1]}, {[10, 6, 5, 7, 3, 4, 8, 9, 2, 1], [10, 9, 5, 6, 3, 2, 4, 7, 8, 1]}, {[10, 6, 5, 7, 4, 8, 9, 2, 3, 1], [10, 8, 9, 5, 3, 2, 4, 6, 7, 1]}, {[10, 6, 5, 7, 8, 3, 4, 9, 2, 1], [10, 9, 6, 7, 3, 2, 4, 5, 8, 1]}, {[10, 6, 5, 7, 8, 4, 9, 2, 3, 1], [10, 8, 9, 6, 3, 2, 4, 5, 7, 1]}, {[10, 6, 5, 7, 8, 9, 3, 2, 4, 1], [10, 8, 7, 9, 3, 2, 4, 5, 6, 1]}, {[10, 6, 7, 4, 3, 5, 8, 9, 2, 1], [10, 9, 5, 4, 6, 2, 3, 7, 8, 1]}, {[10, 6, 7, 4, 5, 8, 3, 9, 2, 1], [10, 9, 7, 4, 5, 2, 3, 6, 8, 1]}, {[10, 6, 7, 5, 8, 3, 4, 9, 2, 1], [10, 9, 6, 7, 4, 2, 3, 5, 8, 1]}, {[10, 6, 7, 5, 8, 4, 9, 2, 3, 1], [10, 8, 9, 6, 4, 2, 3, 5, 7, 1]}, {[10, 6, 7, 5, 8, 9, 3, 2, 4, 1], [10, 8, 7, 9, 4, 2, 3, 5, 6, 1]}, {[10, 6, 7, 8, 4, 3, 5, 9, 2, 1], [10, 9, 6, 5, 7, 2, 3, 4, 8, 1]}, {[10, 6, 7, 8, 5, 9, 3, 2, 4, 1], [10, 8, 7, 9, 5, 2, 3, 4, 6, 1]}, {[10, 7, 4, 3, 5, 6, 8, 9, 2, 1], [10, 9, 4, 3, 5, 6, 2, 7, 8, 1]}, {[10, 7, 4, 5, 3, 6, 8, 9, 2, 1], [10, 9, 5, 3, 4, 6, 2, 7, 8, 1]}, {[10, 7, 4, 5, 6, 8, 3, 9, 2, 1], [10, 9, 7, 3, 4, 5, 2, 6, 8, 1]}, {[10, 7, 5, 3, 4, 6, 8, 9, 2, 1], [10, 9, 4, 5, 3, 6, 2, 7, 8, 1]}, {[10, 7, 5, 4, 6, 8, 9, 2, 3, 1], [10, 8, 9, 4, 3, 5, 2, 6, 7, 1]}, {[10, 7, 5, 6, 8, 3, 4, 9, 2, 1], [10, 9, 6, 7, 3, 4, 2, 5, 8, 1]}, {[10, 7, 5, 6, 8, 4, 9, 2, 3, 1], [10, 8, 9, 6, 3, 4, 2, 5, 7, 1]}, {[10, 7, 5, 6, 8, 9, 3, 2, 4, 1], [10, 8, 7, 9, 3, 4, 2, 5, 6, 1]}, {[10, 7, 6, 8, 3, 4, 5, 9, 2, 1], [10, 9, 5, 6, 7, 3, 2, 4, 8, 1]}, {[10, 7, 6, 8, 4, 5, 9, 2, 3, 1], [10, 8, 9, 5, 6, 3, 2, 4, 7, 1]}, {[10, 7, 6, 8, 5, 9, 2, 3, 4, 1], [10, 7, 8, 9, 5, 3, 2, 4, 6, 1]}, {[10, 7, 6, 8, 9, 3, 4, 2, 5, 1], [10, 8, 6, 7, 9, 3, 2, 4, 5, 1]}, {[10, 7, 6, 8, 9, 4, 2, 3, 5, 1], [10, 7, 8, 6, 9, 3, 2, 4, 5, 1]}, {[10, 7, 8, 4, 3, 5, 6, 9, 2, 1], [10, 9, 5, 4, 6, 7, 2, 3, 8, 1]}, {[10, 7, 8, 4, 5, 3, 6, 9, 2, 1], [10, 9, 6, 4, 5, 7, 2, 3, 8, 1]}, {[10, 7, 8, 5, 3, 4, 6, 9, 2, 1], [10, 9, 5, 6, 4, 7, 2, 3, 8, 1]}, {[10, 7, 8, 5, 4, 6, 9, 2, 3, 1], [10, 8, 9, 5, 4, 6, 2, 3, 7, 1]}, {[10, 7, 8, 5, 6, 9, 3, 2, 4, 1], [10, 8, 7, 9, 4, 5, 2, 3, 6, 1]}, {[10, 7, 8, 6, 9, 3, 4, 2, 5, 1], [10, 8, 6, 7, 9, 4, 2, 3, 5, 1]}, {[10, 7, 8, 9, 4, 3, 5, 2, 6, 1], [10, 8, 6, 5, 7, 9, 2, 3, 4, 1]}, {[10, 8, 4, 3, 5, 6, 7, 9, 2, 1], [10, 9, 4, 3, 5, 6, 7, 2, 8, 1]}, {[10, 8, 4, 5, 3, 6, 7, 9, 2, 1], [10, 9, 5, 3, 4, 6, 7, 2, 8, 1]}, {[10, 8, 4, 5, 6, 3, 7, 9, 2, 1], [10, 9, 6, 3, 4, 5, 7, 2, 8, 1]}, {[10, 8, 5, 3, 4, 6, 7, 9, 2, 1], [10, 9, 4, 5, 3, 6, 7, 2, 8, 1]}, {[10, 8, 5, 4, 6, 7, 9, 2, 3, 1], [10, 8, 9, 4, 3, 5, 6, 2, 7, 1]}, {[10, 8, 5, 6, 3, 4, 7, 9, 2, 1], [10, 9, 5, 6, 3, 4, 7, 2, 8, 1]}, {[10, 8, 5, 6, 4, 7, 9, 2, 3, 1], [10, 8, 9, 5, 3, 4, 6, 2, 7, 1]}, {[10, 8, 5, 6, 7, 9, 3, 2, 4, 1], [10, 8, 7, 9, 3, 4, 5, 2, 6, 1]}, {[10, 8, 6, 3, 4, 5, 7, 9, 2, 1], [10, 9, 4, 5, 6, 3, 7, 2, 8, 1]}, {[10, 8, 6, 4, 5, 7, 9, 2, 3, 1], [10, 8, 9, 4, 5, 3, 6, 2, 7, 1]}, { [6, 5, 4, 3, 7, 2, 8, 9, 1, 10], [6, 5, 4, 3, 7, 2, 8, 9, 10, 1], [9, 6, 4, 3, 2, 1, 5, 7, 8, 10], [10, 6, 4, 3, 2, 1, 5, 7, 8, 9]}, { [6, 5, 4, 3, 7, 8, 2, 9, 1, 10], [6, 5, 4, 3, 7, 8, 2, 9, 10, 1], [9, 7, 4, 3, 2, 1, 5, 6, 8, 10], [10, 7, 4, 3, 2, 1, 5, 6, 8, 9]}, { [6, 5, 7, 4, 3, 2, 8, 9, 1, 10], [6, 5, 7, 4, 3, 2, 8, 9, 10, 1], [9, 6, 5, 4, 2, 1, 3, 7, 8, 10], [10, 6, 5, 4, 2, 1, 3, 7, 8, 9]}, { [6, 5, 7, 8, 4, 3, 2, 9, 1, 10], [6, 5, 7, 8, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 2, 1, 3, 4, 8, 10], [10, 7, 6, 5, 2, 1, 3, 4, 8, 9]}, { [6, 7, 5, 4, 3, 8, 2, 9, 1, 10], [6, 7, 5, 4, 3, 8, 2, 9, 10, 1], [9, 7, 5, 4, 3, 1, 2, 6, 8, 10], [10, 7, 5, 4, 3, 1, 2, 6, 8, 9]}, { [6, 7, 5, 8, 4, 3, 2, 9, 1, 10], [6, 7, 5, 8, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 3, 1, 2, 4, 8, 10], [10, 7, 6, 5, 3, 1, 2, 4, 8, 9]}, { [7, 5, 4, 3, 2, 6, 8, 9, 1, 10], [7, 5, 4, 3, 2, 6, 8, 9, 10, 1], [9, 5, 4, 3, 2, 6, 1, 7, 8, 10], [10, 5, 4, 3, 2, 6, 1, 7, 8, 9]}, { [7, 5, 4, 6, 3, 2, 8, 9, 1, 10], [7, 5, 4, 6, 3, 2, 8, 9, 10, 1], [9, 6, 5, 3, 2, 4, 1, 7, 8, 10], [10, 6, 5, 3, 2, 4, 1, 7, 8, 9]}, { [7, 5, 6, 4, 3, 8, 2, 9, 1, 10], [7, 5, 6, 4, 3, 8, 2, 9, 10, 1], [9, 7, 5, 4, 2, 3, 1, 6, 8, 10], [10, 7, 5, 4, 2, 3, 1, 6, 8, 9]}, { [7, 5, 6, 8, 4, 3, 2, 9, 1, 10], [7, 5, 6, 8, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 2, 3, 1, 4, 8, 10], [10, 7, 6, 5, 2, 3, 1, 4, 8, 9]}, { [7, 6, 4, 3, 5, 2, 8, 9, 1, 10], [7, 6, 4, 3, 5, 2, 8, 9, 10, 1], [9, 6, 4, 3, 5, 2, 1, 7, 8, 10], [10, 6, 4, 3, 5, 2, 1, 7, 8, 9]}, { [7, 6, 4, 5, 3, 8, 2, 9, 1, 10], [7, 6, 4, 5, 3, 8, 2, 9, 10, 1], [9, 7, 5, 3, 4, 2, 1, 6, 8, 10], [10, 7, 5, 3, 4, 2, 1, 6, 8, 9]}, { [7, 6, 5, 3, 2, 4, 8, 9, 1, 10], [7, 6, 5, 3, 2, 4, 8, 9, 10, 1], [9, 5, 4, 6, 3, 2, 1, 7, 8, 10], [10, 5, 4, 6, 3, 2, 1, 7, 8, 9]}, { [7, 6, 5, 3, 4, 8, 2, 9, 1, 10], [7, 6, 5, 3, 4, 8, 2, 9, 10, 1], [9, 7, 4, 5, 3, 2, 1, 6, 8, 10], [10, 7, 4, 5, 3, 2, 1, 6, 8, 9]}, { [7, 6, 5, 4, 8, 2, 3, 9, 1, 10], [7, 6, 5, 4, 8, 2, 3, 9, 10, 1], [9, 6, 7, 4, 3, 2, 1, 5, 8, 10], [10, 6, 7, 4, 3, 2, 1, 5, 8, 9]}, { [7, 6, 8, 4, 5, 3, 2, 9, 1, 10], [7, 6, 8, 4, 5, 3, 2, 9, 10, 1], [9, 7, 6, 4, 5, 2, 1, 3, 8, 10], [10, 7, 6, 4, 5, 2, 1, 3, 8, 9]}, { [7, 6, 8, 5, 3, 4, 2, 9, 1, 10], [7, 6, 8, 5, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 4, 2, 1, 3, 8, 10], [10, 7, 5, 6, 4, 2, 1, 3, 8, 9]}, { [7, 6, 8, 5, 4, 2, 3, 9, 1, 10], [7, 6, 8, 5, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 4, 2, 1, 3, 8, 10], [10, 6, 7, 5, 4, 2, 1, 3, 8, 9]}, { [7, 8, 5, 4, 3, 2, 6, 9, 1, 10], [7, 8, 5, 4, 3, 2, 6, 9, 10, 1], [9, 6, 5, 4, 3, 7, 1, 2, 8, 10], [10, 6, 5, 4, 3, 7, 1, 2, 8, 9]}, { [7, 8, 5, 4, 6, 3, 2, 9, 1, 10], [7, 8, 5, 4, 6, 3, 2, 9, 10, 1], [9, 7, 6, 4, 3, 5, 1, 2, 8, 10], [10, 7, 6, 4, 3, 5, 1, 2, 8, 9]}, { [7, 8, 6, 4, 3, 5, 2, 9, 1, 10], [7, 8, 6, 4, 3, 5, 2, 9, 10, 1], [9, 7, 5, 4, 6, 3, 1, 2, 8, 10], [10, 7, 5, 4, 6, 3, 1, 2, 8, 9]}, { [7, 8, 6, 5, 3, 2, 4, 9, 1, 10], [7, 8, 6, 5, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 4, 3, 1, 2, 8, 10], [10, 6, 5, 7, 4, 3, 1, 2, 8, 9]}, { [8, 5, 4, 3, 2, 6, 7, 9, 1, 10], [8, 5, 4, 3, 2, 6, 7, 9, 10, 1], [9, 5, 4, 3, 2, 6, 7, 1, 8, 10], [10, 5, 4, 3, 2, 6, 7, 1, 8, 9]}, { [8, 5, 4, 6, 7, 3, 2, 9, 1, 10], [8, 5, 4, 6, 7, 3, 2, 9, 10, 1], [9, 7, 6, 3, 2, 4, 5, 1, 8, 10], [10, 7, 6, 3, 2, 4, 5, 1, 8, 9]}, { [8, 5, 6, 4, 3, 2, 7, 9, 1, 10], [8, 5, 6, 4, 3, 2, 7, 9, 10, 1], [9, 6, 5, 4, 2, 3, 7, 1, 8, 10], [10, 6, 5, 4, 2, 3, 7, 1, 8, 9]}, { [8, 5, 6, 4, 7, 3, 2, 9, 1, 10], [8, 5, 6, 4, 7, 3, 2, 9, 10, 1], [9, 7, 6, 4, 2, 3, 5, 1, 8, 10], [10, 7, 6, 4, 2, 3, 5, 1, 8, 9]}, { [8, 6, 4, 5, 3, 2, 7, 9, 1, 10], [8, 6, 4, 5, 3, 2, 7, 9, 10, 1], [9, 6, 5, 3, 4, 2, 7, 1, 8, 10], [10, 6, 5, 3, 4, 2, 7, 1, 8, 9]}, { [8, 6, 4, 5, 7, 3, 2, 9, 1, 10], [8, 6, 4, 5, 7, 3, 2, 9, 10, 1], [9, 7, 6, 3, 4, 2, 5, 1, 8, 10], [10, 7, 6, 3, 4, 2, 5, 1, 8, 9]}, { [8, 6, 5, 3, 4, 2, 7, 9, 1, 10], [8, 6, 5, 3, 4, 2, 7, 9, 10, 1], [9, 6, 4, 5, 3, 2, 7, 1, 8, 10], [10, 6, 4, 5, 3, 2, 7, 1, 8, 9]}, { [8, 6, 5, 4, 2, 3, 7, 9, 1, 10], [8, 6, 5, 4, 2, 3, 7, 9, 10, 1], [9, 5, 6, 4, 3, 2, 7, 1, 8, 10], [10, 5, 6, 4, 3, 2, 7, 1, 8, 9]}, { [8, 6, 5, 7, 3, 4, 2, 9, 1, 10], [8, 6, 5, 7, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 3, 2, 4, 1, 8, 10], [10, 7, 5, 6, 3, 2, 4, 1, 8, 9]}, { [8, 6, 5, 7, 4, 2, 3, 9, 1, 10], [8, 6, 5, 7, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 3, 2, 4, 1, 8, 10], [10, 6, 7, 5, 3, 2, 4, 1, 8, 9]}, { [8, 6, 7, 4, 3, 5, 2, 9, 1, 10], [8, 6, 7, 4, 3, 5, 2, 9, 10, 1], [9, 7, 5, 4, 6, 2, 3, 1, 8, 10], [10, 7, 5, 4, 6, 2, 3, 1, 8, 9]}, { [8, 6, 7, 5, 3, 2, 4, 9, 1, 10], [8, 6, 7, 5, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 4, 2, 3, 1, 8, 10], [10, 6, 5, 7, 4, 2, 3, 1, 8, 9]}, { [8, 7, 4, 3, 5, 6, 2, 9, 1, 10], [8, 7, 4, 3, 5, 6, 2, 9, 10, 1], [9, 7, 4, 3, 5, 6, 2, 1, 8, 10], [10, 7, 4, 3, 5, 6, 2, 1, 8, 9]}, { [8, 7, 4, 5, 3, 6, 2, 9, 1, 10], [8, 7, 4, 5, 3, 6, 2, 9, 10, 1], [9, 7, 5, 3, 4, 6, 2, 1, 8, 10], [10, 7, 5, 3, 4, 6, 2, 1, 8, 9]}, { [8, 7, 5, 3, 4, 6, 2, 9, 1, 10], [8, 7, 5, 3, 4, 6, 2, 9, 10, 1], [9, 7, 4, 5, 3, 6, 2, 1, 8, 10], [10, 7, 4, 5, 3, 6, 2, 1, 8, 9]}, { [8, 7, 5, 4, 6, 2, 3, 9, 1, 10], [8, 7, 5, 4, 6, 2, 3, 9, 10, 1], [9, 6, 7, 4, 3, 5, 2, 1, 8, 10], [10, 6, 7, 4, 3, 5, 2, 1, 8, 9]}, { [8, 7, 5, 6, 3, 2, 4, 9, 1, 10], [8, 7, 5, 6, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 3, 4, 2, 1, 8, 10], [10, 6, 5, 7, 3, 4, 2, 1, 8, 9]}, { [8, 7, 6, 3, 2, 4, 5, 9, 1, 10], [8, 7, 6, 3, 2, 4, 5, 9, 10, 1], [9, 5, 4, 6, 7, 3, 2, 1, 8, 10], [10, 5, 4, 6, 7, 3, 2, 1, 8, 9]}, { [8, 7, 6, 3, 4, 2, 5, 9, 1, 10], [8, 7, 6, 3, 4, 2, 5, 9, 10, 1], [9, 6, 4, 5, 7, 3, 2, 1, 8, 10], [10, 6, 4, 5, 7, 3, 2, 1, 8, 9]}, { [8, 7, 6, 4, 2, 3, 5, 9, 1, 10], [8, 7, 6, 4, 2, 3, 5, 9, 10, 1], [9, 5, 6, 4, 7, 3, 2, 1, 8, 10], [10, 5, 6, 4, 7, 3, 2, 1, 8, 9]}} is given by the following expression / 101 235 2 169 3 397 4 83 5 6\ n / |----- n + ------ n - ----- n - ------ n - ------ n - 1/294912 n | 4 + | \61440 147456 98304 294912 491520 / \ 4007 2 9143 3 77141 4 2281 5 9511 6 -7/4290 n - ------ n - ------- n + -------- n + ------ n + ------- n 720720 2882880 17297280 480480 8648640 23 7 8\ + ------ n + 1/3459456 n | C(n) 411840 / and in Maple input form: (101/61440*n+235/147456*n^2-169/98304*n^3-397/294912*n^4-83/491520*n^5-1/294912 *n^6)*4^n+(-7/4290*n-4007/720720*n^2-9143/2882880*n^3+77141/17297280*n^4+2281/ 480480*n^5+9511/8648640*n^6+23/411840*n^7+1/3459456*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 16 1/2 15 14 1/2 13 12 1/2 11 m Pi m 23 m 679 Pi m 9511 m 18121 Pi m ------- - --------- + ------ - ------------- + -------- - --------------- 3459456 294912 411840 3932160 8648640 11796480 10 1/2 9 8 1/2 7 6 2281 m 2543 Pi m 77141 m 803 Pi m 9143 m + -------- - ------------- + -------- - ------------ - ------- 480480 786432 17297280 2359296 2882880 1/2 5 4 1/2 3 2 6757 Pi m 4007 m 303 Pi m 7 m + ------------- - ------- + ------------ - ---- 1966080 720720 163840 4290 and in Maple input form: 1/3459456*m^16-1/294912*Pi^(1/2)*m^15+23/411840*m^14-679/3932160*Pi^(1/2)*m^13+ 9511/8648640*m^12-18121/11796480*Pi^(1/2)*m^11+2281/480480*m^10-2543/786432*Pi^ (1/2)*m^9+77141/17297280*m^8-803/2359296*Pi^(1/2)*m^7-9143/2882880*m^6+6757/ 1966080*Pi^(1/2)*m^5-4007/720720*m^4+303/163840*Pi^(1/2)*m^3-7/4290*m^2 For the, 28, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[7, 6, 5, 8, 3, 2, 1, 4, 9, 10]}, {[8, 6, 4, 3, 5, 2, 7, 1, 9, 10]}, {[8, 7, 6, 9, 10, 3, 2, 1, 4, 5]}, {[8, 9, 7, 6, 10, 4, 3, 1, 2, 5]}, {[9, 6, 4, 3, 5, 2, 7, 8, 1, 10]}, {[9, 7, 4, 3, 5, 6, 2, 8, 1, 10]}, {[9, 7, 8, 6, 10, 4, 2, 3, 1, 5]}, {[9, 8, 6, 7, 10, 3, 4, 2, 1, 5]}, {[9, 10, 7, 5, 4, 6, 3, 8, 1, 2]}, {[10, 6, 4, 3, 5, 2, 7, 8, 9, 1]}, {[10, 7, 4, 3, 5, 6, 2, 8, 9, 1]}, {[10, 7, 8, 5, 4, 6, 2, 3, 9, 1]}, {[10, 8, 4, 3, 5, 6, 7, 2, 9, 1]}, {[10, 8, 5, 6, 3, 4, 7, 2, 9, 1]}, {[6, 5, 4, 7, 3, 2, 8, 1, 9, 10], [8, 6, 5, 3, 2, 1, 4, 7, 9, 10]}, {[6, 5, 4, 7, 3, 8, 2, 1, 9, 10], [8, 7, 5, 3, 2, 1, 4, 6, 9, 10]}, {[6, 5, 4, 7, 3, 8, 9, 2, 1, 10], [9, 8, 5, 3, 2, 1, 4, 6, 7, 10]}, {[6, 5, 4, 7, 3, 8, 9, 10, 2, 1], [10, 9, 5, 3, 2, 1, 4, 6, 7, 8]}, {[6, 5, 4, 7, 8, 3, 9, 2, 1, 10], [9, 8, 6, 3, 2, 1, 4, 5, 7, 10]}, {[6, 5, 4, 7, 8, 3, 9, 10, 2, 1], [10, 9, 6, 3, 2, 1, 4, 5, 7, 8]}, {[6, 5, 4, 7, 8, 9, 3, 2, 10, 1], [10, 8, 7, 3, 2, 1, 4, 5, 6, 9]}, {[6, 5, 4, 7, 8, 9, 3, 10, 2, 1], [10, 9, 7, 3, 2, 1, 4, 5, 6, 8]}, {[6, 5, 7, 4, 3, 8, 2, 1, 9, 10], [8, 7, 5, 4, 2, 1, 3, 6, 9, 10]}, {[6, 5, 7, 4, 3, 8, 9, 2, 1, 10], [9, 8, 5, 4, 2, 1, 3, 6, 7, 10]}, {[6, 5, 7, 4, 3, 8, 9, 10, 2, 1], [10, 9, 5, 4, 2, 1, 3, 6, 7, 8]}, {[6, 5, 7, 8, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 2, 1, 3, 4, 7, 10]}, {[6, 5, 7, 8, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 2, 1, 3, 4, 7, 8]}, {[6, 5, 7, 8, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 2, 1, 3, 4, 5, 8]}, {[6, 7, 5, 4, 8, 3, 9, 2, 1, 10], [9, 8, 6, 4, 3, 1, 2, 5, 7, 10]}, {[6, 7, 5, 4, 8, 3, 9, 10, 2, 1], [10, 9, 6, 4, 3, 1, 2, 5, 7, 8]}, {[6, 7, 5, 4, 8, 9, 3, 2, 10, 1], [10, 8, 7, 4, 3, 1, 2, 5, 6, 9]}, {[6, 7, 5, 4, 8, 9, 3, 10, 2, 1], [10, 9, 7, 4, 3, 1, 2, 5, 6, 8]}, {[6, 7, 5, 8, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 3, 1, 2, 4, 7, 10]}, {[6, 7, 5, 8, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 3, 1, 2, 4, 7, 8]}, {[6, 7, 5, 8, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 3, 1, 2, 4, 5, 8]}, {[6, 7, 8, 5, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 4, 1, 2, 3, 6, 9]}, {[6, 7, 8, 5, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 4, 1, 2, 3, 6, 8]}, {[6, 7, 8, 5, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 4, 1, 2, 3, 5, 8]}, {[7, 5, 4, 3, 6, 2, 8, 1, 9, 10], [8, 6, 4, 3, 2, 5, 1, 7, 9, 10]}, {[7, 5, 4, 3, 6, 8, 2, 1, 9, 10], [8, 7, 4, 3, 2, 5, 1, 6, 9, 10]}, {[7, 5, 4, 3, 6, 8, 9, 2, 1, 10], [9, 8, 4, 3, 2, 5, 1, 6, 7, 10]}, {[7, 5, 4, 3, 6, 8, 9, 10, 2, 1], [10, 9, 4, 3, 2, 5, 1, 6, 7, 8]}, {[7, 5, 4, 6, 3, 8, 2, 1, 9, 10], [8, 7, 5, 3, 2, 4, 1, 6, 9, 10]}, {[7, 5, 4, 6, 3, 8, 9, 2, 1, 10], [9, 8, 5, 3, 2, 4, 1, 6, 7, 10]}, {[7, 5, 4, 6, 3, 8, 9, 10, 2, 1], [10, 9, 5, 3, 2, 4, 1, 6, 7, 8]}, {[7, 5, 6, 4, 8, 3, 9, 2, 1, 10], [9, 8, 6, 4, 2, 3, 1, 5, 7, 10]}, {[7, 5, 6, 4, 8, 3, 9, 10, 2, 1], [10, 9, 6, 4, 2, 3, 1, 5, 7, 8]}, {[7, 5, 6, 4, 8, 9, 3, 2, 10, 1], [10, 8, 7, 4, 2, 3, 1, 5, 6, 9]}, {[7, 5, 6, 4, 8, 9, 3, 10, 2, 1], [10, 9, 7, 4, 2, 3, 1, 5, 6, 8]}, {[7, 5, 6, 8, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 2, 3, 1, 4, 7, 10]}, {[7, 5, 6, 8, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 2, 3, 1, 4, 7, 8]}, {[7, 5, 6, 8, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 2, 3, 1, 4, 5, 8]}, {[7, 6, 4, 3, 2, 5, 8, 1, 9, 10], [8, 5, 4, 3, 6, 2, 1, 7, 9, 10]}, {[7, 6, 4, 3, 5, 8, 2, 1, 9, 10], [8, 7, 4, 3, 5, 2, 1, 6, 9, 10]}, {[7, 6, 4, 3, 5, 8, 9, 2, 1, 10], [9, 8, 4, 3, 5, 2, 1, 6, 7, 10]}, {[7, 6, 4, 3, 5, 8, 9, 10, 2, 1], [10, 9, 4, 3, 5, 2, 1, 6, 7, 8]}, {[7, 6, 4, 5, 8, 3, 9, 2, 1, 10], [9, 8, 6, 3, 4, 2, 1, 5, 7, 10]}, {[7, 6, 4, 5, 8, 3, 9, 10, 2, 1], [10, 9, 6, 3, 4, 2, 1, 5, 7, 8]}, {[7, 6, 4, 5, 8, 9, 3, 2, 10, 1], [10, 8, 7, 3, 4, 2, 1, 5, 6, 9]}, {[7, 6, 4, 5, 8, 9, 3, 10, 2, 1], [10, 9, 7, 3, 4, 2, 1, 5, 6, 8]}, {[7, 6, 5, 8, 3, 2, 4, 1, 9, 10], [8, 6, 5, 7, 3, 2, 1, 4, 9, 10]}, {[7, 6, 5, 8, 3, 4, 9, 2, 1, 10], [9, 8, 5, 6, 3, 2, 1, 4, 7, 10]}, {[7, 6, 5, 8, 3, 4, 9, 10, 2, 1], [10, 9, 5, 6, 3, 2, 1, 4, 7, 8]}, {[7, 6, 5, 8, 4, 2, 1, 3, 9, 10], [7, 6, 8, 5, 3, 2, 1, 4, 9, 10]}, {[7, 6, 5, 8, 4, 3, 9, 1, 2, 10], [8, 9, 6, 5, 3, 2, 1, 4, 7, 10]}, {[7, 6, 5, 8, 4, 3, 9, 10, 1, 2], [9, 10, 6, 5, 3, 2, 1, 4, 7, 8]}, {[7, 6, 5, 8, 4, 9, 2, 3, 1, 10], [9, 7, 8, 5, 3, 2, 1, 4, 6, 10]}, {[7, 6, 5, 8, 4, 9, 3, 1, 2, 10], [8, 9, 7, 5, 3, 2, 1, 4, 6, 10]}, {[7, 6, 5, 8, 4, 9, 10, 2, 3, 1], [10, 8, 9, 5, 3, 2, 1, 4, 6, 7]}, {[7, 6, 5, 8, 4, 9, 10, 3, 1, 2], [9, 10, 8, 5, 3, 2, 1, 4, 6, 7]}, {[7, 6, 5, 8, 9, 3, 2, 1, 4, 10], [8, 7, 6, 9, 3, 2, 1, 4, 5, 10]}, {[7, 6, 5, 8, 9, 3, 2, 4, 1, 10], [9, 7, 6, 8, 3, 2, 1, 4, 5, 10]}, {[7, 6, 5, 8, 9, 3, 4, 2, 10, 1], [10, 8, 6, 7, 3, 2, 1, 4, 5, 9]}, {[7, 6, 5, 8, 9, 3, 4, 10, 2, 1], [10, 9, 6, 7, 3, 2, 1, 4, 5, 8]}, {[7, 6, 5, 8, 9, 4, 2, 1, 3, 10], [8, 7, 9, 6, 3, 2, 1, 4, 5, 10]}, {[7, 6, 5, 8, 9, 4, 2, 3, 10, 1], [10, 7, 8, 6, 3, 2, 1, 4, 5, 9]}, {[7, 6, 5, 8, 9, 4, 3, 10, 1, 2], [9, 10, 7, 6, 3, 2, 1, 4, 5, 8]}, {[7, 6, 5, 8, 9, 4, 10, 2, 3, 1], [10, 8, 9, 6, 3, 2, 1, 4, 5, 7]}, {[7, 6, 5, 8, 9, 4, 10, 3, 1, 2], [9, 10, 8, 6, 3, 2, 1, 4, 5, 7]}, {[7, 6, 5, 8, 9, 10, 3, 2, 1, 4], [9, 8, 7, 10, 3, 2, 1, 4, 5, 6]}, {[7, 6, 5, 8, 9, 10, 3, 2, 4, 1], [10, 8, 7, 9, 3, 2, 1, 4, 5, 6]}, {[7, 6, 5, 8, 9, 10, 4, 2, 1, 3], [9, 8, 10, 7, 3, 2, 1, 4, 5, 6]}, {[7, 6, 8, 4, 3, 2, 5, 1, 9, 10], [8, 6, 5, 4, 7, 2, 1, 3, 9, 10]}, {[7, 6, 8, 4, 5, 3, 9, 2, 1, 10], [9, 8, 6, 4, 5, 2, 1, 3, 7, 10]}, {[7, 6, 8, 4, 5, 3, 9, 10, 2, 1], [10, 9, 6, 4, 5, 2, 1, 3, 7, 8]}, {[7, 6, 8, 5, 3, 4, 9, 2, 1, 10], [9, 8, 5, 6, 4, 2, 1, 3, 7, 10]}, {[7, 6, 8, 5, 3, 4, 9, 10, 2, 1], [10, 9, 5, 6, 4, 2, 1, 3, 7, 8]}, {[7, 6, 8, 5, 4, 9, 2, 3, 1, 10], [9, 7, 8, 5, 4, 2, 1, 3, 6, 10]}, {[7, 6, 8, 5, 4, 9, 3, 1, 2, 10], [8, 9, 7, 5, 4, 2, 1, 3, 6, 10]}, {[7, 6, 8, 5, 4, 9, 10, 2, 3, 1], [10, 8, 9, 5, 4, 2, 1, 3, 6, 7]}, {[7, 6, 8, 5, 4, 9, 10, 3, 1, 2], [9, 10, 8, 5, 4, 2, 1, 3, 6, 7]}, {[7, 6, 8, 9, 4, 3, 2, 5, 1, 10], [9, 7, 6, 5, 8, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 4, 5, 3, 10, 2, 1], [10, 9, 7, 5, 6, 2, 1, 3, 4, 8]}, {[7, 6, 8, 9, 5, 3, 2, 1, 4, 10], [8, 7, 6, 9, 5, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 5, 3, 4, 10, 2, 1], [10, 9, 6, 7, 5, 2, 1, 3, 4, 8]}, {[7, 6, 8, 9, 5, 4, 10, 2, 3, 1], [10, 8, 9, 6, 5, 2, 1, 3, 4, 7]}, {[7, 6, 8, 9, 5, 4, 10, 3, 1, 2], [9, 10, 8, 6, 5, 2, 1, 3, 4, 7]}, {[7, 6, 8, 9, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 2, 1, 3, 4, 5]}, {[7, 6, 8, 9, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 2, 1, 3, 4, 5]}, {[7, 8, 5, 4, 3, 6, 9, 2, 1, 10], [9, 8, 5, 4, 3, 6, 1, 2, 7, 10]}, {[7, 8, 5, 4, 3, 6, 9, 10, 2, 1], [10, 9, 5, 4, 3, 6, 1, 2, 7, 8]}, {[7, 8, 5, 4, 6, 3, 9, 2, 1, 10], [9, 8, 6, 4, 3, 5, 1, 2, 7, 10]}, {[7, 8, 5, 4, 6, 3, 9, 10, 2, 1], [10, 9, 6, 4, 3, 5, 1, 2, 7, 8]}, {[7, 8, 5, 6, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 3, 4, 1, 2, 6, 9]}, {[7, 8, 5, 6, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 3, 4, 1, 2, 6, 8]}, {[7, 8, 5, 6, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 3, 4, 1, 2, 5, 8]}, {[7, 8, 6, 4, 3, 5, 9, 2, 1, 10], [9, 8, 5, 4, 6, 3, 1, 2, 7, 10]}, {[7, 8, 6, 4, 3, 5, 9, 10, 2, 1], [10, 9, 5, 4, 6, 3, 1, 2, 7, 8]}, {[7, 8, 6, 4, 5, 9, 3, 2, 10, 1], [10, 8, 7, 4, 5, 3, 1, 2, 6, 9]}, {[7, 8, 6, 4, 5, 9, 3, 10, 2, 1], [10, 9, 7, 4, 5, 3, 1, 2, 6, 8]}, {[7, 8, 6, 5, 9, 3, 2, 1, 4, 10], [8, 7, 6, 9, 4, 3, 1, 2, 5, 10]}, {[7, 8, 6, 5, 9, 3, 2, 4, 1, 10], [9, 7, 6, 8, 4, 3, 1, 2, 5, 10]}, {[7, 8, 6, 5, 9, 3, 4, 2, 10, 1], [10, 8, 6, 7, 4, 3, 1, 2, 5, 9]}, {[7, 8, 6, 5, 9, 3, 4, 10, 2, 1], [10, 9, 6, 7, 4, 3, 1, 2, 5, 8]}, {[7, 8, 6, 5, 9, 4, 2, 1, 3, 10], [8, 7, 9, 6, 4, 3, 1, 2, 5, 10]}, {[7, 8, 6, 5, 9, 4, 2, 3, 10, 1], [10, 7, 8, 6, 4, 3, 1, 2, 5, 9]}, {[7, 8, 6, 5, 9, 4, 3, 10, 1, 2], [9, 10, 7, 6, 4, 3, 1, 2, 5, 8]}, {[7, 8, 6, 5, 9, 4, 10, 2, 3, 1], [10, 8, 9, 6, 4, 3, 1, 2, 5, 7]}, {[7, 8, 6, 5, 9, 4, 10, 3, 1, 2], [9, 10, 8, 6, 4, 3, 1, 2, 5, 7]}, {[7, 8, 6, 5, 9, 10, 3, 2, 1, 4], [9, 8, 7, 10, 4, 3, 1, 2, 5, 6]}, {[7, 8, 6, 5, 9, 10, 3, 2, 4, 1], [10, 8, 7, 9, 4, 3, 1, 2, 5, 6]}, {[7, 8, 6, 5, 9, 10, 4, 2, 1, 3], [9, 8, 10, 7, 4, 3, 1, 2, 5, 6]}, {[7, 8, 6, 9, 4, 3, 2, 5, 1, 10], [9, 7, 6, 5, 8, 3, 1, 2, 4, 10]}, {[7, 8, 6, 9, 4, 5, 3, 10, 2, 1], [10, 9, 7, 5, 6, 3, 1, 2, 4, 8]}, {[7, 8, 6, 9, 5, 3, 2, 1, 4, 10], [8, 7, 6, 9, 5, 3, 1, 2, 4, 10]}, {[7, 8, 6, 9, 5, 3, 4, 10, 2, 1], [10, 9, 6, 7, 5, 3, 1, 2, 4, 8]}, {[7, 8, 6, 9, 5, 4, 10, 2, 3, 1], [10, 8, 9, 6, 5, 3, 1, 2, 4, 7]}, {[7, 8, 6, 9, 5, 4, 10, 3, 1, 2], [9, 10, 8, 6, 5, 3, 1, 2, 4, 7]}, {[7, 8, 6, 9, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 3, 1, 2, 4, 5]}, {[7, 8, 6, 9, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 3, 1, 2, 4, 5]}, {[7, 8, 9, 5, 4, 3, 6, 2, 10, 1], [10, 8, 6, 5, 4, 7, 1, 2, 3, 9]}, {[7, 8, 9, 5, 4, 3, 6, 10, 2, 1], [10, 9, 6, 5, 4, 7, 1, 2, 3, 8]}, {[7, 8, 9, 5, 4, 6, 3, 10, 2, 1], [10, 9, 7, 5, 4, 6, 1, 2, 3, 8]}, {[7, 8, 9, 6, 4, 3, 2, 5, 10, 1], [10, 7, 6, 5, 8, 4, 1, 2, 3, 9]}, {[7, 8, 9, 6, 4, 3, 5, 10, 2, 1], [10, 9, 6, 5, 7, 4, 1, 2, 3, 8]}, {[7, 8, 9, 6, 5, 10, 3, 2, 1, 4], [9, 8, 7, 10, 5, 4, 1, 2, 3, 6]}, {[7, 8, 9, 6, 5, 10, 3, 2, 4, 1], [10, 8, 7, 9, 5, 4, 1, 2, 3, 6]}, {[7, 8, 9, 6, 5, 10, 4, 2, 1, 3], [9, 8, 10, 7, 5, 4, 1, 2, 3, 6]}, {[7, 8, 9, 6, 10, 4, 3, 2, 5, 1], [10, 8, 7, 6, 9, 4, 1, 2, 3, 5]}, {[7, 8, 9, 6, 10, 5, 3, 2, 1, 4], [9, 8, 7, 10, 6, 4, 1, 2, 3, 5]}, {[8, 5, 4, 3, 6, 2, 7, 1, 9, 10], [8, 6, 4, 3, 2, 5, 7, 1, 9, 10]}, {[8, 5, 4, 3, 6, 7, 9, 2, 1, 10], [9, 8, 4, 3, 2, 5, 6, 1, 7, 10]}, {[8, 5, 4, 3, 6, 7, 9, 10, 2, 1], [10, 9, 4, 3, 2, 5, 6, 1, 7, 8]}, {[8, 5, 4, 6, 3, 2, 7, 1, 9, 10], [8, 6, 5, 3, 2, 4, 7, 1, 9, 10]}, {[8, 5, 4, 6, 7, 3, 9, 2, 1, 10], [9, 8, 6, 3, 2, 4, 5, 1, 7, 10]}, {[8, 5, 4, 6, 7, 3, 9, 10, 2, 1], [10, 9, 6, 3, 2, 4, 5, 1, 7, 8]}, {[8, 5, 6, 4, 3, 7, 9, 2, 1, 10], [9, 8, 5, 4, 2, 3, 6, 1, 7, 10]}, {[8, 5, 6, 4, 3, 7, 9, 10, 2, 1], [10, 9, 5, 4, 2, 3, 6, 1, 7, 8]}, {[8, 5, 6, 4, 7, 3, 9, 2, 1, 10], [9, 8, 6, 4, 2, 3, 5, 1, 7, 10]}, {[8, 5, 6, 4, 7, 3, 9, 10, 2, 1], [10, 9, 6, 4, 2, 3, 5, 1, 7, 8]}, {[8, 5, 6, 7, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 2, 3, 4, 1, 6, 9]}, {[8, 5, 6, 7, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 2, 3, 4, 1, 6, 8]}, {[8, 5, 6, 7, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 2, 3, 4, 1, 5, 8]}, {[8, 6, 4, 5, 3, 7, 9, 2, 1, 10], [9, 8, 5, 3, 4, 2, 6, 1, 7, 10]}, {[8, 6, 4, 5, 3, 7, 9, 10, 2, 1], [10, 9, 5, 3, 4, 2, 6, 1, 7, 8]}, {[8, 6, 4, 5, 7, 3, 9, 2, 1, 10], [9, 8, 6, 3, 4, 2, 5, 1, 7, 10]}, {[8, 6, 4, 5, 7, 3, 9, 10, 2, 1], [10, 9, 6, 3, 4, 2, 5, 1, 7, 8]}, {[8, 6, 5, 3, 4, 7, 9, 2, 1, 10], [9, 8, 4, 5, 3, 2, 6, 1, 7, 10]}, {[8, 6, 5, 3, 4, 7, 9, 10, 2, 1], [10, 9, 4, 5, 3, 2, 6, 1, 7, 8]}, {[8, 6, 5, 4, 7, 3, 9, 1, 2, 10], [8, 9, 6, 4, 3, 2, 5, 1, 7, 10]}, {[8, 6, 5, 4, 7, 3, 9, 10, 1, 2], [9, 10, 6, 4, 3, 2, 5, 1, 7, 8]}, {[8, 6, 5, 4, 7, 9, 2, 3, 1, 10], [9, 7, 8, 4, 3, 2, 5, 1, 6, 10]}, {[8, 6, 5, 4, 7, 9, 3, 1, 2, 10], [8, 9, 7, 4, 3, 2, 5, 1, 6, 10]}, {[8, 6, 5, 4, 7, 9, 10, 2, 3, 1], [10, 8, 9, 4, 3, 2, 5, 1, 6, 7]}, {[8, 6, 5, 4, 7, 9, 10, 3, 1, 2], [9, 10, 8, 4, 3, 2, 5, 1, 6, 7]}, {[8, 6, 5, 7, 3, 4, 9, 2, 1, 10], [9, 8, 5, 6, 3, 2, 4, 1, 7, 10]}, {[8, 6, 5, 7, 3, 4, 9, 10, 2, 1], [10, 9, 5, 6, 3, 2, 4, 1, 7, 8]}, {[8, 6, 5, 7, 4, 9, 2, 3, 1, 10], [9, 7, 8, 5, 3, 2, 4, 1, 6, 10]}, {[8, 6, 5, 7, 4, 9, 3, 1, 2, 10], [8, 9, 7, 5, 3, 2, 4, 1, 6, 10]}, {[8, 6, 5, 7, 4, 9, 10, 2, 3, 1], [10, 8, 9, 5, 3, 2, 4, 1, 6, 7]}, {[8, 6, 5, 7, 4, 9, 10, 3, 1, 2], [9, 10, 8, 5, 3, 2, 4, 1, 6, 7]}, {[8, 6, 7, 4, 3, 5, 9, 2, 1, 10], [9, 8, 5, 4, 6, 2, 3, 1, 7, 10]}, {[8, 6, 7, 4, 3, 5, 9, 10, 2, 1], 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7, 5, 6, 8, 3, 4, 2, 9, 1], [10, 8, 6, 7, 3, 4, 2, 5, 9, 1]}, {[10, 7, 5, 6, 8, 4, 2, 3, 9, 1], [10, 7, 8, 6, 3, 4, 2, 5, 9, 1]}, {[10, 7, 6, 3, 4, 5, 8, 2, 9, 1], [10, 8, 4, 5, 6, 3, 2, 7, 9, 1]}, {[10, 7, 6, 4, 5, 8, 2, 3, 9, 1], [10, 7, 8, 4, 5, 3, 2, 6, 9, 1]}, {[10, 7, 6, 8, 3, 4, 5, 2, 9, 1], [10, 8, 5, 6, 7, 3, 2, 4, 9, 1]}, {[10, 7, 6, 8, 4, 5, 2, 3, 9, 1], [10, 7, 8, 5, 6, 3, 2, 4, 9, 1]}, {[10, 7, 8, 4, 3, 5, 6, 2, 9, 1], [10, 8, 5, 4, 6, 7, 2, 3, 9, 1]}, {[10, 7, 8, 4, 5, 3, 6, 2, 9, 1], [10, 8, 6, 4, 5, 7, 2, 3, 9, 1]}, {[10, 7, 8, 5, 3, 4, 6, 2, 9, 1], [10, 8, 5, 6, 4, 7, 2, 3, 9, 1]}, {[10, 8, 4, 5, 3, 6, 7, 2, 9, 1], [10, 8, 5, 3, 4, 6, 7, 2, 9, 1]}, {[10, 8, 4, 5, 6, 3, 7, 2, 9, 1], [10, 8, 6, 3, 4, 5, 7, 2, 9, 1]}, { [6, 5, 4, 7, 3, 2, 8, 9, 1, 10], [6, 5, 4, 7, 3, 2, 8, 9, 10, 1], [9, 6, 5, 3, 2, 1, 4, 7, 8, 10], [10, 6, 5, 3, 2, 1, 4, 7, 8, 9]}, { [6, 5, 4, 7, 8, 3, 2, 9, 1, 10], [6, 5, 4, 7, 8, 3, 2, 9, 10, 1], [9, 7, 6, 3, 2, 1, 4, 5, 8, 10], [10, 7, 6, 3, 2, 1, 4, 5, 8, 9]}, { [6, 7, 5, 4, 8, 3, 2, 9, 1, 10], [6, 7, 5, 4, 8, 3, 2, 9, 10, 1], [9, 7, 6, 4, 3, 1, 2, 5, 8, 10], [10, 7, 6, 4, 3, 1, 2, 5, 8, 9]}, { [7, 5, 4, 3, 6, 2, 8, 9, 1, 10], [7, 5, 4, 3, 6, 2, 8, 9, 10, 1], [9, 6, 4, 3, 2, 5, 1, 7, 8, 10], [10, 6, 4, 3, 2, 5, 1, 7, 8, 9]}, { [7, 5, 6, 4, 8, 3, 2, 9, 1, 10], [7, 5, 6, 4, 8, 3, 2, 9, 10, 1], [9, 7, 6, 4, 2, 3, 1, 5, 8, 10], [10, 7, 6, 4, 2, 3, 1, 5, 8, 9]}, { [7, 6, 4, 3, 2, 5, 8, 9, 1, 10], [7, 6, 4, 3, 2, 5, 8, 9, 10, 1], [9, 5, 4, 3, 6, 2, 1, 7, 8, 10], [10, 5, 4, 3, 6, 2, 1, 7, 8, 9]}, { [7, 6, 4, 5, 8, 3, 2, 9, 1, 10], [7, 6, 4, 5, 8, 3, 2, 9, 10, 1], [9, 7, 6, 3, 4, 2, 1, 5, 8, 10], [10, 7, 6, 3, 4, 2, 1, 5, 8, 9]}, { [7, 6, 5, 8, 3, 4, 2, 9, 1, 10], [7, 6, 5, 8, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 3, 2, 1, 4, 8, 10], [10, 7, 5, 6, 3, 2, 1, 4, 8, 9]}, { [7, 6, 5, 8, 4, 2, 3, 9, 1, 10], [7, 6, 5, 8, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 3, 2, 1, 4, 8, 10], [10, 6, 7, 5, 3, 2, 1, 4, 8, 9]}, { [7, 8, 5, 4, 3, 6, 2, 9, 1, 10], [7, 8, 5, 4, 3, 6, 2, 9, 10, 1], [9, 7, 5, 4, 3, 6, 1, 2, 8, 10], [10, 7, 5, 4, 3, 6, 1, 2, 8, 9]}, { [7, 8, 6, 4, 3, 2, 5, 9, 1, 10], [7, 8, 6, 4, 3, 2, 5, 9, 10, 1], [9, 6, 5, 4, 7, 3, 1, 2, 8, 10], [10, 6, 5, 4, 7, 3, 1, 2, 8, 9]}, { [8, 5, 4, 3, 6, 7, 2, 9, 1, 10], [8, 5, 4, 3, 6, 7, 2, 9, 10, 1], [9, 7, 4, 3, 2, 5, 6, 1, 8, 10], [10, 7, 4, 3, 2, 5, 6, 1, 8, 9]}, { [8, 5, 6, 4, 3, 7, 2, 9, 1, 10], [8, 5, 6, 4, 3, 7, 2, 9, 10, 1], [9, 7, 5, 4, 2, 3, 6, 1, 8, 10], [10, 7, 5, 4, 2, 3, 6, 1, 8, 9]}, { [8, 6, 4, 5, 3, 7, 2, 9, 1, 10], [8, 6, 4, 5, 3, 7, 2, 9, 10, 1], [9, 7, 5, 3, 4, 2, 6, 1, 8, 10], [10, 7, 5, 3, 4, 2, 6, 1, 8, 9]}, { [8, 6, 5, 3, 4, 7, 2, 9, 1, 10], [8, 6, 5, 3, 4, 7, 2, 9, 10, 1], [9, 7, 4, 5, 3, 2, 6, 1, 8, 10], [10, 7, 4, 5, 3, 2, 6, 1, 8, 9]}, { [8, 6, 5, 4, 7, 2, 3, 9, 1, 10], [8, 6, 5, 4, 7, 2, 3, 9, 10, 1], [9, 6, 7, 4, 3, 2, 5, 1, 8, 10], [10, 6, 7, 4, 3, 2, 5, 1, 8, 9]}, { [8, 6, 7, 4, 3, 2, 5, 9, 1, 10], [8, 6, 7, 4, 3, 2, 5, 9, 10, 1], [9, 6, 5, 4, 7, 2, 3, 1, 8, 10], [10, 6, 5, 4, 7, 2, 3, 1, 8, 9]}, { [8, 7, 4, 3, 2, 5, 6, 9, 1, 10], [8, 7, 4, 3, 2, 5, 6, 9, 10, 1], [9, 5, 4, 3, 6, 7, 2, 1, 8, 10], [10, 5, 4, 3, 6, 7, 2, 1, 8, 9]}, { [8, 7, 4, 5, 3, 2, 6, 9, 1, 10], [8, 7, 4, 5, 3, 2, 6, 9, 10, 1], [9, 6, 5, 3, 4, 7, 2, 1, 8, 10], [10, 6, 5, 3, 4, 7, 2, 1, 8, 9]}, { [8, 7, 5, 3, 4, 2, 6, 9, 1, 10], [8, 7, 5, 3, 4, 2, 6, 9, 10, 1], [9, 6, 4, 5, 3, 7, 2, 1, 8, 10], [10, 6, 4, 5, 3, 7, 2, 1, 8, 9]}, { [8, 7, 5, 4, 2, 3, 6, 9, 1, 10], [8, 7, 5, 4, 2, 3, 6, 9, 10, 1], [9, 5, 6, 4, 3, 7, 2, 1, 8, 10], [10, 5, 6, 4, 3, 7, 2, 1, 8, 9]}} is given by the following expression / 17 223 2 17 3 89 4 17 5 6\ n / |---- n + ------ n - ---- n - ----- n - ------ n - 1/368640 n | 4 + | \7680 184320 8192 73728 122880 / \ 19 3119 2 20443 3 4811 4 19603 5 73 6 - ---- n - ------ n - ------- n + ------ n + ------- n + ----- n 8580 480480 8648640 864864 4324320 78624 389 7 8\ + ------- n + 1/4324320 n | C(n) 8648640 / and in Maple input form: (17/7680*n+223/184320*n^2-17/8192*n^3-89/73728*n^4-17/122880*n^5-1/368640*n^6)* 4^n+(-19/8580*n-3119/480480*n^2-20443/8648640*n^3+4811/864864*n^4+19603/4324320 *n^5+73/78624*n^6+389/8648640*n^7+1/4324320*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 16 1/2 15 14 1/2 13 12 1/2 11 m Pi m 389 m 139 Pi m 73 m 4019 Pi m ------- - --------- + ------- - ------------- + ------ - -------------- 4324320 368640 8648640 983040 78624 2949120 10 1/2 9 8 1/2 7 6 19603 m 225 Pi m 4811 m 3317 Pi m 20443 m + --------- - ------------ + ------- - ------------- - -------- 4324320 65536 864864 2949120 8648640 1/2 5 4 1/2 3 2 1757 Pi m 3119 m 51 Pi m 19 m + ------------- - ------- + ----------- - ----- 491520 480480 20480 8580 and in Maple input form: 1/4324320*m^16-1/368640*Pi^(1/2)*m^15+389/8648640*m^14-139/983040*Pi^(1/2)*m^13 +73/78624*m^12-4019/2949120*Pi^(1/2)*m^11+19603/4324320*m^10-225/65536*Pi^(1/2) *m^9+4811/864864*m^8-3317/2949120*Pi^(1/2)*m^7-20443/8648640*m^6+1757/491520*Pi ^(1/2)*m^5-3119/480480*m^4+51/20480*Pi^(1/2)*m^3-19/8580*m^2 For the, 29, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[8, 7, 9, 5, 4, 6, 2, 1, 3, 10]}, {[9, 6, 5, 7, 3, 2, 4, 8, 1, 10]}, {[9, 8, 10, 5, 4, 6, 7, 2, 1, 3]}, {[10, 6, 5, 7, 3, 2, 4, 8, 9, 1]}, {[6, 5, 4, 7, 3, 8, 9, 2, 10, 1], [10, 8, 5, 3, 2, 1, 4, 6, 7, 9]}, {[6, 5, 4, 7, 8, 3, 9, 2, 10, 1], [10, 8, 6, 3, 2, 1, 4, 5, 7, 9]}, {[6, 5, 7, 4, 3, 8, 9, 2, 10, 1], [10, 8, 5, 4, 2, 1, 3, 6, 7, 9]}, {[6, 5, 7, 4, 8, 3, 9, 2, 1, 10], [9, 8, 6, 4, 2, 1, 3, 5, 7, 10]}, {[6, 5, 7, 4, 8, 3, 9, 10, 2, 1], [10, 9, 6, 4, 2, 1, 3, 5, 7, 8]}, {[6, 5, 7, 4, 8, 9, 3, 2, 10, 1], [10, 8, 7, 4, 2, 1, 3, 5, 6, 9]}, {[6, 5, 7, 4, 8, 9, 3, 10, 2, 1], [10, 9, 7, 4, 2, 1, 3, 5, 6, 8]}, {[6, 5, 7, 8, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 2, 1, 3, 4, 7, 9]}, {[6, 5, 7, 8, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 2, 1, 3, 4, 6, 9]}, {[6, 5, 7, 8, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 2, 1, 3, 4, 6, 8]}, {[6, 7, 5, 4, 8, 3, 9, 2, 10, 1], [10, 8, 6, 4, 3, 1, 2, 5, 7, 9]}, {[6, 7, 5, 8, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 3, 1, 2, 4, 7, 9]}, {[6, 7, 5, 8, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 3, 1, 2, 4, 6, 9]}, {[6, 7, 5, 8, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 3, 1, 2, 4, 6, 8]}, {[7, 5, 4, 3, 6, 8, 9, 2, 10, 1], [10, 8, 4, 3, 2, 5, 1, 6, 7, 9]}, {[7, 5, 4, 6, 3, 8, 9, 2, 10, 1], [10, 8, 5, 3, 2, 4, 1, 6, 7, 9]}, {[7, 5, 4, 6, 8, 3, 9, 2, 1, 10], [9, 8, 6, 3, 2, 4, 1, 5, 7, 10]}, {[7, 5, 4, 6, 8, 3, 9, 10, 2, 1], [10, 9, 6, 3, 2, 4, 1, 5, 7, 8]}, {[7, 5, 4, 6, 8, 9, 3, 2, 10, 1], [10, 8, 7, 3, 2, 4, 1, 5, 6, 9]}, {[7, 5, 4, 6, 8, 9, 3, 10, 2, 1], [10, 9, 7, 3, 2, 4, 1, 5, 6, 8]}, {[7, 5, 6, 4, 8, 3, 9, 2, 10, 1], [10, 8, 6, 4, 2, 3, 1, 5, 7, 9]}, {[7, 5, 6, 8, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 2, 3, 1, 4, 7, 9]}, {[7, 5, 6, 8, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 2, 3, 1, 4, 6, 9]}, {[7, 5, 6, 8, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 2, 3, 1, 4, 6, 8]}, {[7, 6, 4, 3, 5, 8, 9, 2, 10, 1], [10, 8, 4, 3, 5, 2, 1, 6, 7, 9]}, {[7, 6, 4, 5, 8, 3, 9, 2, 10, 1], [10, 8, 6, 3, 4, 2, 1, 5, 7, 9]}, {[7, 6, 5, 8, 3, 4, 9, 2, 10, 1], [10, 8, 5, 6, 3, 2, 1, 4, 7, 9]}, {[7, 6, 5, 8, 4, 9, 2, 1, 3, 10], [8, 7, 9, 5, 3, 2, 1, 4, 6, 10]}, {[7, 6, 5, 8, 4, 9, 2, 3, 10, 1], [10, 7, 8, 5, 3, 2, 1, 4, 6, 9]}, {[7, 6, 5, 8, 4, 9, 3, 10, 1, 2], [9, 10, 7, 5, 3, 2, 1, 4, 6, 8]}, {[7, 6, 5, 8, 4, 9, 10, 2, 1, 3], [9, 8, 10, 5, 3, 2, 1, 4, 6, 7]}, {[7, 6, 5, 8, 9, 3, 2, 4, 10, 1], [10, 7, 6, 8, 3, 2, 1, 4, 5, 9]}, {[7, 6, 5, 8, 9, 4, 10, 2, 1, 3], [9, 8, 10, 6, 3, 2, 1, 4, 5, 7]}, {[7, 6, 8, 4, 3, 5, 9, 2, 1, 10], [9, 8, 5, 4, 6, 2, 1, 3, 7, 10]}, {[7, 6, 8, 4, 3, 5, 9, 10, 2, 1], [10, 9, 5, 4, 6, 2, 1, 3, 7, 8]}, {[7, 6, 8, 4, 5, 3, 9, 2, 10, 1], [10, 8, 6, 4, 5, 2, 1, 3, 7, 9]}, {[7, 6, 8, 4, 5, 9, 3, 2, 10, 1], [10, 8, 7, 4, 5, 2, 1, 3, 6, 9]}, {[7, 6, 8, 4, 5, 9, 3, 10, 2, 1], [10, 9, 7, 4, 5, 2, 1, 3, 6, 8]}, {[7, 6, 8, 5, 3, 4, 9, 2, 10, 1], [10, 8, 5, 6, 4, 2, 1, 3, 7, 9]}, {[7, 6, 8, 5, 4, 9, 2, 1, 3, 10], [8, 7, 9, 5, 4, 2, 1, 3, 6, 10]}, {[7, 6, 8, 5, 4, 9, 2, 3, 10, 1], [10, 7, 8, 5, 4, 2, 1, 3, 6, 9]}, {[7, 6, 8, 5, 4, 9, 3, 10, 1, 2], [9, 10, 7, 5, 4, 2, 1, 3, 6, 8]}, {[7, 6, 8, 5, 4, 9, 10, 2, 1, 3], [9, 8, 10, 5, 4, 2, 1, 3, 6, 7]}, {[7, 6, 8, 5, 9, 3, 2, 1, 4, 10], [8, 7, 6, 9, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 3, 2, 4, 1, 10], [9, 7, 6, 8, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 3, 4, 2, 10, 1], [10, 8, 6, 7, 4, 2, 1, 3, 5, 9]}, {[7, 6, 8, 5, 9, 3, 4, 10, 2, 1], [10, 9, 6, 7, 4, 2, 1, 3, 5, 8]}, {[7, 6, 8, 5, 9, 4, 2, 1, 3, 10], [8, 7, 9, 6, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 4, 2, 3, 10, 1], [10, 7, 8, 6, 4, 2, 1, 3, 5, 9]}, {[7, 6, 8, 5, 9, 4, 3, 10, 1, 2], [9, 10, 7, 6, 4, 2, 1, 3, 5, 8]}, {[7, 6, 8, 5, 9, 4, 10, 2, 3, 1], [10, 8, 9, 6, 4, 2, 1, 3, 5, 7]}, {[7, 6, 8, 5, 9, 4, 10, 3, 1, 2], [9, 10, 8, 6, 4, 2, 1, 3, 5, 7]}, {[7, 6, 8, 5, 9, 10, 3, 2, 1, 4], [9, 8, 7, 10, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 5, 9, 10, 3, 2, 4, 1], [10, 8, 7, 9, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 5, 9, 10, 4, 2, 1, 3], [9, 8, 10, 7, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 9, 4, 3, 2, 5, 10, 1], [10, 7, 6, 5, 8, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 4, 3, 5, 2, 10, 1], [10, 8, 6, 5, 7, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 4, 3, 5, 10, 2, 1], [10, 9, 6, 5, 7, 2, 1, 3, 4, 8]}, {[7, 6, 8, 9, 5, 3, 2, 4, 10, 1], [10, 7, 6, 8, 5, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 5, 4, 10, 2, 1, 3], [9, 8, 10, 6, 5, 2, 1, 3, 4, 7]}, {[7, 6, 8, 9, 5, 10, 3, 2, 1, 4], [9, 8, 7, 10, 5, 2, 1, 3, 4, 6]}, {[7, 6, 8, 9, 5, 10, 3, 2, 4, 1], [10, 8, 7, 9, 5, 2, 1, 3, 4, 6]}, {[7, 6, 8, 9, 5, 10, 4, 2, 1, 3], [9, 8, 10, 7, 5, 2, 1, 3, 4, 6]}, {[7, 8, 5, 4, 3, 6, 9, 2, 10, 1], [10, 8, 5, 4, 3, 6, 1, 2, 7, 9]}, {[7, 8, 5, 4, 6, 3, 9, 2, 10, 1], [10, 8, 6, 4, 3, 5, 1, 2, 7, 9]}, {[7, 8, 5, 4, 6, 9, 3, 2, 10, 1], [10, 8, 7, 4, 3, 5, 1, 2, 6, 9]}, {[7, 8, 5, 4, 6, 9, 3, 10, 2, 1], [10, 9, 7, 4, 3, 5, 1, 2, 6, 8]}, {[7, 8, 6, 4, 3, 5, 9, 2, 10, 1], [10, 8, 5, 4, 6, 3, 1, 2, 7, 9]}, {[7, 8, 6, 5, 9, 3, 2, 4, 10, 1], [10, 7, 6, 8, 4, 3, 1, 2, 5, 9]}, {[7, 8, 6, 5, 9, 4, 10, 2, 1, 3], [9, 8, 10, 6, 4, 3, 1, 2, 5, 7]}, {[7, 8, 6, 9, 4, 3, 2, 5, 10, 1], [10, 7, 6, 5, 8, 3, 1, 2, 4, 9]}, {[7, 8, 6, 9, 4, 3, 5, 2, 10, 1], [10, 8, 6, 5, 7, 3, 1, 2, 4, 9]}, {[7, 8, 6, 9, 4, 3, 5, 10, 2, 1], [10, 9, 6, 5, 7, 3, 1, 2, 4, 8]}, {[7, 8, 6, 9, 5, 3, 2, 4, 10, 1], [10, 7, 6, 8, 5, 3, 1, 2, 4, 9]}, {[7, 8, 6, 9, 5, 4, 10, 2, 1, 3], [9, 8, 10, 6, 5, 3, 1, 2, 4, 7]}, {[7, 8, 6, 9, 5, 10, 3, 2, 1, 4], [9, 8, 7, 10, 5, 3, 1, 2, 4, 6]}, {[7, 8, 6, 9, 5, 10, 3, 2, 4, 1], [10, 8, 7, 9, 5, 3, 1, 2, 4, 6]}, {[7, 8, 6, 9, 5, 10, 4, 2, 1, 3], [9, 8, 10, 7, 5, 3, 1, 2, 4, 6]}, {[8, 5, 4, 3, 6, 7, 9, 2, 10, 1], [10, 8, 4, 3, 2, 5, 6, 1, 7, 9]}, {[8, 5, 4, 6, 3, 7, 9, 2, 1, 10], [9, 8, 5, 3, 2, 4, 6, 1, 7, 10]}, {[8, 5, 4, 6, 3, 7, 9, 10, 2, 1], [10, 9, 5, 3, 2, 4, 6, 1, 7, 8]}, {[8, 5, 4, 6, 7, 3, 9, 2, 10, 1], [10, 8, 6, 3, 2, 4, 5, 1, 7, 9]}, {[8, 5, 4, 6, 7, 9, 3, 2, 10, 1], [10, 8, 7, 3, 2, 4, 5, 1, 6, 9]}, {[8, 5, 4, 6, 7, 9, 3, 10, 2, 1], [10, 9, 7, 3, 2, 4, 5, 1, 6, 8]}, {[8, 5, 6, 4, 3, 7, 9, 2, 10, 1], [10, 8, 5, 4, 2, 3, 6, 1, 7, 9]}, {[8, 5, 6, 4, 7, 3, 9, 2, 10, 1], [10, 8, 6, 4, 2, 3, 5, 1, 7, 9]}, {[8, 5, 6, 4, 7, 9, 3, 2, 10, 1], [10, 8, 7, 4, 2, 3, 5, 1, 6, 9]}, {[8, 5, 6, 4, 7, 9, 3, 10, 2, 1], [10, 9, 7, 4, 2, 3, 5, 1, 6, 8]}, {[8, 6, 4, 3, 5, 7, 9, 2, 1, 10], [9, 8, 4, 3, 5, 2, 6, 1, 7, 10]}, {[8, 6, 4, 3, 5, 7, 9, 10, 2, 1], [10, 9, 4, 3, 5, 2, 6, 1, 7, 8]}, {[8, 6, 4, 5, 3, 7, 9, 2, 10, 1], [10, 8, 5, 3, 4, 2, 6, 1, 7, 9]}, {[8, 6, 4, 5, 7, 3, 9, 2, 10, 1], [10, 8, 6, 3, 4, 2, 5, 1, 7, 9]}, {[8, 6, 4, 5, 7, 9, 3, 2, 10, 1], [10, 8, 7, 3, 4, 2, 5, 1, 6, 9]}, {[8, 6, 4, 5, 7, 9, 3, 10, 2, 1], [10, 9, 7, 3, 4, 2, 5, 1, 6, 8]}, {[8, 6, 5, 3, 4, 7, 9, 2, 10, 1], [10, 8, 4, 5, 3, 2, 6, 1, 7, 9]}, {[8, 6, 5, 4, 7, 9, 2, 1, 3, 10], [8, 7, 9, 4, 3, 2, 5, 1, 6, 10]}, {[8, 6, 5, 4, 7, 9, 2, 3, 10, 1], [10, 7, 8, 4, 3, 2, 5, 1, 6, 9]}, {[8, 6, 5, 4, 7, 9, 3, 10, 1, 2], [9, 10, 7, 4, 3, 2, 5, 1, 6, 8]}, {[8, 6, 5, 4, 7, 9, 10, 2, 1, 3], [9, 8, 10, 4, 3, 2, 5, 1, 6, 7]}, {[8, 6, 5, 7, 3, 4, 9, 2, 10, 1], [10, 8, 5, 6, 3, 2, 4, 1, 7, 9]}, {[8, 6, 5, 7, 4, 9, 2, 1, 3, 10], [8, 7, 9, 5, 3, 2, 4, 1, 6, 10]}, {[8, 6, 5, 7, 4, 9, 2, 3, 10, 1], [10, 7, 8, 5, 3, 2, 4, 1, 6, 9]}, {[8, 6, 5, 7, 4, 9, 3, 10, 1, 2], [9, 10, 7, 5, 3, 2, 4, 1, 6, 8]}, {[8, 6, 5, 7, 4, 9, 10, 2, 1, 3], [9, 8, 10, 5, 3, 2, 4, 1, 6, 7]}, {[8, 6, 5, 7, 9, 3, 2, 1, 4, 10], [8, 7, 6, 9, 3, 2, 4, 1, 5, 10]}, {[8, 6, 5, 7, 9, 3, 2, 4, 1, 10], [9, 7, 6, 8, 3, 2, 4, 1, 5, 10]}, {[8, 6, 5, 7, 9, 3, 4, 2, 10, 1], [10, 8, 6, 7, 3, 2, 4, 1, 5, 9]}, {[8, 6, 5, 7, 9, 3, 4, 10, 2, 1], [10, 9, 6, 7, 3, 2, 4, 1, 5, 8]}, {[8, 6, 5, 7, 9, 4, 2, 1, 3, 10], [8, 7, 9, 6, 3, 2, 4, 1, 5, 10]}, {[8, 6, 5, 7, 9, 4, 2, 3, 10, 1], [10, 7, 8, 6, 3, 2, 4, 1, 5, 9]}, {[8, 6, 5, 7, 9, 4, 3, 10, 1, 2], [9, 10, 7, 6, 3, 2, 4, 1, 5, 8]}, {[8, 6, 5, 7, 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2, 5, 9, 1]}, { [6, 5, 4, 7, 3, 8, 2, 9, 1, 10], [6, 5, 4, 7, 3, 8, 2, 9, 10, 1], [9, 7, 5, 3, 2, 1, 4, 6, 8, 10], [10, 7, 5, 3, 2, 1, 4, 6, 8, 9]}, { [6, 5, 7, 4, 3, 8, 2, 9, 1, 10], [6, 5, 7, 4, 3, 8, 2, 9, 10, 1], [9, 7, 5, 4, 2, 1, 3, 6, 8, 10], [10, 7, 5, 4, 2, 1, 3, 6, 8, 9]}, { [6, 5, 7, 4, 8, 3, 2, 9, 1, 10], [6, 5, 7, 4, 8, 3, 2, 9, 10, 1], [9, 7, 6, 4, 2, 1, 3, 5, 8, 10], [10, 7, 6, 4, 2, 1, 3, 5, 8, 9]}, { [7, 5, 4, 3, 6, 8, 2, 9, 1, 10], [7, 5, 4, 3, 6, 8, 2, 9, 10, 1], [9, 7, 4, 3, 2, 5, 1, 6, 8, 10], [10, 7, 4, 3, 2, 5, 1, 6, 8, 9]}, { [7, 5, 4, 6, 3, 8, 2, 9, 1, 10], [7, 5, 4, 6, 3, 8, 2, 9, 10, 1], [9, 7, 5, 3, 2, 4, 1, 6, 8, 10], [10, 7, 5, 3, 2, 4, 1, 6, 8, 9]}, { [7, 5, 4, 6, 8, 3, 2, 9, 1, 10], [7, 5, 4, 6, 8, 3, 2, 9, 10, 1], [9, 7, 6, 3, 2, 4, 1, 5, 8, 10], [10, 7, 6, 3, 2, 4, 1, 5, 8, 9]}, { [7, 6, 4, 3, 5, 8, 2, 9, 1, 10], [7, 6, 4, 3, 5, 8, 2, 9, 10, 1], [9, 7, 4, 3, 5, 2, 1, 6, 8, 10], [10, 7, 4, 3, 5, 2, 1, 6, 8, 9]}, { [7, 6, 5, 8, 3, 2, 4, 9, 1, 10], [7, 6, 5, 8, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 3, 2, 1, 4, 8, 10], [10, 6, 5, 7, 3, 2, 1, 4, 8, 9]}, { [7, 6, 8, 4, 3, 2, 5, 9, 1, 10], [7, 6, 8, 4, 3, 2, 5, 9, 10, 1], [9, 6, 5, 4, 7, 2, 1, 3, 8, 10], [10, 6, 5, 4, 7, 2, 1, 3, 8, 9]}, { [7, 6, 8, 4, 3, 5, 2, 9, 1, 10], [7, 6, 8, 4, 3, 5, 2, 9, 10, 1], [9, 7, 5, 4, 6, 2, 1, 3, 8, 10], [10, 7, 5, 4, 6, 2, 1, 3, 8, 9]}, { [7, 6, 8, 5, 3, 2, 4, 9, 1, 10], [7, 6, 8, 5, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 4, 2, 1, 3, 8, 10], [10, 6, 5, 7, 4, 2, 1, 3, 8, 9]}, { [8, 5, 4, 3, 6, 2, 7, 9, 1, 10], [8, 5, 4, 3, 6, 2, 7, 9, 10, 1], [9, 6, 4, 3, 2, 5, 7, 1, 8, 10], [10, 6, 4, 3, 2, 5, 7, 1, 8, 9]}, { [8, 5, 4, 6, 3, 2, 7, 9, 1, 10], [8, 5, 4, 6, 3, 2, 7, 9, 10, 1], [9, 6, 5, 3, 2, 4, 7, 1, 8, 10], [10, 6, 5, 3, 2, 4, 7, 1, 8, 9]}, { [8, 5, 4, 6, 3, 7, 2, 9, 1, 10], [8, 5, 4, 6, 3, 7, 2, 9, 10, 1], [9, 7, 5, 3, 2, 4, 6, 1, 8, 10], [10, 7, 5, 3, 2, 4, 6, 1, 8, 9]}, { [8, 6, 4, 3, 2, 5, 7, 9, 1, 10], [8, 6, 4, 3, 2, 5, 7, 9, 10, 1], [9, 5, 4, 3, 6, 2, 7, 1, 8, 10], [10, 5, 4, 3, 6, 2, 7, 1, 8, 9]}, { [8, 6, 4, 3, 5, 2, 7, 9, 1, 10], [8, 6, 4, 3, 5, 2, 7, 9, 10, 1], [9, 6, 4, 3, 5, 2, 7, 1, 8, 10], [10, 6, 4, 3, 5, 2, 7, 1, 8, 9]}, { [8, 6, 4, 3, 5, 7, 2, 9, 1, 10], [8, 6, 4, 3, 5, 7, 2, 9, 10, 1], [9, 7, 4, 3, 5, 2, 6, 1, 8, 10], [10, 7, 4, 3, 5, 2, 6, 1, 8, 9]}, { [8, 6, 5, 3, 2, 4, 7, 9, 1, 10], [8, 6, 5, 3, 2, 4, 7, 9, 10, 1], [9, 5, 4, 6, 3, 2, 7, 1, 8, 10], [10, 5, 4, 6, 3, 2, 7, 1, 8, 9]}, { [8, 6, 5, 7, 3, 2, 4, 9, 1, 10], [8, 6, 5, 7, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 3, 2, 4, 1, 8, 10], [10, 6, 5, 7, 3, 2, 4, 1, 8, 9]}, { [8, 7, 4, 3, 5, 2, 6, 9, 1, 10], [8, 7, 4, 3, 5, 2, 6, 9, 10, 1], [9, 6, 4, 3, 5, 7, 2, 1, 8, 10], [10, 6, 4, 3, 5, 7, 2, 1, 8, 9]}, { [8, 7, 5, 3, 2, 4, 6, 9, 1, 10], [8, 7, 5, 3, 2, 4, 6, 9, 10, 1], [9, 5, 4, 6, 3, 7, 2, 1, 8, 10], [10, 5, 4, 6, 3, 7, 2, 1, 8, 9]}} is given by the following expression / 101 481 2 51 3 119 4 77 5 6\ |- ------ n + ------- n + ------ n - ------- n - ------- n - 7/5898240 n | \ 245760 2949120 131072 1179648 1966080 / n / 2369 2 133 3 1741 4 173 5 4 + |7/17160 n + ------- n - ------ n - ------- n + ------- n \ 2882880 274560 1729728 2882880 1597 6 19 7 8\ + ------- n + ------- n + 1/8648640 n | C(n) 8648640 1153152 / and in Maple input form: (-101/245760*n+481/2949120*n^2+51/131072*n^3-119/1179648*n^4-77/1966080*n^5-7/ 5898240*n^6)*4^n+(7/17160*n+2369/2882880*n^2-133/274560*n^3-1741/1729728*n^4+ 173/2882880*n^5+1597/8648640*n^6+19/1153152*n^7+1/8648640*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 16 1/2 15 14 1/2 13 12 1/2 11 m 7 Pi m 19 m 637 Pi m 1597 m 6839 Pi m ------- - ----------- + ------- - ------------- + -------- - -------------- 8648640 5898240 1153152 15728640 8648640 47185920 10 1/2 9 8 1/2 7 6 173 m 289 Pi m 1741 m 28351 Pi m 133 m + ------- + ------------ - ------- + -------------- - ------ 2882880 1048576 1729728 47185920 274560 1/2 5 4 1/2 3 2 1789 Pi m 2369 m 303 Pi m 7 m - ------------- + ------- - ------------ + ----- 7864320 2882880 655360 17160 and in Maple input form: 1/8648640*m^16-7/5898240*Pi^(1/2)*m^15+19/1153152*m^14-637/15728640*Pi^(1/2)*m^ 13+1597/8648640*m^12-6839/47185920*Pi^(1/2)*m^11+173/2882880*m^10+289/1048576* Pi^(1/2)*m^9-1741/1729728*m^8+28351/47185920*Pi^(1/2)*m^7-133/274560*m^6-1789/ 7864320*Pi^(1/2)*m^5+2369/2882880*m^4-303/655360*Pi^(1/2)*m^3+7/17160*m^2 For the, 30, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[8, 7, 9, 6, 10, 4, 2, 1, 3, 5]}, {[9, 7, 6, 8, 10, 3, 2, 4, 1, 5]}, {[6, 5, 7, 4, 8, 3, 9, 2, 10, 1], [10, 8, 6, 4, 2, 1, 3, 5, 7, 9]}, {[7, 5, 4, 6, 8, 3, 9, 2, 10, 1], [10, 8, 6, 3, 2, 4, 1, 5, 7, 9]}, {[7, 6, 8, 4, 3, 5, 9, 2, 10, 1], [10, 8, 5, 4, 6, 2, 1, 3, 7, 9]}, {[7, 6, 8, 5, 9, 3, 2, 4, 10, 1], [10, 7, 6, 8, 4, 2, 1, 3, 5, 9]}, {[7, 6, 8, 5, 9, 4, 10, 2, 1, 3], [9, 8, 10, 6, 4, 2, 1, 3, 5, 7]}, {[8, 5, 4, 6, 3, 7, 9, 2, 10, 1], [10, 8, 5, 3, 2, 4, 6, 1, 7, 9]}, {[8, 6, 4, 3, 5, 7, 9, 2, 10, 1], [10, 8, 4, 3, 5, 2, 6, 1, 7, 9]}, {[8, 6, 5, 7, 9, 3, 2, 4, 10, 1], [10, 7, 6, 8, 3, 2, 4, 1, 5, 9]}, {[8, 6, 5, 7, 9, 4, 10, 2, 1, 3], [9, 8, 10, 6, 3, 2, 4, 1, 5, 7]}, {[8, 7, 9, 4, 3, 5, 2, 6, 10, 1], [10, 7, 5, 4, 6, 8, 2, 1, 3, 9]}, {[8, 7, 9, 5, 3, 2, 4, 6, 10, 1], [10, 6, 5, 7, 4, 8, 2, 1, 3, 9]}, {[8, 7, 9, 5, 4, 6, 10, 2, 1, 3], [9, 8, 10, 5, 4, 6, 2, 1, 3, 7]}, {[8, 7, 9, 6, 10, 3, 2, 4, 1, 5], [9, 7, 6, 8, 10, 4, 2, 1, 3, 5]}, {[9, 5, 4, 6, 3, 7, 2, 8, 10, 1], [10, 7, 5, 3, 2, 4, 6, 8, 1, 9]}, {[9, 6, 4, 3, 5, 7, 2, 8, 10, 1], [10, 7, 4, 3, 5, 2, 6, 8, 1, 9]}, {[9, 6, 5, 7, 3, 2, 4, 8, 10, 1], [10, 6, 5, 7, 3, 2, 4, 8, 1, 9]}, {[9, 6, 5, 7, 4, 8, 10, 2, 1, 3], [9, 8, 10, 5, 3, 2, 4, 6, 1, 7]}, {[9, 7, 4, 3, 5, 2, 6, 8, 10, 1], [10, 6, 4, 3, 5, 7, 2, 8, 1, 9]}, {[9, 7, 5, 3, 2, 4, 6, 8, 10, 1], [10, 5, 4, 6, 3, 7, 2, 8, 1, 9]}, {[9, 7, 5, 4, 6, 8, 10, 2, 1, 3], [9, 8, 10, 4, 3, 5, 2, 6, 1, 7]}} is given by the following expression / 13 217 2 13 3 4 17 5 6\ n |----- n - ------ n + ------ n + 5/131072 n - ------- n - 1/1966080 n | 4 \81920 983040 393216 1966080 / / 317 2 799 3 1669 4 1333 5 + |-1/5720 n - ------- n + ------- n + -------- n - ------- n \ 2882880 2471040 17297280 8648640 29 6 97 7 8\ + ------- n + -------- n + 1/17297280 n | C(n) 2162160 17297280 / and in Maple input form: (13/81920*n-217/983040*n^2+13/393216*n^3+5/131072*n^4-17/1966080*n^5-1/1966080* n^6)*4^n+(-1/5720*n-317/2882880*n^2+799/2471040*n^3+1669/17297280*n^4-1333/ 8648640*n^5+29/2162160*n^6+97/17297280*n^7+1/17297280*n^8)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 16 1/2 15 14 1/2 13 12 1/2 11 m Pi m 97 m 29 Pi m 29 m 149 Pi m -------- - --------- + -------- - ------------ + ------- + ------------- 17297280 1966080 17297280 3145728 2162160 5242880 10 1/2 9 8 1/2 7 6 1333 m 239 Pi m 1669 m 2887 Pi m 799 m - -------- + ------------ + -------- - ------------- + ------- 8648640 3145728 17297280 15728640 2471040 1/2 5 4 1/2 3 2 47 Pi m 317 m 117 Pi m m - ----------- - ------- + ------------ - ---- 524288 2882880 655360 5720 and in Maple input form: 1/17297280*m^16-1/1966080*Pi^(1/2)*m^15+97/17297280*m^14-29/3145728*Pi^(1/2)*m^ 13+29/2162160*m^12+149/5242880*Pi^(1/2)*m^11-1333/8648640*m^10+239/3145728*Pi^( 1/2)*m^9+1669/17297280*m^8-2887/15728640*Pi^(1/2)*m^7+799/2471040*m^6-47/524288 *Pi^(1/2)*m^5-317/2882880*m^4+117/655360*Pi^(1/2)*m^3-1/5720*m^2 For the, 31, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[5, 4, 3, 2, 1, 6, 7, 8, 9, 10]}, {[6, 5, 3, 4, 2, 1, 7, 8, 9, 10]}, {[6, 7, 5, 4, 3, 1, 2, 8, 9, 10]}, {[7, 5, 6, 4, 2, 3, 1, 8, 9, 10]}, {[7, 6, 3, 4, 5, 2, 1, 8, 9, 10]}, {[7, 8, 6, 4, 5, 3, 1, 2, 9, 10]}, {[7, 8, 9, 6, 5, 4, 1, 2, 3, 10]}, {[8, 6, 7, 4, 5, 2, 3, 1, 9, 10]}, {[8, 7, 3, 4, 5, 6, 2, 1, 9, 10]}, {[8, 9, 6, 7, 5, 3, 4, 1, 2, 10]}, {[8, 9, 7, 4, 5, 6, 3, 1, 2, 10]}, {[8, 9, 10, 7, 5, 6, 4, 1, 2, 3]}, {[9, 6, 7, 8, 5, 2, 3, 4, 1, 10]}, {[9, 7, 8, 4, 5, 6, 2, 3, 1, 10]}, {[9, 8, 3, 4, 5, 6, 7, 2, 1, 10]}, {[9, 10, 7, 8, 5, 6, 3, 4, 1, 2]}, {[9, 10, 8, 4, 5, 6, 7, 3, 1, 2]}, {[10, 7, 8, 9, 5, 6, 2, 3, 4, 1]}, {[10, 8, 9, 4, 5, 6, 7, 2, 3, 1]}, {[10, 9, 3, 4, 5, 6, 7, 8, 2, 1]}, {[5, 6, 4, 3, 2, 1, 7, 8, 9, 10], [6, 5, 4, 3, 1, 2, 7, 8, 9, 10]}, {[5, 6, 7, 4, 3, 2, 1, 8, 9, 10], [7, 6, 5, 4, 1, 2, 3, 8, 9, 10]}, {[5, 6, 7, 8, 4, 3, 2, 1, 9, 10], [8, 7, 6, 5, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 9, 4, 3, 2, 1, 10], [9, 8, 7, 6, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 10, 4, 3, 2, 1], [10, 9, 8, 7, 1, 2, 3, 4, 5, 6]}, {[6, 4, 5, 3, 2, 1, 7, 8, 9, 10], [6, 5, 4, 2, 3, 1, 7, 8, 9, 10]}, {[6, 7, 4, 5, 3, 2, 1, 8, 9, 10], [7, 6, 5, 3, 4, 1, 2, 8, 9, 10]}, {[6, 7, 5, 3, 4, 2, 1, 8, 9, 10], [7, 6, 4, 5, 3, 1, 2, 8, 9, 10]}, {[6, 7, 5, 4, 2, 3, 1, 8, 9, 10], [7, 5, 6, 4, 3, 1, 2, 8, 9, 10]}, {[6, 7, 8, 4, 5, 3, 2, 1, 9, 10], [8, 7, 6, 4, 5, 1, 2, 3, 9, 10]}, {[6, 7, 8, 5, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 4, 1, 2, 3, 9, 10]}, {[6, 7, 8, 5, 4, 2, 3, 1, 9, 10], [8, 6, 7, 5, 4, 1, 2, 3, 9, 10]}, {[6, 7, 8, 5, 4, 3, 1, 2, 9, 10], [7, 8, 6, 5, 4, 1, 2, 3, 9, 10]}, {[6, 7, 8, 9, 4, 5, 3, 2, 1, 10], [9, 8, 7, 5, 6, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 5, 3, 4, 2, 1, 10], [9, 8, 6, 7, 5, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 5, 4, 2, 3, 1, 10], [9, 7, 8, 6, 5, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 5, 4, 3, 1, 2, 10], [8, 9, 7, 6, 5, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 10, 4, 5, 3, 2, 1], [10, 9, 8, 6, 7, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 5, 3, 4, 2, 1], [10, 9, 7, 8, 6, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 5, 4, 2, 3, 1], [10, 8, 9, 7, 6, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 5, 4, 3, 1, 2], [9, 10, 8, 7, 6, 1, 2, 3, 4, 5]}, {[7, 4, 5, 6, 3, 2, 1, 8, 9, 10], [7, 6, 5, 2, 3, 4, 1, 8, 9, 10]}, {[7, 5, 6, 3, 4, 2, 1, 8, 9, 10], [7, 6, 4, 5, 2, 3, 1, 8, 9, 10]}, {[7, 8, 4, 5, 6, 3, 2, 1, 9, 10], [8, 7, 6, 3, 4, 5, 1, 2, 9, 10]}, {[7, 8, 5, 6, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 3, 4, 1, 2, 9, 10]}, {[7, 8, 5, 6, 4, 2, 3, 1, 9, 10], [8, 6, 7, 5, 3, 4, 1, 2, 9, 10]}, {[7, 8, 5, 6, 4, 3, 1, 2, 9, 10], [7, 8, 6, 5, 3, 4, 1, 2, 9, 10]}, {[7, 8, 6, 3, 4, 5, 2, 1, 9, 10], [8, 7, 4, 5, 6, 3, 1, 2, 9, 10]}, {[7, 8, 6, 4, 5, 2, 3, 1, 9, 10], [8, 6, 7, 4, 5, 3, 1, 2, 9, 10]}, {[7, 8, 6, 5, 2, 3, 4, 1, 9, 10], [8, 5, 6, 7, 4, 3, 1, 2, 9, 10]}, {[7, 8, 9, 4, 5, 6, 3, 2, 1, 10], [9, 8, 7, 4, 5, 6, 1, 2, 3, 10]}, {[7, 8, 9, 5, 6, 3, 4, 2, 1, 10], [9, 8, 6, 7, 4, 5, 1, 2, 3, 10]}, {[7, 8, 9, 5, 6, 4, 2, 3, 1, 10], [9, 7, 8, 6, 4, 5, 1, 2, 3, 10]}, {[7, 8, 9, 5, 6, 4, 3, 1, 2, 10], [8, 9, 7, 6, 4, 5, 1, 2, 3, 10]}, {[7, 8, 9, 6, 3, 4, 5, 2, 1, 10], [9, 8, 5, 6, 7, 4, 1, 2, 3, 10]}, {[7, 8, 9, 6, 4, 5, 2, 3, 1, 10], [9, 7, 8, 5, 6, 4, 1, 2, 3, 10]}, {[7, 8, 9, 6, 4, 5, 3, 1, 2, 10], [8, 9, 7, 5, 6, 4, 1, 2, 3, 10]}, {[7, 8, 9, 6, 5, 2, 3, 4, 1, 10], [9, 6, 7, 8, 5, 4, 1, 2, 3, 10]}, {[7, 8, 9, 6, 5, 3, 4, 1, 2, 10], [8, 9, 6, 7, 5, 4, 1, 2, 3, 10]}, {[7, 8, 9, 10, 4, 5, 6, 3, 2, 1], [10, 9, 8, 5, 6, 7, 1, 2, 3, 4]}, {[7, 8, 9, 10, 5, 6, 3, 4, 2, 1], [10, 9, 7, 8, 5, 6, 1, 2, 3, 4]}, {[7, 8, 9, 10, 5, 6, 4, 2, 3, 1], [10, 8, 9, 7, 5, 6, 1, 2, 3, 4]}, {[7, 8, 9, 10, 5, 6, 4, 3, 1, 2], [9, 10, 8, 7, 5, 6, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 4, 5, 3, 1, 2], [9, 10, 8, 6, 7, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 5, 3, 4, 1, 2], [9, 10, 7, 8, 6, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 5, 4, 1, 2, 3], [8, 9, 10, 7, 6, 5, 1, 2, 3, 4]}, {[8, 4, 5, 6, 7, 3, 2, 1, 9, 10], [8, 7, 6, 2, 3, 4, 5, 1, 9, 10]}, {[8, 5, 6, 7, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 2, 3, 4, 1, 9, 10]}, {[8, 5, 6, 7, 4, 2, 3, 1, 9, 10], [8, 6, 7, 5, 2, 3, 4, 1, 9, 10]}, {[8, 6, 7, 3, 4, 5, 2, 1, 9, 10], [8, 7, 4, 5, 6, 2, 3, 1, 9, 10]}, {[8, 9, 4, 5, 6, 7, 3, 2, 1, 10], [9, 8, 7, 3, 4, 5, 6, 1, 2, 10]}, {[8, 9, 5, 6, 7, 3, 4, 2, 1, 10], [9, 8, 6, 7, 3, 4, 5, 1, 2, 10]}, {[8, 9, 5, 6, 7, 4, 2, 3, 1, 10], [9, 7, 8, 6, 3, 4, 5, 1, 2, 10]}, {[8, 9, 5, 6, 7, 4, 3, 1, 2, 10], [8, 9, 7, 6, 3, 4, 5, 1, 2, 10]}, {[8, 9, 6, 7, 3, 4, 5, 2, 1, 10], [9, 8, 5, 6, 7, 3, 4, 1, 2, 10]}, {[8, 9, 6, 7, 4, 5, 2, 3, 1, 10], [9, 7, 8, 5, 6, 3, 4, 1, 2, 10]}, {[8, 9, 6, 7, 4, 5, 3, 1, 2, 10], [8, 9, 7, 5, 6, 3, 4, 1, 2, 10]}, {[8, 9, 6, 7, 5, 2, 3, 4, 1, 10], [9, 6, 7, 8, 5, 3, 4, 1, 2, 10]}, {[8, 9, 7, 3, 4, 5, 6, 2, 1, 10], [9, 8, 4, 5, 6, 7, 3, 1, 2, 10]}, {[8, 9, 7, 4, 5, 6, 2, 3, 1, 10], [9, 7, 8, 4, 5, 6, 3, 1, 2, 10]}, {[8, 9, 7, 5, 6, 2, 3, 4, 1, 10], [9, 6, 7, 8, 4, 5, 3, 1, 2, 10]}, {[8, 9, 7, 6, 2, 3, 4, 5, 1, 10], [9, 5, 6, 7, 8, 4, 3, 1, 2, 10]}, {[8, 9, 10, 4, 5, 6, 7, 3, 2, 1], [10, 9, 8, 4, 5, 6, 7, 1, 2, 3]}, {[8, 9, 10, 5, 6, 7, 3, 4, 2, 1], [10, 9, 7, 8, 4, 5, 6, 1, 2, 3]}, {[8, 9, 10, 5, 6, 7, 4, 2, 3, 1], [10, 8, 9, 7, 4, 5, 6, 1, 2, 3]}, {[8, 9, 10, 5, 6, 7, 4, 3, 1, 2], [9, 10, 8, 7, 4, 5, 6, 1, 2, 3]}, {[8, 9, 10, 6, 7, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 4, 5, 3, 1, 2], [9, 10, 8, 6, 7, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 5, 3, 4, 1, 2], [9, 10, 7, 8, 6, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 5, 4, 1, 2, 3], [8, 9, 10, 7, 6, 4, 5, 1, 2, 3]}, {[8, 9, 10, 7, 3, 4, 5, 6, 2, 1], [10, 9, 5, 6, 7, 8, 4, 1, 2, 3]}, {[8, 9, 10, 7, 4, 5, 6, 2, 3, 1], [10, 8, 9, 5, 6, 7, 4, 1, 2, 3]}, {[8, 9, 10, 7, 4, 5, 6, 3, 1, 2], [9, 10, 8, 5, 6, 7, 4, 1, 2, 3]}, {[8, 9, 10, 7, 5, 6, 2, 3, 4, 1], [10, 7, 8, 9, 5, 6, 4, 1, 2, 3]}, {[8, 9, 10, 7, 5, 6, 3, 4, 1, 2], [9, 10, 7, 8, 5, 6, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 5, 4, 1, 2, 3]}, {[8, 9, 10, 7, 6, 3, 4, 5, 1, 2], [9, 10, 6, 7, 8, 5, 4, 1, 2, 3]}, {[9, 4, 5, 6, 7, 8, 3, 2, 1, 10], [9, 8, 7, 2, 3, 4, 5, 6, 1, 10]}, {[9, 5, 6, 7, 8, 3, 4, 2, 1, 10], [9, 8, 6, 7, 2, 3, 4, 5, 1, 10]}, {[9, 5, 6, 7, 8, 4, 2, 3, 1, 10], [9, 7, 8, 6, 2, 3, 4, 5, 1, 10]}, {[9, 6, 7, 8, 3, 4, 5, 2, 1, 10], [9, 8, 5, 6, 7, 2, 3, 4, 1, 10]}, {[9, 6, 7, 8, 4, 5, 2, 3, 1, 10], [9, 7, 8, 5, 6, 2, 3, 4, 1, 10]}, {[9, 7, 8, 3, 4, 5, 6, 2, 1, 10], [9, 8, 4, 5, 6, 7, 2, 3, 1, 10]}, {[9, 10, 4, 5, 6, 7, 8, 3, 2, 1], [10, 9, 8, 3, 4, 5, 6, 7, 1, 2]}, {[9, 10, 5, 6, 7, 8, 3, 4, 2, 1], [10, 9, 7, 8, 3, 4, 5, 6, 1, 2]}, {[9, 10, 5, 6, 7, 8, 4, 2, 3, 1], [10, 8, 9, 7, 3, 4, 5, 6, 1, 2]}, {[9, 10, 5, 6, 7, 8, 4, 3, 1, 2], [9, 10, 8, 7, 3, 4, 5, 6, 1, 2]}, {[9, 10, 6, 7, 8, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 3, 4, 5, 1, 2]}, {[9, 10, 6, 7, 8, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 3, 4, 5, 1, 2]}, {[9, 10, 6, 7, 8, 4, 5, 3, 1, 2], [9, 10, 8, 6, 7, 3, 4, 5, 1, 2]}, {[9, 10, 6, 7, 8, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 3, 4, 5, 1, 2]}, {[9, 10, 6, 7, 8, 5, 3, 4, 1, 2], [9, 10, 7, 8, 6, 3, 4, 5, 1, 2]}, {[9, 10, 7, 8, 3, 4, 5, 6, 2, 1], [10, 9, 5, 6, 7, 8, 3, 4, 1, 2]}, {[9, 10, 7, 8, 4, 5, 6, 2, 3, 1], [10, 8, 9, 5, 6, 7, 3, 4, 1, 2]}, {[9, 10, 7, 8, 4, 5, 6, 3, 1, 2], [9, 10, 8, 5, 6, 7, 3, 4, 1, 2]}, {[9, 10, 7, 8, 5, 6, 2, 3, 4, 1], [10, 7, 8, 9, 5, 6, 3, 4, 1, 2]}, {[9, 10, 7, 8, 6, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 5, 3, 4, 1, 2]}, {[9, 10, 8, 3, 4, 5, 6, 7, 2, 1], [10, 9, 4, 5, 6, 7, 8, 3, 1, 2]}, {[9, 10, 8, 4, 5, 6, 7, 2, 3, 1], [10, 8, 9, 4, 5, 6, 7, 3, 1, 2]}, {[9, 10, 8, 5, 6, 7, 2, 3, 4, 1], [10, 7, 8, 9, 4, 5, 6, 3, 1, 2]}, {[9, 10, 8, 6, 7, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 4, 5, 3, 1, 2]}, {[9, 10, 8, 7, 2, 3, 4, 5, 6, 1], [10, 5, 6, 7, 8, 9, 4, 3, 1, 2]}, {[10, 4, 5, 6, 7, 8, 9, 3, 2, 1], [10, 9, 8, 2, 3, 4, 5, 6, 7, 1]}, {[10, 5, 6, 7, 8, 9, 3, 4, 2, 1], [10, 9, 7, 8, 2, 3, 4, 5, 6, 1]}, {[10, 5, 6, 7, 8, 9, 4, 2, 3, 1], [10, 8, 9, 7, 2, 3, 4, 5, 6, 1]}, {[10, 6, 7, 8, 9, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 2, 3, 4, 5, 1]}, {[10, 6, 7, 8, 9, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 2, 3, 4, 5, 1]}, {[10, 6, 7, 8, 9, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 2, 3, 4, 5, 1]}, {[10, 7, 8, 9, 3, 4, 5, 6, 2, 1], [10, 9, 5, 6, 7, 8, 2, 3, 4, 1]}, {[10, 7, 8, 9, 4, 5, 6, 2, 3, 1], [10, 8, 9, 5, 6, 7, 2, 3, 4, 1]}, {[10, 8, 9, 3, 4, 5, 6, 7, 2, 1], [10, 9, 4, 5, 6, 7, 8, 2, 3, 1]}} is given by the following expression / 44503 1162859 2 44371 3 13871 4 673 5 6\ |1/2 + ----- n + ------- n + ------ n + ------ n + ------ n + 7/2949120 n | \ 40960 1474560 196608 589824 983040 / n / 126383 11287 2 53459 3 134231 4 104989 5 4 + |- 1/2 - ------ n - ----- n - ----- n - ------ n - ------ n \ 55440 3024 19008 133056 665280 1157 6 7\ - ------ n - 1/9504 n | C(n) 133056 / and in Maple input form: (1/2+44503/40960*n+1162859/1474560*n^2+44371/196608*n^3+13871/589824*n^4+673/ 983040*n^5+7/2949120*n^6)*4^n+(-1/2-126383/55440*n-11287/3024*n^2-53459/19008*n ^3-134231/133056*n^4-104989/665280*n^5-1157/133056*n^6-1/9504*n^7)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 15 14 1/2 13 12 1/2 11 10 7 Pi m m 1081 Pi m 1157 m 573011 Pi m 104989 m ----------- - ---- + -------------- - -------- + ---------------- - ---------- 2949120 9504 1572864 133056 23592960 665280 1/2 9 8 1/2 7 6 396581 Pi m 134231 m 24595829 Pi m 53459 m + --------------- - --------- + ----------------- - -------- 1572864 133056 23592960 19008 1/2 5 4 1/2 3 2 1/2 517391 Pi m 11287 m 564367 Pi m 126383 m 9 Pi m + --------------- - -------- + --------------- - --------- + --------- 262144 3024 327680 55440 16 - 1/2 and in Maple input form: 7/2949120*Pi^(1/2)*m^15-1/9504*m^14+1081/1572864*Pi^(1/2)*m^13-1157/133056*m^12 +573011/23592960*Pi^(1/2)*m^11-104989/665280*m^10+396581/1572864*Pi^(1/2)*m^9-\ 134231/133056*m^8+24595829/23592960*Pi^(1/2)*m^7-53459/19008*m^6+517391/262144* Pi^(1/2)*m^5-11287/3024*m^4+564367/327680*Pi^(1/2)*m^3-126383/55440*m^2+9/16*Pi ^(1/2)*m-1/2 For the, 32, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[5, 4, 3, 2, 6, 1, 7, 8, 9, 10], [6, 4, 3, 2, 1, 5, 7, 8, 9, 10]}, {[5, 4, 3, 2, 6, 7, 1, 8, 9, 10], [7, 4, 3, 2, 1, 5, 6, 8, 9, 10]}, {[5, 4, 3, 2, 6, 7, 8, 1, 9, 10], [8, 4, 3, 2, 1, 5, 6, 7, 9, 10]}, {[5, 4, 6, 3, 2, 1, 7, 8, 9, 10], [6, 5, 4, 2, 1, 3, 7, 8, 9, 10]}, {[5, 4, 6, 7, 3, 2, 1, 8, 9, 10], [7, 6, 5, 2, 1, 3, 4, 8, 9, 10]}, {[5, 4, 6, 7, 8, 3, 2, 1, 9, 10], [8, 7, 6, 2, 1, 3, 4, 5, 9, 10]}, {[5, 4, 6, 7, 8, 9, 3, 2, 1, 10], [9, 8, 7, 2, 1, 3, 4, 5, 6, 10]}, {[5, 4, 6, 7, 8, 9, 10, 3, 2, 1], [10, 9, 8, 2, 1, 3, 4, 5, 6, 7]}, {[5, 6, 4, 3, 2, 7, 1, 8, 9, 10], [7, 5, 4, 3, 1, 2, 6, 8, 9, 10]}, {[5, 6, 4, 3, 2, 7, 8, 1, 9, 10], [8, 5, 4, 3, 1, 2, 6, 7, 9, 10]}, {[5, 6, 4, 7, 3, 2, 1, 8, 9, 10], [7, 6, 5, 3, 1, 2, 4, 8, 9, 10]}, {[5, 6, 4, 7, 8, 3, 2, 1, 9, 10], [8, 7, 6, 3, 1, 2, 4, 5, 9, 10]}, {[5, 6, 4, 7, 8, 9, 3, 2, 1, 10], [9, 8, 7, 3, 1, 2, 4, 5, 6, 10]}, {[5, 6, 4, 7, 8, 9, 10, 3, 2, 1], [10, 9, 8, 3, 1, 2, 4, 5, 6, 7]}, {[5, 6, 7, 4, 3, 2, 8, 1, 9, 10], [8, 6, 5, 4, 1, 2, 3, 7, 9, 10]}, {[5, 6, 7, 4, 8, 3, 2, 1, 9, 10], [8, 7, 6, 4, 1, 2, 3, 5, 9, 10]}, {[5, 6, 7, 4, 8, 9, 3, 2, 1, 10], [9, 8, 7, 4, 1, 2, 3, 5, 6, 10]}, {[5, 6, 7, 4, 8, 9, 10, 3, 2, 1], [10, 9, 8, 4, 1, 2, 3, 5, 6, 7]}, {[5, 6, 7, 8, 4, 9, 3, 2, 1, 10], [9, 8, 7, 5, 1, 2, 3, 4, 6, 10]}, {[5, 6, 7, 8, 4, 9, 10, 3, 2, 1], [10, 9, 8, 5, 1, 2, 3, 4, 6, 7]}, {[5, 6, 7, 8, 9, 4, 3, 2, 10, 1], [10, 8, 7, 6, 1, 2, 3, 4, 5, 9]}, {[5, 6, 7, 8, 9, 4, 10, 3, 2, 1], [10, 9, 8, 6, 1, 2, 3, 4, 5, 7]}, {[6, 4, 3, 5, 2, 1, 7, 8, 9, 10], [6, 5, 3, 2, 4, 1, 7, 8, 9, 10]}, {[6, 4, 5, 3, 2, 7, 1, 8, 9, 10], [7, 5, 4, 2, 3, 1, 6, 8, 9, 10]}, {[6, 4, 5, 3, 2, 7, 8, 1, 9, 10], [8, 5, 4, 2, 3, 1, 6, 7, 9, 10]}, {[6, 4, 5, 7, 3, 2, 1, 8, 9, 10], [7, 6, 5, 2, 3, 1, 4, 8, 9, 10]}, {[6, 4, 5, 7, 8, 3, 2, 1, 9, 10], [8, 7, 6, 2, 3, 1, 4, 5, 9, 10]}, {[6, 4, 5, 7, 8, 9, 3, 2, 1, 10], [9, 8, 7, 2, 3, 1, 4, 5, 6, 10]}, {[6, 4, 5, 7, 8, 9, 10, 3, 2, 1], [10, 9, 8, 2, 3, 1, 4, 5, 6, 7]}, {[6, 5, 3, 4, 2, 7, 1, 8, 9, 10], [7, 5, 3, 4, 2, 1, 6, 8, 9, 10]}, {[6, 5, 3, 4, 2, 7, 8, 1, 9, 10], [8, 5, 3, 4, 2, 1, 6, 7, 9, 10]}, {[6, 5, 4, 2, 3, 7, 1, 8, 9, 10], [7, 4, 5, 3, 2, 1, 6, 8, 9, 10]}, {[6, 5, 4, 2, 3, 7, 8, 1, 9, 10], [8, 4, 5, 3, 2, 1, 6, 7, 9, 10]}, {[6, 5, 4, 3, 7, 1, 2, 8, 9, 10], [6, 7, 4, 3, 2, 1, 5, 8, 9, 10]}, {[6, 5, 4, 3, 7, 8, 1, 2, 9, 10], [7, 8, 4, 3, 2, 1, 5, 6, 9, 10]}, {[6, 5, 4, 3, 7, 8, 9, 1, 2, 10], [8, 9, 4, 3, 2, 1, 5, 6, 7, 10]}, {[6, 5, 4, 3, 7, 8, 9, 10, 1, 2], [9, 10, 4, 3, 2, 1, 5, 6, 7, 8]}, {[6, 5, 7, 3, 4, 2, 1, 8, 9, 10], [7, 6, 4, 5, 2, 1, 3, 8, 9, 10]}, {[6, 5, 7, 4, 2, 3, 1, 8, 9, 10], [7, 5, 6, 4, 2, 1, 3, 8, 9, 10]}, {[6, 5, 7, 4, 3, 1, 2, 8, 9, 10], [6, 7, 5, 4, 2, 1, 3, 8, 9, 10]}, {[6, 5, 7, 8, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 2, 1, 3, 4, 9, 10]}, {[6, 5, 7, 8, 4, 2, 3, 1, 9, 10], [8, 6, 7, 5, 2, 1, 3, 4, 9, 10]}, {[6, 5, 7, 8, 4, 3, 1, 2, 9, 10], [7, 8, 6, 5, 2, 1, 3, 4, 9, 10]}, {[6, 5, 7, 8, 9, 3, 4, 2, 1, 10], [9, 8, 6, 7, 2, 1, 3, 4, 5, 10]}, {[6, 5, 7, 8, 9, 4, 2, 3, 1, 10], [9, 7, 8, 6, 2, 1, 3, 4, 5, 10]}, {[6, 5, 7, 8, 9, 4, 3, 1, 2, 10], [8, 9, 7, 6, 2, 1, 3, 4, 5, 10]}, {[6, 5, 7, 8, 9, 10, 3, 4, 2, 1], [10, 9, 7, 8, 2, 1, 3, 4, 5, 6]}, {[6, 5, 7, 8, 9, 10, 4, 2, 3, 1], [10, 8, 9, 7, 2, 1, 3, 4, 5, 6]}, {[6, 5, 7, 8, 9, 10, 4, 3, 1, 2], [9, 10, 8, 7, 2, 1, 3, 4, 5, 6]}, {[6, 7, 4, 3, 5, 2, 1, 8, 9, 10], [7, 6, 4, 3, 5, 1, 2, 8, 9, 10]}, {[6, 7, 4, 5, 3, 2, 8, 1, 9, 10], [8, 6, 5, 3, 4, 1, 2, 7, 9, 10]}, {[6, 7, 4, 5, 8, 3, 2, 1, 9, 10], [8, 7, 6, 3, 4, 1, 2, 5, 9, 10]}, {[6, 7, 4, 5, 8, 9, 3, 2, 1, 10], [9, 8, 7, 3, 4, 1, 2, 5, 6, 10]}, {[6, 7, 4, 5, 8, 9, 10, 3, 2, 1], [10, 9, 8, 3, 4, 1, 2, 5, 6, 7]}, {[6, 7, 5, 3, 2, 4, 1, 8, 9, 10], [7, 5, 4, 6, 3, 1, 2, 8, 9, 10]}, {[6, 7, 5, 3, 4, 2, 8, 1, 9, 10], [8, 6, 4, 5, 3, 1, 2, 7, 9, 10]}, {[6, 7, 5, 4, 2, 3, 8, 1, 9, 10], [8, 5, 6, 4, 3, 1, 2, 7, 9, 10]}, {[6, 7, 5, 4, 3, 8, 1, 2, 9, 10], [7, 8, 5, 4, 3, 1, 2, 6, 9, 10]}, {[6, 7, 5, 4, 3, 8, 9, 1, 2, 10], [8, 9, 5, 4, 3, 1, 2, 6, 7, 10]}, {[6, 7, 5, 4, 3, 8, 9, 10, 1, 2], [9, 10, 5, 4, 3, 1, 2, 6, 7, 8]}, {[6, 7, 5, 8, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 3, 1, 2, 4, 9, 10]}, {[6, 7, 5, 8, 4, 2, 3, 1, 9, 10], [8, 6, 7, 5, 3, 1, 2, 4, 9, 10]}, {[6, 7, 5, 8, 4, 3, 1, 2, 9, 10], [7, 8, 6, 5, 3, 1, 2, 4, 9, 10]}, {[6, 7, 5, 8, 9, 3, 4, 2, 1, 10], [9, 8, 6, 7, 3, 1, 2, 4, 5, 10]}, {[6, 7, 5, 8, 9, 4, 2, 3, 1, 10], [9, 7, 8, 6, 3, 1, 2, 4, 5, 10]}, {[6, 7, 5, 8, 9, 4, 3, 1, 2, 10], [8, 9, 7, 6, 3, 1, 2, 4, 5, 10]}, {[6, 7, 5, 8, 9, 10, 3, 4, 2, 1], [10, 9, 7, 8, 3, 1, 2, 4, 5, 6]}, {[6, 7, 5, 8, 9, 10, 4, 2, 3, 1], [10, 8, 9, 7, 3, 1, 2, 4, 5, 6]}, {[6, 7, 5, 8, 9, 10, 4, 3, 1, 2], [9, 10, 8, 7, 3, 1, 2, 4, 5, 6]}, {[6, 7, 8, 4, 3, 2, 1, 5, 9, 10], [7, 6, 5, 4, 8, 1, 2, 3, 9, 10]}, {[6, 7, 8, 4, 3, 5, 2, 1, 9, 10], [8, 7, 5, 4, 6, 1, 2, 3, 9, 10]}, {[6, 7, 8, 4, 5, 9, 3, 2, 1, 10], [9, 8, 7, 4, 5, 1, 2, 3, 6, 10]}, {[6, 7, 8, 4, 5, 9, 10, 3, 2, 1], [10, 9, 8, 4, 5, 1, 2, 3, 6, 7]}, {[6, 7, 8, 5, 3, 2, 4, 1, 9, 10], [8, 6, 5, 7, 4, 1, 2, 3, 9, 10]}, {[6, 7, 8, 5, 4, 2, 1, 3, 9, 10], [7, 6, 8, 5, 4, 1, 2, 3, 9, 10]}, {[6, 7, 8, 5, 4, 3, 9, 1, 2, 10], [8, 9, 6, 5, 4, 1, 2, 3, 7, 10]}, {[6, 7, 8, 5, 4, 3, 9, 10, 1, 2], [9, 10, 6, 5, 4, 1, 2, 3, 7, 8]}, {[6, 7, 8, 5, 9, 3, 4, 2, 1, 10], [9, 8, 6, 7, 4, 1, 2, 3, 5, 10]}, {[6, 7, 8, 5, 9, 4, 2, 3, 1, 10], [9, 7, 8, 6, 4, 1, 2, 3, 5, 10]}, {[6, 7, 8, 5, 9, 4, 3, 1, 2, 10], [8, 9, 7, 6, 4, 1, 2, 3, 5, 10]}, {[6, 7, 8, 5, 9, 10, 3, 4, 2, 1], [10, 9, 7, 8, 4, 1, 2, 3, 5, 6]}, {[6, 7, 8, 5, 9, 10, 4, 2, 3, 1], [10, 8, 9, 7, 4, 1, 2, 3, 5, 6]}, {[6, 7, 8, 5, 9, 10, 4, 3, 1, 2], [9, 10, 8, 7, 4, 1, 2, 3, 5, 6]}, {[6, 7, 8, 9, 4, 3, 2, 1, 5, 10], [8, 7, 6, 5, 9, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 4, 3, 5, 2, 1, 10], [9, 8, 6, 5, 7, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 4, 5, 3, 2, 10, 1], [10, 8, 7, 5, 6, 1, 2, 3, 4, 9]}, {[6, 7, 8, 9, 4, 5, 10, 3, 2, 1], [10, 9, 8, 5, 6, 1, 2, 3, 4, 7]}, {[6, 7, 8, 9, 5, 3, 2, 4, 1, 10], [9, 7, 6, 8, 5, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 5, 3, 4, 2, 10, 1], [10, 8, 6, 7, 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4, 2, 5, 1], [10, 8, 6, 7, 9, 3, 4, 5, 1, 2]}, {[9, 10, 6, 7, 8, 4, 2, 3, 5, 1], [10, 7, 8, 6, 9, 3, 4, 5, 1, 2]}, {[9, 10, 6, 7, 8, 4, 3, 5, 1, 2], [9, 10, 7, 6, 8, 3, 4, 5, 1, 2]}, {[9, 10, 7, 3, 4, 5, 6, 8, 2, 1], [10, 9, 4, 5, 6, 7, 3, 8, 1, 2]}, {[9, 10, 7, 4, 5, 6, 8, 2, 3, 1], [10, 8, 9, 4, 5, 6, 3, 7, 1, 2]}, {[9, 10, 7, 4, 5, 6, 8, 3, 1, 2], [9, 10, 8, 4, 5, 6, 3, 7, 1, 2]}, {[9, 10, 7, 5, 6, 8, 2, 3, 4, 1], [10, 7, 8, 9, 4, 5, 3, 6, 1, 2]}, {[9, 10, 7, 5, 6, 8, 3, 4, 1, 2], [9, 10, 7, 8, 4, 5, 3, 6, 1, 2]}, {[9, 10, 7, 6, 8, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 4, 3, 5, 1, 2]}, {[9, 10, 7, 8, 3, 2, 4, 5, 6, 1], [10, 6, 5, 7, 8, 9, 3, 4, 1, 2]}, {[9, 10, 7, 8, 3, 4, 2, 5, 6, 1], [10, 7, 5, 6, 8, 9, 3, 4, 1, 2]}, {[9, 10, 7, 8, 3, 4, 5, 2, 6, 1], [10, 8, 5, 6, 7, 9, 3, 4, 1, 2]}, {[9, 10, 7, 8, 4, 2, 3, 5, 6, 1], [10, 6, 7, 5, 8, 9, 3, 4, 1, 2]}, {[9, 10, 7, 8, 4, 5, 2, 3, 6, 1], [10, 7, 8, 5, 6, 9, 3, 4, 1, 2]}, {[9, 10, 7, 8, 5, 2, 3, 4, 6, 1], [10, 6, 7, 8, 5, 9, 3, 4, 1, 2]}, {[9, 10, 8, 3, 2, 4, 5, 6, 7, 1], [10, 5, 4, 6, 7, 8, 9, 3, 1, 2]}, {[9, 10, 8, 3, 4, 2, 5, 6, 7, 1], [10, 6, 4, 5, 7, 8, 9, 3, 1, 2]}, {[9, 10, 8, 3, 4, 5, 2, 6, 7, 1], [10, 7, 4, 5, 6, 8, 9, 3, 1, 2]}, {[9, 10, 8, 3, 4, 5, 6, 2, 7, 1], [10, 8, 4, 5, 6, 7, 9, 3, 1, 2]}, {[9, 10, 8, 4, 2, 3, 5, 6, 7, 1], [10, 5, 6, 4, 7, 8, 9, 3, 1, 2]}, {[9, 10, 8, 4, 5, 2, 3, 6, 7, 1], [10, 6, 7, 4, 5, 8, 9, 3, 1, 2]}, {[9, 10, 8, 4, 5, 6, 2, 3, 7, 1], [10, 7, 8, 4, 5, 6, 9, 3, 1, 2]}, {[9, 10, 8, 5, 2, 3, 4, 6, 7, 1], [10, 5, 6, 7, 4, 8, 9, 3, 1, 2]}, {[9, 10, 8, 5, 6, 2, 3, 4, 7, 1], [10, 6, 7, 8, 4, 5, 9, 3, 1, 2]}, {[9, 10, 8, 6, 2, 3, 4, 5, 7, 1], [10, 5, 6, 7, 8, 4, 9, 3, 1, 2]}, {[10, 4, 3, 5, 6, 7, 8, 9, 2, 1], [10, 9, 3, 2, 4, 5, 6, 7, 8, 1]}, {[10, 4, 5, 3, 6, 7, 8, 9, 2, 1], [10, 9, 4, 2, 3, 5, 6, 7, 8, 1]}, {[10, 4, 5, 6, 3, 7, 8, 9, 2, 1], [10, 9, 5, 2, 3, 4, 6, 7, 8, 1]}, {[10, 4, 5, 6, 7, 3, 8, 9, 2, 1], [10, 9, 6, 2, 3, 4, 5, 7, 8, 1]}, {[10, 4, 5, 6, 7, 8, 3, 9, 2, 1], [10, 9, 7, 2, 3, 4, 5, 6, 8, 1]}, {[10, 5, 3, 4, 6, 7, 8, 9, 2, 1], [10, 9, 3, 4, 2, 5, 6, 7, 8, 1]}, {[10, 5, 4, 6, 7, 8, 9, 2, 3, 1], [10, 8, 9, 3, 2, 4, 5, 6, 7, 1]}, {[10, 5, 6, 3, 4, 7, 8, 9, 2, 1], [10, 9, 4, 5, 2, 3, 6, 7, 8, 1]}, {[10, 5, 6, 4, 7, 8, 9, 2, 3, 1], [10, 8, 9, 4, 2, 3, 5, 6, 7, 1]}, {[10, 5, 6, 7, 3, 4, 8, 9, 2, 1], [10, 9, 5, 6, 2, 3, 4, 7, 8, 1]}, {[10, 5, 6, 7, 4, 8, 9, 2, 3, 1], [10, 8, 9, 5, 2, 3, 4, 6, 7, 1]}, {[10, 5, 6, 7, 8, 3, 4, 9, 2, 1], [10, 9, 6, 7, 2, 3, 4, 5, 8, 1]}, {[10, 5, 6, 7, 8, 4, 9, 2, 3, 1], [10, 8, 9, 6, 2, 3, 4, 5, 7, 1]}, {[10, 5, 6, 7, 8, 9, 3, 2, 4, 1], [10, 8, 7, 9, 2, 3, 4, 5, 6, 1]}, {[10, 6, 3, 4, 5, 7, 8, 9, 2, 1], [10, 9, 3, 4, 5, 2, 6, 7, 8, 1]}, {[10, 6, 4, 5, 7, 8, 9, 2, 3, 1], [10, 8, 9, 3, 4, 2, 5, 6, 7, 1]}, {[10, 6, 5, 7, 8, 9, 2, 3, 4, 1], [10, 7, 8, 9, 3, 2, 4, 5, 6, 1]}, {[10, 6, 7, 3, 4, 5, 8, 9, 2, 1], [10, 9, 4, 5, 6, 2, 3, 7, 8, 1]}, {[10, 6, 7, 4, 5, 8, 9, 2, 3, 1], [10, 8, 9, 4, 5, 2, 3, 6, 7, 1]}, {[10, 6, 7, 5, 8, 9, 2, 3, 4, 1], [10, 7, 8, 9, 4, 2, 3, 5, 6, 1]}, {[10, 6, 7, 8, 3, 4, 5, 9, 2, 1], [10, 9, 5, 6, 7, 2, 3, 4, 8, 1]}, {[10, 6, 7, 8, 4, 5, 9, 2, 3, 1], [10, 8, 9, 5, 6, 2, 3, 4, 7, 1]}, {[10, 6, 7, 8, 5, 9, 2, 3, 4, 1], [10, 7, 8, 9, 5, 2, 3, 4, 6, 1]}, {[10, 6, 7, 8, 9, 3, 2, 4, 5, 1], [10, 7, 6, 8, 9, 2, 3, 4, 5, 1]}, {[10, 6, 7, 8, 9, 3, 4, 2, 5, 1], [10, 8, 6, 7, 9, 2, 3, 4, 5, 1]}, {[10, 6, 7, 8, 9, 4, 2, 3, 5, 1], [10, 7, 8, 6, 9, 2, 3, 4, 5, 1]}, {[10, 7, 3, 4, 5, 6, 8, 9, 2, 1], [10, 9, 3, 4, 5, 6, 2, 7, 8, 1]}, {[10, 7, 4, 5, 6, 8, 9, 2, 3, 1], [10, 8, 9, 3, 4, 5, 2, 6, 7, 1]}, {[10, 7, 5, 6, 8, 9, 2, 3, 4, 1], [10, 7, 8, 9, 3, 4, 2, 5, 6, 1]}, {[10, 7, 8, 3, 4, 5, 6, 9, 2, 1], [10, 9, 4, 5, 6, 7, 2, 3, 8, 1]}, {[10, 7, 8, 4, 5, 6, 9, 2, 3, 1], [10, 8, 9, 4, 5, 6, 2, 3, 7, 1]}, {[10, 7, 8, 5, 6, 9, 2, 3, 4, 1], [10, 7, 8, 9, 4, 5, 2, 3, 6, 1]}, {[10, 7, 8, 9, 3, 4, 5, 2, 6, 1], [10, 8, 5, 6, 7, 9, 2, 3, 4, 1]}, {[10, 8, 3, 4, 5, 6, 7, 9, 2, 1], [10, 9, 3, 4, 5, 6, 7, 2, 8, 1]}, {[10, 8, 4, 5, 6, 7, 9, 2, 3, 1], [10, 8, 9, 3, 4, 5, 6, 2, 7, 1]}, { [5, 4, 3, 2, 6, 7, 8, 9, 1, 10], [5, 4, 3, 2, 6, 7, 8, 9, 10, 1], [9, 4, 3, 2, 1, 5, 6, 7, 8, 10], [10, 4, 3, 2, 1, 5, 6, 7, 8, 9]}, { [5, 6, 4, 3, 2, 7, 8, 9, 1, 10], [5, 6, 4, 3, 2, 7, 8, 9, 10, 1], [9, 5, 4, 3, 1, 2, 6, 7, 8, 10], [10, 5, 4, 3, 1, 2, 6, 7, 8, 9]}, { [5, 6, 7, 4, 3, 2, 8, 9, 1, 10], [5, 6, 7, 4, 3, 2, 8, 9, 10, 1], [9, 6, 5, 4, 1, 2, 3, 7, 8, 10], [10, 6, 5, 4, 1, 2, 3, 7, 8, 9]}, { [5, 6, 7, 8, 4, 3, 2, 9, 1, 10], [5, 6, 7, 8, 4, 3, 2, 9, 10, 1], [9, 7, 6, 5, 1, 2, 3, 4, 8, 10], [10, 7, 6, 5, 1, 2, 3, 4, 8, 9]}, { [6, 4, 5, 3, 2, 7, 8, 9, 1, 10], [6, 4, 5, 3, 2, 7, 8, 9, 10, 1], [9, 5, 4, 2, 3, 1, 6, 7, 8, 10], [10, 5, 4, 2, 3, 1, 6, 7, 8, 9]}, { [6, 5, 3, 4, 2, 7, 8, 9, 1, 10], [6, 5, 3, 4, 2, 7, 8, 9, 10, 1], [9, 5, 3, 4, 2, 1, 6, 7, 8, 10], [10, 5, 3, 4, 2, 1, 6, 7, 8, 9]}, { [6, 5, 4, 2, 3, 7, 8, 9, 1, 10], [6, 5, 4, 2, 3, 7, 8, 9, 10, 1], [9, 4, 5, 3, 2, 1, 6, 7, 8, 10], [10, 4, 5, 3, 2, 1, 6, 7, 8, 9]}, { [6, 7, 4, 5, 3, 2, 8, 9, 1, 10], [6, 7, 4, 5, 3, 2, 8, 9, 10, 1], [9, 6, 5, 3, 4, 1, 2, 7, 8, 10], [10, 6, 5, 3, 4, 1, 2, 7, 8, 9]}, { [6, 7, 5, 3, 4, 2, 8, 9, 1, 10], [6, 7, 5, 3, 4, 2, 8, 9, 10, 1], [9, 6, 4, 5, 3, 1, 2, 7, 8, 10], [10, 6, 4, 5, 3, 1, 2, 7, 8, 9]}, { [6, 7, 5, 4, 2, 3, 8, 9, 1, 10], [6, 7, 5, 4, 2, 3, 8, 9, 10, 1], [9, 5, 6, 4, 3, 1, 2, 7, 8, 10], [10, 5, 6, 4, 3, 1, 2, 7, 8, 9]}, { [6, 7, 8, 4, 5, 3, 2, 9, 1, 10], [6, 7, 8, 4, 5, 3, 2, 9, 10, 1], [9, 7, 6, 4, 5, 1, 2, 3, 8, 10], [10, 7, 6, 4, 5, 1, 2, 3, 8, 9]}, { [6, 7, 8, 5, 3, 4, 2, 9, 1, 10], [6, 7, 8, 5, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 4, 1, 2, 3, 8, 10], [10, 7, 5, 6, 4, 1, 2, 3, 8, 9]}, { [6, 7, 8, 5, 4, 2, 3, 9, 1, 10], [6, 7, 8, 5, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 4, 1, 2, 3, 8, 10], [10, 6, 7, 5, 4, 1, 2, 3, 8, 9]}, { [7, 4, 5, 6, 3, 2, 8, 9, 1, 10], [7, 4, 5, 6, 3, 2, 8, 9, 10, 1], [9, 6, 5, 2, 3, 4, 1, 7, 8, 10], [10, 6, 5, 2, 3, 4, 1, 7, 8, 9]}, { [7, 5, 6, 3, 4, 2, 8, 9, 1, 10], [7, 5, 6, 3, 4, 2, 8, 9, 10, 1], [9, 6, 4, 5, 2, 3, 1, 7, 8, 10], [10, 6, 4, 5, 2, 3, 1, 7, 8, 9]}, { [7, 5, 6, 4, 2, 3, 8, 9, 1, 10], [7, 5, 6, 4, 2, 3, 8, 9, 10, 1], [9, 5, 6, 4, 2, 3, 1, 7, 8, 10], [10, 5, 6, 4, 2, 3, 1, 7, 8, 9]}, { [7, 6, 3, 4, 5, 2, 8, 9, 1, 10], [7, 6, 3, 4, 5, 2, 8, 9, 10, 1], [9, 6, 3, 4, 5, 2, 1, 7, 8, 10], [10, 6, 3, 4, 5, 2, 1, 7, 8, 9]}, { [7, 6, 4, 5, 2, 3, 8, 9, 1, 10], [7, 6, 4, 5, 2, 3, 8, 9, 10, 1], [9, 5, 6, 3, 4, 2, 1, 7, 8, 10], [10, 5, 6, 3, 4, 2, 1, 7, 8, 9]}, { [7, 6, 5, 2, 3, 4, 8, 9, 1, 10], [7, 6, 5, 2, 3, 4, 8, 9, 10, 1], [9, 4, 5, 6, 3, 2, 1, 7, 8, 10], [10, 4, 5, 6, 3, 2, 1, 7, 8, 9]}, { [7, 8, 4, 5, 6, 3, 2, 9, 1, 10], [7, 8, 4, 5, 6, 3, 2, 9, 10, 1], [9, 7, 6, 3, 4, 5, 1, 2, 8, 10], [10, 7, 6, 3, 4, 5, 1, 2, 8, 9]}, { [7, 8, 5, 6, 3, 4, 2, 9, 1, 10], [7, 8, 5, 6, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 3, 4, 1, 2, 8, 10], [10, 7, 5, 6, 3, 4, 1, 2, 8, 9]}, { [7, 8, 5, 6, 4, 2, 3, 9, 1, 10], [7, 8, 5, 6, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 3, 4, 1, 2, 8, 10], [10, 6, 7, 5, 3, 4, 1, 2, 8, 9]}, { [7, 8, 6, 3, 4, 5, 2, 9, 1, 10], [7, 8, 6, 3, 4, 5, 2, 9, 10, 1], [9, 7, 4, 5, 6, 3, 1, 2, 8, 10], [10, 7, 4, 5, 6, 3, 1, 2, 8, 9]}, { [7, 8, 6, 4, 5, 2, 3, 9, 1, 10], [7, 8, 6, 4, 5, 2, 3, 9, 10, 1], [9, 6, 7, 4, 5, 3, 1, 2, 8, 10], [10, 6, 7, 4, 5, 3, 1, 2, 8, 9]}, { [7, 8, 6, 5, 2, 3, 4, 9, 1, 10], [7, 8, 6, 5, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 4, 3, 1, 2, 8, 10], [10, 5, 6, 7, 4, 3, 1, 2, 8, 9]}, { [8, 4, 5, 6, 7, 3, 2, 9, 1, 10], [8, 4, 5, 6, 7, 3, 2, 9, 10, 1], [9, 7, 6, 2, 3, 4, 5, 1, 8, 10], [10, 7, 6, 2, 3, 4, 5, 1, 8, 9]}, { [8, 5, 6, 7, 3, 4, 2, 9, 1, 10], [8, 5, 6, 7, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 2, 3, 4, 1, 8, 10], [10, 7, 5, 6, 2, 3, 4, 1, 8, 9]}, { [8, 5, 6, 7, 4, 2, 3, 9, 1, 10], [8, 5, 6, 7, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 2, 3, 4, 1, 8, 10], [10, 6, 7, 5, 2, 3, 4, 1, 8, 9]}, { [8, 6, 7, 3, 4, 5, 2, 9, 1, 10], [8, 6, 7, 3, 4, 5, 2, 9, 10, 1], [9, 7, 4, 5, 6, 2, 3, 1, 8, 10], [10, 7, 4, 5, 6, 2, 3, 1, 8, 9]}, { [8, 6, 7, 4, 5, 2, 3, 9, 1, 10], [8, 6, 7, 4, 5, 2, 3, 9, 10, 1], [9, 6, 7, 4, 5, 2, 3, 1, 8, 10], [10, 6, 7, 4, 5, 2, 3, 1, 8, 9]}, { [8, 6, 7, 5, 2, 3, 4, 9, 1, 10], [8, 6, 7, 5, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 4, 2, 3, 1, 8, 10], [10, 5, 6, 7, 4, 2, 3, 1, 8, 9]}, { [8, 7, 3, 4, 5, 6, 2, 9, 1, 10], [8, 7, 3, 4, 5, 6, 2, 9, 10, 1], [9, 7, 3, 4, 5, 6, 2, 1, 8, 10], [10, 7, 3, 4, 5, 6, 2, 1, 8, 9]}, { [8, 7, 4, 5, 6, 2, 3, 9, 1, 10], [8, 7, 4, 5, 6, 2, 3, 9, 10, 1], [9, 6, 7, 3, 4, 5, 2, 1, 8, 10], [10, 6, 7, 3, 4, 5, 2, 1, 8, 9]}, { [8, 7, 5, 6, 2, 3, 4, 9, 1, 10], [8, 7, 5, 6, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 3, 4, 2, 1, 8, 10], [10, 5, 6, 7, 3, 4, 2, 1, 8, 9]}, { [8, 7, 6, 2, 3, 4, 5, 9, 1, 10], [8, 7, 6, 2, 3, 4, 5, 9, 10, 1], [9, 4, 5, 6, 7, 3, 2, 1, 8, 10], [10, 4, 5, 6, 7, 3, 2, 1, 8, 9]}} is given by the following expression / 7639 34289 2 12061 3 5797 4 383 5 6\ n |------ n + ------ n + ------ n + ------- n + ------- n + 1/1179648 n | 4 \245760 589824 393216 1179648 1966080 / / 41 2669 2 9417 3 25603 4 257 5 239 6 + |- ---- n - ----- n - ----- n - ------ n - ---- n - ------ n \ 1320 20160 49280 221760 9240 110880 7\ - 1/29568 n | C(n) / and in Maple input form: (7639/245760*n+34289/589824*n^2+12061/393216*n^3+5797/1179648*n^4+383/1966080*n ^5+1/1179648*n^6)*4^n+(-41/1320*n-2669/20160*n^2-9417/49280*n^3-25603/221760*n^ 4-257/9240*n^5-239/110880*n^6-1/29568*n^7)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 15 14 1/2 13 12 1/2 11 10 Pi m m 3079 Pi m 239 m 242221 Pi m 257 m --------- - ----- + -------------- - ------- + ---------------- - ------- 1179648 29568 15728640 110880 47185920 9240 1/2 9 8 1/2 7 6 1/2 5 113879 Pi m 25603 m 874271 Pi m 9417 m 758783 Pi m + --------------- - -------- + --------------- - ------- + --------------- 3145728 221760 9437184 49280 7864320 4 1/2 3 2 2669 m 22917 Pi m 41 m - ------- + -------------- - ----- 20160 655360 1320 and in Maple input form: 1/1179648*Pi^(1/2)*m^15-1/29568*m^14+3079/15728640*Pi^(1/2)*m^13-239/110880*m^ 12+242221/47185920*Pi^(1/2)*m^11-257/9240*m^10+113879/3145728*Pi^(1/2)*m^9-\ 25603/221760*m^8+874271/9437184*Pi^(1/2)*m^7-9417/49280*m^6+758783/7864320*Pi^( 1/2)*m^5-2669/20160*m^4+22917/655360*Pi^(1/2)*m^3-41/1320*m^2 For the, 33, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[6, 4, 3, 2, 5, 1, 7, 8, 9, 10]}, {[7, 4, 3, 2, 5, 6, 1, 8, 9, 10]}, {[7, 5, 3, 4, 2, 6, 1, 8, 9, 10]}, {[7, 8, 5, 4, 3, 6, 1, 2, 9, 10]}, {[8, 4, 3, 2, 5, 6, 7, 1, 9, 10]}, {[8, 5, 3, 4, 2, 6, 7, 1, 9, 10]}, {[8, 5, 6, 4, 2, 3, 7, 1, 9, 10]}, {[8, 6, 3, 4, 5, 2, 7, 1, 9, 10]}, {[8, 9, 5, 4, 3, 6, 7, 1, 2, 10]}, {[8, 9, 6, 4, 5, 3, 7, 1, 2, 10]}, {[8, 9, 10, 6, 5, 4, 7, 1, 2, 3]}, {[9, 4, 3, 2, 5, 6, 7, 8, 1, 10]}, {[9, 5, 3, 4, 2, 6, 7, 8, 1, 10]}, {[9, 5, 6, 4, 2, 3, 7, 8, 1, 10]}, {[9, 6, 3, 4, 5, 2, 7, 8, 1, 10]}, {[9, 6, 7, 4, 5, 2, 3, 8, 1, 10]}, {[9, 7, 3, 4, 5, 6, 2, 8, 1, 10]}, {[9, 10, 5, 4, 3, 6, 7, 8, 1, 2]}, {[9, 10, 6, 4, 5, 3, 7, 8, 1, 2]}, {[9, 10, 6, 7, 5, 3, 4, 8, 1, 2]}, {[9, 10, 7, 4, 5, 6, 3, 8, 1, 2]}, {[10, 4, 3, 2, 5, 6, 7, 8, 9, 1]}, {[10, 5, 3, 4, 2, 6, 7, 8, 9, 1]}, {[10, 5, 6, 4, 2, 3, 7, 8, 9, 1]}, {[10, 6, 3, 4, 5, 2, 7, 8, 9, 1]}, {[10, 6, 7, 4, 5, 2, 3, 8, 9, 1]}, {[10, 6, 7, 8, 5, 2, 3, 4, 9, 1]}, {[10, 7, 3, 4, 5, 6, 2, 8, 9, 1]}, {[10, 7, 8, 4, 5, 6, 2, 3, 9, 1]}, {[10, 8, 3, 4, 5, 6, 7, 2, 9, 1]}, {[5, 4, 3, 6, 2, 1, 7, 8, 9, 10], [6, 5, 3, 2, 1, 4, 7, 8, 9, 10]}, {[5, 4, 3, 6, 7, 2, 1, 8, 9, 10], [7, 6, 3, 2, 1, 4, 5, 8, 9, 10]}, {[5, 4, 3, 6, 7, 8, 2, 1, 9, 10], [8, 7, 3, 2, 1, 4, 5, 6, 9, 10]}, {[5, 4, 3, 6, 7, 8, 9, 2, 1, 10], [9, 8, 3, 2, 1, 4, 5, 6, 7, 10]}, {[5, 4, 3, 6, 7, 8, 9, 10, 2, 1], [10, 9, 3, 2, 1, 4, 5, 6, 7, 8]}, {[5, 6, 4, 3, 7, 2, 1, 8, 9, 10], [7, 6, 4, 3, 1, 2, 5, 8, 9, 10]}, {[5, 6, 4, 3, 7, 8, 2, 1, 9, 10], [8, 7, 4, 3, 1, 2, 5, 6, 9, 10]}, {[5, 6, 4, 3, 7, 8, 9, 2, 1, 10], [9, 8, 4, 3, 1, 2, 5, 6, 7, 10]}, {[5, 6, 4, 3, 7, 8, 9, 10, 2, 1], [10, 9, 4, 3, 1, 2, 5, 6, 7, 8]}, {[5, 6, 7, 4, 3, 8, 2, 1, 9, 10], [8, 7, 5, 4, 1, 2, 3, 6, 9, 10]}, {[5, 6, 7, 4, 3, 8, 9, 2, 1, 10], [9, 8, 5, 4, 1, 2, 3, 6, 7, 10]}, {[5, 6, 7, 4, 3, 8, 9, 10, 2, 1], [10, 9, 5, 4, 1, 2, 3, 6, 7, 8]}, {[5, 6, 7, 8, 4, 3, 9, 2, 1, 10], [9, 8, 6, 5, 1, 2, 3, 4, 7, 10]}, {[5, 6, 7, 8, 4, 3, 9, 10, 2, 1], [10, 9, 6, 5, 1, 2, 3, 4, 7, 8]}, {[5, 6, 7, 8, 9, 4, 3, 10, 2, 1], [10, 9, 7, 6, 1, 2, 3, 4, 5, 8]}, {[6, 4, 5, 3, 7, 2, 1, 8, 9, 10], [7, 6, 4, 2, 3, 1, 5, 8, 9, 10]}, {[6, 4, 5, 3, 7, 8, 2, 1, 9, 10], [8, 7, 4, 2, 3, 1, 5, 6, 9, 10]}, {[6, 4, 5, 3, 7, 8, 9, 2, 1, 10], [9, 8, 4, 2, 3, 1, 5, 6, 7, 10]}, {[6, 4, 5, 3, 7, 8, 9, 10, 2, 1], [10, 9, 4, 2, 3, 1, 5, 6, 7, 8]}, {[6, 5, 3, 4, 7, 2, 1, 8, 9, 10], [7, 6, 3, 4, 2, 1, 5, 8, 9, 10]}, {[6, 5, 3, 4, 7, 8, 2, 1, 9, 10], [8, 7, 3, 4, 2, 1, 5, 6, 9, 10]}, {[6, 5, 3, 4, 7, 8, 9, 2, 1, 10], [9, 8, 3, 4, 2, 1, 5, 6, 7, 10]}, {[6, 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5, 6, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 3, 2, 1, 4, 5], [8, 7, 6, 9, 10, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 3, 4, 2, 1, 5], [9, 8, 6, 7, 10, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 4, 2, 3, 1, 5], [9, 7, 8, 6, 10, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 4, 3, 1, 2, 5], [8, 9, 7, 6, 10, 5, 1, 2, 3, 4]}, {[8, 4, 5, 3, 2, 6, 7, 1, 9, 10], [8, 5, 4, 2, 3, 6, 7, 1, 9, 10]}, {[8, 4, 5, 6, 3, 2, 7, 1, 9, 10], [8, 6, 5, 2, 3, 4, 7, 1, 9, 10]}, {[8, 4, 5, 6, 7, 3, 9, 2, 1, 10], [9, 8, 6, 2, 3, 4, 5, 1, 7, 10]}, {[8, 4, 5, 6, 7, 3, 9, 10, 2, 1], [10, 9, 6, 2, 3, 4, 5, 1, 7, 8]}, {[8, 5, 6, 3, 4, 2, 7, 1, 9, 10], [8, 6, 4, 5, 2, 3, 7, 1, 9, 10]}, {[8, 5, 6, 7, 3, 4, 9, 2, 1, 10], [9, 8, 5, 6, 2, 3, 4, 1, 7, 10]}, {[8, 5, 6, 7, 3, 4, 9, 10, 2, 1], [10, 9, 5, 6, 2, 3, 4, 1, 7, 8]}, {[8, 5, 6, 7, 4, 9, 2, 3, 1, 10], [9, 7, 8, 5, 2, 3, 4, 1, 6, 10]}, {[8, 5, 6, 7, 4, 9, 3, 1, 2, 10], [8, 9, 7, 5, 2, 3, 4, 1, 6, 10]}, {[8, 5, 6, 7, 4, 9, 10, 2, 3, 1], [10, 8, 9, 5, 2, 3, 4, 1, 6, 7]}, {[8, 5, 6, 7, 4, 9, 10, 3, 1, 2], [9, 10, 8, 5, 2, 3, 4, 1, 6, 7]}, {[8, 6, 7, 3, 4, 5, 9, 2, 1, 10], [9, 8, 4, 5, 6, 2, 3, 1, 7, 10]}, {[8, 6, 7, 3, 4, 5, 9, 10, 2, 1], [10, 9, 4, 5, 6, 2, 3, 1, 7, 8]}, {[8, 6, 7, 4, 5, 9, 2, 3, 1, 10], [9, 7, 8, 4, 5, 2, 3, 1, 6, 10]}, {[8, 6, 7, 4, 5, 9, 3, 1, 2, 10], [8, 9, 7, 4, 5, 2, 3, 1, 6, 10]}, {[8, 6, 7, 4, 5, 9, 10, 2, 3, 1], [10, 8, 9, 4, 5, 2, 3, 1, 6, 7]}, {[8, 6, 7, 4, 5, 9, 10, 3, 1, 2], [9, 10, 8, 4, 5, 2, 3, 1, 6, 7]}, {[8, 6, 7, 5, 9, 2, 3, 4, 1, 10], [9, 6, 7, 8, 4, 2, 3, 1, 5, 10]}, {[8, 6, 7, 5, 9, 3, 4, 1, 2, 10], [8, 9, 6, 7, 4, 2, 3, 1, 5, 10]}, {[8, 6, 7, 5, 9, 10, 2, 3, 4, 1], [10, 7, 8, 9, 4, 2, 3, 1, 5, 6]}, {[8, 6, 7, 5, 9, 10, 3, 4, 1, 2], [9, 10, 7, 8, 4, 2, 3, 1, 5, 6]}, {[8, 6, 7, 5, 9, 10, 4, 1, 2, 3], [8, 9, 10, 7, 4, 2, 3, 1, 5, 6]}, {[8, 7, 3, 4, 5, 6, 9, 2, 1, 10], [9, 8, 3, 4, 5, 6, 2, 1, 7, 10]}, {[8, 7, 3, 4, 5, 6, 9, 10, 2, 1], [10, 9, 3, 4, 5, 6, 2, 1, 7, 8]}, {[8, 7, 4, 5, 6, 9, 2, 3, 1, 10], [9, 7, 8, 3, 4, 5, 2, 1, 6, 10]}, {[8, 7, 4, 5, 6, 9, 3, 1, 2, 10], [8, 9, 7, 3, 4, 5, 2, 1, 6, 10]}, {[8, 7, 4, 5, 6, 9, 10, 2, 3, 1], [10, 8, 9, 3, 4, 5, 2, 1, 6, 7]}, {[8, 7, 4, 5, 6, 9, 10, 3, 1, 2], [9, 10, 8, 3, 4, 5, 2, 1, 6, 7]}, {[8, 7, 5, 6, 9, 2, 3, 4, 1, 10], [9, 6, 7, 8, 3, 4, 2, 1, 5, 10]}, {[8, 7, 5, 6, 9, 3, 4, 1, 2, 10], [8, 9, 6, 7, 3, 4, 2, 1, 5, 10]}, {[8, 7, 5, 6, 9, 10, 2, 3, 4, 1], [10, 7, 8, 9, 3, 4, 2, 1, 5, 6]}, {[8, 7, 5, 6, 9, 10, 3, 4, 1, 2], [9, 10, 7, 8, 3, 4, 2, 1, 5, 6]}, {[8, 7, 5, 6, 9, 10, 4, 1, 2, 3], [8, 9, 10, 7, 3, 4, 2, 1, 5, 6]}, {[8, 7, 6, 9, 2, 3, 4, 5, 1, 10], [9, 5, 6, 7, 8, 3, 2, 1, 4, 10]}, {[8, 7, 6, 9, 3, 4, 5, 1, 2, 10], [8, 9, 5, 6, 7, 3, 2, 1, 4, 10]}, {[8, 7, 6, 9, 10, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 3, 2, 1, 4, 5]}, {[8, 7, 6, 9, 10, 3, 4, 5, 1, 2], [9, 10, 6, 7, 8, 3, 2, 1, 4, 5]}, {[8, 7, 6, 9, 10, 4, 5, 1, 2, 3], [8, 9, 10, 6, 7, 3, 2, 1, 4, 5]}, {[8, 9, 4, 3, 2, 5, 6, 7, 1, 10], [9, 5, 4, 3, 6, 7, 8, 1, 2, 10]}, {[8, 9, 4, 5, 3, 2, 6, 7, 1, 10], [9, 6, 5, 3, 4, 7, 8, 1, 2, 10]}, {[8, 9, 4, 5, 6, 3, 2, 7, 1, 10], [9, 7, 6, 3, 4, 5, 8, 1, 2, 10]}, {[8, 9, 4, 5, 6, 7, 3, 10, 2, 1], [10, 9, 7, 3, 4, 5, 6, 1, 2, 8]}, {[8, 9, 5, 3, 4, 2, 6, 7, 1, 10], [9, 6, 4, 5, 3, 7, 8, 1, 2, 10]}, {[8, 9, 5, 4, 2, 3, 6, 7, 1, 10], [9, 5, 6, 4, 3, 7, 8, 1, 2, 10]}, {[8, 9, 5, 6, 3, 4, 2, 7, 1, 10], [9, 7, 5, 6, 3, 4, 8, 1, 2, 10]}, {[8, 9, 5, 6, 4, 2, 3, 7, 1, 10], [9, 6, 7, 5, 3, 4, 8, 1, 2, 10]}, {[8, 9, 5, 6, 4, 3, 7, 1, 2, 10], [8, 9, 6, 5, 3, 4, 7, 1, 2, 10]}, {[8, 9, 5, 6, 7, 3, 4, 10, 2, 1], [10, 9, 6, 7, 3, 4, 5, 1, 2, 8]}, {[8, 9, 5, 6, 7, 4, 10, 2, 3, 1], [10, 8, 9, 6, 3, 4, 5, 1, 2, 7]}, {[8, 9, 5, 6, 7, 4, 10, 3, 1, 2], [9, 10, 8, 6, 3, 4, 5, 1, 2, 7]}, {[8, 9, 6, 3, 4, 5, 2, 7, 1, 10], [9, 7, 4, 5, 6, 3, 8, 1, 2, 10]}, {[8, 9, 6, 4, 5, 2, 3, 7, 1, 10], [9, 6, 7, 4, 5, 3, 8, 1, 2, 10]}, {[8, 9, 6, 5, 2, 3, 4, 7, 1, 10], [9, 5, 6, 7, 4, 3, 8, 1, 2, 10]}, {[8, 9, 6, 7, 3, 4, 5, 10, 2, 1], [10, 9, 5, 6, 7, 3, 4, 1, 2, 8]}, {[8, 9, 6, 7, 4, 5, 10, 2, 3, 1], [10, 8, 9, 5, 6, 3, 4, 1, 2, 7]}, {[8, 9, 6, 7, 4, 5, 10, 3, 1, 2], [9, 10, 8, 5, 6, 3, 4, 1, 2, 7]}, {[8, 9, 6, 7, 5, 10, 2, 3, 4, 1], [10, 7, 8, 9, 5, 3, 4, 1, 2, 6]}, {[8, 9, 6, 7, 5, 10, 3, 4, 1, 2], [9, 10, 7, 8, 5, 3, 4, 1, 2, 6]}, {[8, 9, 6, 7, 5, 10, 4, 1, 2, 3], [8, 9, 10, 7, 5, 3, 4, 1, 2, 6]}, {[8, 9, 7, 3, 4, 5, 6, 10, 2, 1], [10, 9, 4, 5, 6, 7, 3, 1, 2, 8]}, {[8, 9, 7, 4, 5, 6, 10, 2, 3, 1], [10, 8, 9, 4, 5, 6, 3, 1, 2, 7]}, {[8, 9, 7, 4, 5, 6, 10, 3, 1, 2], [9, 10, 8, 4, 5, 6, 3, 1, 2, 7]}, {[8, 9, 7, 5, 6, 10, 2, 3, 4, 1], [10, 7, 8, 9, 4, 5, 3, 1, 2, 6]}, {[8, 9, 7, 5, 6, 10, 3, 4, 1, 2], [9, 10, 7, 8, 4, 5, 3, 1, 2, 6]}, {[8, 9, 7, 5, 6, 10, 4, 1, 2, 3], [8, 9, 10, 7, 4, 5, 3, 1, 2, 6]}, {[8, 9, 7, 6, 10, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 4, 3, 1, 2, 5]}, {[8, 9, 7, 6, 10, 3, 4, 5, 1, 2], [9, 10, 6, 7, 8, 4, 3, 1, 2, 5]}, {[8, 9, 7, 6, 10, 4, 5, 1, 2, 3], [8, 9, 10, 6, 7, 4, 3, 1, 2, 5]}, {[8, 9, 10, 4, 3, 2, 5, 6, 7, 1], [10, 6, 5, 4, 7, 8, 9, 1, 2, 3]}, {[8, 9, 10, 4, 5, 3, 2, 6, 7, 1], [10, 7, 6, 4, 5, 8, 9, 1, 2, 3]}, {[8, 9, 10, 4, 5, 6, 3, 2, 7, 1], [10, 8, 7, 4, 5, 6, 9, 1, 2, 3]}, {[8, 9, 10, 5, 3, 4, 2, 6, 7, 1], [10, 7, 5, 6, 4, 8, 9, 1, 2, 3]}, {[8, 9, 10, 5, 4, 2, 3, 6, 7, 1], [10, 6, 7, 5, 4, 8, 9, 1, 2, 3]}, {[8, 9, 10, 5, 4, 3, 6, 7, 1, 2], [9, 10, 6, 5, 4, 7, 8, 1, 2, 3]}, {[8, 9, 10, 5, 6, 3, 4, 2, 7, 1], [10, 8, 6, 7, 4, 5, 9, 1, 2, 3]}, {[8, 9, 10, 5, 6, 4, 2, 3, 7, 1], [10, 7, 8, 6, 4, 5, 9, 1, 2, 3]}, {[8, 9, 10, 5, 6, 4, 3, 7, 1, 2], [9, 10, 7, 6, 4, 5, 8, 1, 2, 3]}, {[8, 9, 10, 5, 6, 7, 3, 2, 1, 4], [9, 8, 7, 10, 4, 5, 6, 1, 2, 3]}, {[8, 9, 10, 6, 3, 4, 5, 2, 7, 1], [10, 8, 5, 6, 7, 4, 9, 1, 2, 3]}, {[8, 9, 10, 6, 4, 5, 2, 3, 7, 1], [10, 7, 8, 5, 6, 4, 9, 1, 2, 3]}, {[8, 9, 10, 6, 4, 5, 3, 7, 1, 2], [9, 10, 7, 5, 6, 4, 8, 1, 2, 3]}, {[8, 9, 10, 6, 5, 2, 3, 4, 7, 1], [10, 6, 7, 8, 5, 4, 9, 1, 2, 3]}, {[8, 9, 10, 6, 5, 3, 4, 7, 1, 2], [9, 10, 6, 7, 5, 4, 8, 1, 2, 3]}, {[8, 9, 10, 6, 7, 3, 4, 2, 1, 5], [9, 8, 6, 7, 10, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 4, 2, 3, 1, 5], [9, 7, 8, 6, 10, 4, 5, 1, 2, 3]}, {[8, 9, 10, 7, 3, 4, 5, 2, 1, 6], [9, 8, 5, 6, 7, 10, 4, 1, 2, 3]}, {[8, 9, 10, 7, 4, 5, 2, 3, 1, 6], [9, 7, 8, 5, 6, 10, 4, 1, 2, 3]}, {[8, 9, 10, 7, 5, 2, 3, 4, 1, 6], [9, 6, 7, 8, 5, 10, 4, 1, 2, 3]}, {[9, 4, 5, 3, 2, 6, 7, 8, 1, 10], [9, 5, 4, 2, 3, 6, 7, 8, 1, 10]}, {[9, 4, 5, 6, 3, 2, 7, 8, 1, 10], [9, 6, 5, 2, 3, 4, 7, 8, 1, 10]}, {[9, 4, 5, 6, 7, 3, 2, 8, 1, 10], [9, 7, 6, 2, 3, 4, 5, 8, 1, 10]}, {[9, 4, 5, 6, 7, 8, 3, 10, 2, 1], [10, 9, 7, 2, 3, 4, 5, 6, 1, 8]}, {[9, 5, 6, 3, 4, 2, 7, 8, 1, 10], [9, 6, 4, 5, 2, 3, 7, 8, 1, 10]}, {[9, 5, 6, 7, 3, 4, 2, 8, 1, 10], [9, 7, 5, 6, 2, 3, 4, 8, 1, 10]}, {[9, 5, 6, 7, 4, 2, 3, 8, 1, 10], [9, 6, 7, 5, 2, 3, 4, 8, 1, 10]}, {[9, 5, 6, 7, 8, 3, 4, 10, 2, 1], [10, 9, 6, 7, 2, 3, 4, 5, 1, 8]}, {[9, 5, 6, 7, 8, 4, 10, 2, 3, 1], [10, 8, 9, 6, 2, 3, 4, 5, 1, 7]}, {[9, 5, 6, 7, 8, 4, 10, 3, 1, 2], [9, 10, 8, 6, 2, 3, 4, 5, 1, 7]}, {[9, 6, 7, 3, 4, 5, 2, 8, 1, 10], [9, 7, 4, 5, 6, 2, 3, 8, 1, 10]}, {[9, 6, 7, 8, 3, 4, 5, 10, 2, 1], [10, 9, 5, 6, 7, 2, 3, 4, 1, 8]}, {[9, 6, 7, 8, 4, 5, 10, 2, 3, 1], [10, 8, 9, 5, 6, 2, 3, 4, 1, 7]}, {[9, 6, 7, 8, 4, 5, 10, 3, 1, 2], [9, 10, 8, 5, 6, 2, 3, 4, 1, 7]}, {[9, 6, 7, 8, 5, 10, 2, 3, 4, 1], [10, 7, 8, 9, 5, 2, 3, 4, 1, 6]}, {[9, 6, 7, 8, 5, 10, 3, 4, 1, 2], [9, 10, 7, 8, 5, 2, 3, 4, 1, 6]}, {[9, 7, 8, 3, 4, 5, 6, 10, 2, 1], [10, 9, 4, 5, 6, 7, 2, 3, 1, 8]}, {[9, 7, 8, 4, 5, 6, 10, 2, 3, 1], [10, 8, 9, 4, 5, 6, 2, 3, 1, 7]}, {[9, 7, 8, 4, 5, 6, 10, 3, 1, 2], [9, 10, 8, 4, 5, 6, 2, 3, 1, 7]}, {[9, 7, 8, 5, 6, 10, 2, 3, 4, 1], [10, 7, 8, 9, 4, 5, 2, 3, 1, 6]}, {[9, 7, 8, 5, 6, 10, 3, 4, 1, 2], [9, 10, 7, 8, 4, 5, 2, 3, 1, 6]}, {[9, 7, 8, 6, 10, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 4, 2, 3, 1, 5]}, {[9, 7, 8, 6, 10, 3, 4, 5, 1, 2], [9, 10, 6, 7, 8, 4, 2, 3, 1, 5]}, {[9, 8, 3, 4, 5, 6, 7, 10, 2, 1], [10, 9, 3, 4, 5, 6, 7, 2, 1, 8]}, {[9, 8, 4, 5, 6, 7, 10, 2, 3, 1], [10, 8, 9, 3, 4, 5, 6, 2, 1, 7]}, {[9, 8, 4, 5, 6, 7, 10, 3, 1, 2], [9, 10, 8, 3, 4, 5, 6, 2, 1, 7]}, {[9, 8, 5, 6, 7, 10, 2, 3, 4, 1], [10, 7, 8, 9, 3, 4, 5, 2, 1, 6]}, {[9, 8, 5, 6, 7, 10, 3, 4, 1, 2], [9, 10, 7, 8, 3, 4, 5, 2, 1, 6]}, {[9, 8, 6, 7, 10, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 3, 4, 2, 1, 5]}, {[9, 8, 6, 7, 10, 3, 4, 5, 1, 2], [9, 10, 6, 7, 8, 3, 4, 2, 1, 5]}, {[9, 8, 7, 10, 2, 3, 4, 5, 6, 1], [10, 5, 6, 7, 8, 9, 3, 2, 1, 4]}, {[9, 8, 7, 10, 3, 4, 5, 6, 1, 2], [9, 10, 5, 6, 7, 8, 3, 2, 1, 4]}, {[9, 10, 4, 3, 2, 5, 6, 7, 8, 1], [10, 5, 4, 3, 6, 7, 8, 9, 1, 2]}, {[9, 10, 4, 5, 3, 2, 6, 7, 8, 1], [10, 6, 5, 3, 4, 7, 8, 9, 1, 2]}, {[9, 10, 4, 5, 6, 3, 2, 7, 8, 1], [10, 7, 6, 3, 4, 5, 8, 9, 1, 2]}, {[9, 10, 4, 5, 6, 7, 3, 2, 8, 1], [10, 8, 7, 3, 4, 5, 6, 9, 1, 2]}, {[9, 10, 5, 3, 4, 2, 6, 7, 8, 1], [10, 6, 4, 5, 3, 7, 8, 9, 1, 2]}, {[9, 10, 5, 4, 2, 3, 6, 7, 8, 1], [10, 5, 6, 4, 3, 7, 8, 9, 1, 2]}, {[9, 10, 5, 6, 3, 4, 2, 7, 8, 1], [10, 7, 5, 6, 3, 4, 8, 9, 1, 2]}, {[9, 10, 5, 6, 4, 2, 3, 7, 8, 1], [10, 6, 7, 5, 3, 4, 8, 9, 1, 2]}, {[9, 10, 5, 6, 4, 3, 7, 8, 1, 2], [9, 10, 6, 5, 3, 4, 7, 8, 1, 2]}, {[9, 10, 5, 6, 7, 3, 4, 2, 8, 1], [10, 8, 6, 7, 3, 4, 5, 9, 1, 2]}, {[9, 10, 5, 6, 7, 4, 2, 3, 8, 1], [10, 7, 8, 6, 3, 4, 5, 9, 1, 2]}, {[9, 10, 5, 6, 7, 4, 3, 8, 1, 2], [9, 10, 7, 6, 3, 4, 5, 8, 1, 2]}, {[9, 10, 6, 3, 4, 5, 2, 7, 8, 1], [10, 7, 4, 5, 6, 3, 8, 9, 1, 2]}, {[9, 10, 6, 4, 5, 2, 3, 7, 8, 1], [10, 6, 7, 4, 5, 3, 8, 9, 1, 2]}, {[9, 10, 6, 5, 2, 3, 4, 7, 8, 1], [10, 5, 6, 7, 4, 3, 8, 9, 1, 2]}, {[9, 10, 6, 7, 3, 4, 5, 2, 8, 1], [10, 8, 5, 6, 7, 3, 4, 9, 1, 2]}, {[9, 10, 6, 7, 4, 5, 2, 3, 8, 1], [10, 7, 8, 5, 6, 3, 4, 9, 1, 2]}, {[9, 10, 6, 7, 4, 5, 3, 8, 1, 2], [9, 10, 7, 5, 6, 3, 4, 8, 1, 2]}, {[9, 10, 6, 7, 5, 2, 3, 4, 8, 1], [10, 6, 7, 8, 5, 3, 4, 9, 1, 2]}, {[9, 10, 7, 3, 4, 5, 6, 2, 8, 1], [10, 8, 4, 5, 6, 7, 3, 9, 1, 2]}, {[9, 10, 7, 4, 5, 6, 2, 3, 8, 1], [10, 7, 8, 4, 5, 6, 3, 9, 1, 2]}, {[9, 10, 7, 5, 6, 2, 3, 4, 8, 1], [10, 6, 7, 8, 4, 5, 3, 9, 1, 2]}, {[9, 10, 7, 6, 2, 3, 4, 5, 8, 1], [10, 5, 6, 7, 8, 4, 3, 9, 1, 2]}, {[10, 4, 5, 3, 2, 6, 7, 8, 9, 1], [10, 5, 4, 2, 3, 6, 7, 8, 9, 1]}, {[10, 4, 5, 6, 3, 2, 7, 8, 9, 1], [10, 6, 5, 2, 3, 4, 7, 8, 9, 1]}, {[10, 4, 5, 6, 7, 3, 2, 8, 9, 1], [10, 7, 6, 2, 3, 4, 5, 8, 9, 1]}, {[10, 4, 5, 6, 7, 8, 3, 2, 9, 1], [10, 8, 7, 2, 3, 4, 5, 6, 9, 1]}, {[10, 5, 6, 3, 4, 2, 7, 8, 9, 1], [10, 6, 4, 5, 2, 3, 7, 8, 9, 1]}, {[10, 5, 6, 7, 3, 4, 2, 8, 9, 1], [10, 7, 5, 6, 2, 3, 4, 8, 9, 1]}, {[10, 5, 6, 7, 4, 2, 3, 8, 9, 1], [10, 6, 7, 5, 2, 3, 4, 8, 9, 1]}, {[10, 5, 6, 7, 8, 3, 4, 2, 9, 1], [10, 8, 6, 7, 2, 3, 4, 5, 9, 1]}, {[10, 5, 6, 7, 8, 4, 2, 3, 9, 1], [10, 7, 8, 6, 2, 3, 4, 5, 9, 1]}, {[10, 6, 7, 3, 4, 5, 2, 8, 9, 1], [10, 7, 4, 5, 6, 2, 3, 8, 9, 1]}, {[10, 6, 7, 8, 3, 4, 5, 2, 9, 1], [10, 8, 5, 6, 7, 2, 3, 4, 9, 1]}, {[10, 6, 7, 8, 4, 5, 2, 3, 9, 1], [10, 7, 8, 5, 6, 2, 3, 4, 9, 1]}, {[10, 7, 8, 3, 4, 5, 6, 2, 9, 1], [10, 8, 4, 5, 6, 7, 2, 3, 9, 1]}} is given by the following expression /2141 43067 2 901 3 1205 4 77 5 6\ n / |----- n + ------ n + ----- n + ------ n + ------ n + 1/1474560 n | 4 + | \61440 737280 32768 294912 491520 / \ 23 1427 2 943 3 23657 4 251 5 389 6 - --- n - ----- n - ---- n - ------ n - ----- n - ------ n 660 10080 4928 221760 10560 221760 7\ - 1/36960 n | C(n) / and in Maple input form: (2141/61440*n+43067/737280*n^2+901/32768*n^3+1205/294912*n^4+77/491520*n^5+1/ 1474560*n^6)*4^n+(-23/660*n-1427/10080*n^2-943/4928*n^3-23657/221760*n^4-251/ 10560*n^5-389/221760*n^6-1/36960*n^7)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 15 14 1/2 13 12 1/2 11 10 Pi m m 619 Pi m 389 m 50279 Pi m 251 m --------- - ----- + ------------- - ------- + --------------- - ------- 1474560 36960 3932160 221760 11796480 10560 1/2 9 8 1/2 7 6 1/2 5 8413 Pi m 23657 m 1053977 Pi m 943 m 197713 Pi m + ------------- - -------- + ---------------- - ------ + --------------- 262144 221760 11796480 4928 1966080 4 1/2 3 2 1427 m 6423 Pi m 23 m - ------- + ------------- - ----- 10080 163840 660 and in Maple input form: 1/1474560*Pi^(1/2)*m^15-1/36960*m^14+619/3932160*Pi^(1/2)*m^13-389/221760*m^12+ 50279/11796480*Pi^(1/2)*m^11-251/10560*m^10+8413/262144*Pi^(1/2)*m^9-23657/ 221760*m^8+1053977/11796480*Pi^(1/2)*m^7-943/4928*m^6+197713/1966080*Pi^(1/2)*m ^5-1427/10080*m^4+6423/163840*Pi^(1/2)*m^3-23/660*m^2 For the, 34, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[6, 5, 7, 4, 2, 1, 3, 8, 9, 10]}, {[7, 6, 8, 4, 5, 2, 1, 3, 9, 10]}, {[7, 6, 8, 9, 5, 2, 1, 3, 4, 10]}, {[7, 8, 6, 9, 5, 3, 1, 2, 4, 10]}, {[8, 6, 7, 9, 5, 2, 3, 1, 4, 10]}, {[8, 7, 9, 4, 5, 6, 2, 1, 3, 10]}, {[8, 7, 9, 10, 5, 6, 2, 1, 3, 4]}, {[8, 9, 7, 10, 5, 6, 3, 1, 2, 4]}, {[9, 7, 8, 10, 5, 6, 2, 3, 1, 4]}, {[9, 8, 10, 4, 5, 6, 7, 2, 1, 3]}, {[5, 4, 3, 6, 2, 7, 1, 8, 9, 10], [7, 5, 3, 2, 1, 4, 6, 8, 9, 10]}, {[5, 4, 3, 6, 2, 7, 8, 1, 9, 10], [8, 5, 3, 2, 1, 4, 6, 7, 9, 10]}, {[5, 4, 3, 6, 7, 2, 8, 1, 9, 10], [8, 6, 3, 2, 1, 4, 5, 7, 9, 10]}, {[5, 4, 3, 6, 7, 8, 9, 2, 10, 1], [10, 8, 3, 2, 1, 4, 5, 6, 7, 9]}, {[5, 4, 6, 3, 2, 7, 1, 8, 9, 10], [7, 5, 4, 2, 1, 3, 6, 8, 9, 10]}, {[5, 4, 6, 3, 2, 7, 8, 1, 9, 10], [8, 5, 4, 2, 1, 3, 6, 7, 9, 10]}, {[5, 4, 6, 3, 7, 2, 1, 8, 9, 10], [7, 6, 4, 2, 1, 3, 5, 8, 9, 10]}, {[5, 4, 6, 3, 7, 8, 2, 1, 9, 10], [8, 7, 4, 2, 1, 3, 5, 6, 9, 10]}, {[5, 4, 6, 3, 7, 8, 9, 2, 1, 10], [9, 8, 4, 2, 1, 3, 5, 6, 7, 10]}, {[5, 4, 6, 3, 7, 8, 9, 10, 2, 1], [10, 9, 4, 2, 1, 3, 5, 6, 7, 8]}, {[5, 4, 6, 7, 3, 2, 8, 1, 9, 10], [8, 6, 5, 2, 1, 3, 4, 7, 9, 10]}, {[5, 4, 6, 7, 3, 8, 2, 1, 9, 10], [8, 7, 5, 2, 1, 3, 4, 6, 9, 10]}, {[5, 4, 6, 7, 3, 8, 9, 2, 1, 10], [9, 8, 5, 2, 1, 3, 4, 6, 7, 10]}, {[5, 4, 6, 7, 3, 8, 9, 10, 2, 1], [10, 9, 5, 2, 1, 3, 4, 6, 7, 8]}, {[5, 4, 6, 7, 8, 3, 9, 2, 1, 10], [9, 8, 6, 2, 1, 3, 4, 5, 7, 10]}, {[5, 4, 6, 7, 8, 3, 9, 10, 2, 1], [10, 9, 6, 2, 1, 3, 4, 5, 7, 8]}, {[5, 4, 6, 7, 8, 9, 3, 2, 10, 1], [10, 8, 7, 2, 1, 3, 4, 5, 6, 9]}, {[5, 4, 6, 7, 8, 9, 3, 10, 2, 1], [10, 9, 7, 2, 1, 3, 4, 5, 6, 8]}, {[5, 6, 4, 3, 7, 2, 8, 1, 9, 10], [8, 6, 4, 3, 1, 2, 5, 7, 9, 10]}, {[5, 6, 4, 3, 7, 8, 9, 2, 10, 1], [10, 8, 4, 3, 1, 2, 5, 6, 7, 9]}, {[5, 6, 4, 7, 3, 2, 8, 1, 9, 10], [8, 6, 5, 3, 1, 2, 4, 7, 9, 10]}, {[5, 6, 4, 7, 3, 8, 2, 1, 9, 10], [8, 7, 5, 3, 1, 2, 4, 6, 9, 10]}, {[5, 6, 4, 7, 3, 8, 9, 2, 1, 10], [9, 8, 5, 3, 1, 2, 4, 6, 7, 10]}, {[5, 6, 4, 7, 3, 8, 9, 10, 2, 1], [10, 9, 5, 3, 1, 2, 4, 6, 7, 8]}, {[5, 6, 4, 7, 8, 3, 9, 2, 1, 10], [9, 8, 6, 3, 1, 2, 4, 5, 7, 10]}, {[5, 6, 4, 7, 8, 3, 9, 10, 2, 1], [10, 9, 6, 3, 1, 2, 4, 5, 7, 8]}, {[5, 6, 4, 7, 8, 9, 3, 2, 10, 1], [10, 8, 7, 3, 1, 2, 4, 5, 6, 9]}, {[5, 6, 4, 7, 8, 9, 3, 10, 2, 1], [10, 9, 7, 3, 1, 2, 4, 5, 6, 8]}, {[5, 6, 7, 4, 3, 8, 9, 2, 10, 1], [10, 8, 5, 4, 1, 2, 3, 6, 7, 9]}, {[5, 6, 7, 4, 8, 3, 9, 2, 1, 10], [9, 8, 6, 4, 1, 2, 3, 5, 7, 10]}, {[5, 6, 7, 4, 8, 3, 9, 10, 2, 1], [10, 9, 6, 4, 1, 2, 3, 5, 7, 8]}, {[5, 6, 7, 4, 8, 9, 3, 2, 10, 1], [10, 8, 7, 4, 1, 2, 3, 5, 6, 9]}, {[5, 6, 7, 4, 8, 9, 3, 10, 2, 1], [10, 9, 7, 4, 1, 2, 3, 5, 6, 8]}, {[5, 6, 7, 8, 4, 3, 9, 2, 10, 1], [10, 8, 6, 5, 1, 2, 3, 4, 7, 9]}, {[5, 6, 7, 8, 4, 9, 3, 2, 10, 1], [10, 8, 7, 5, 1, 2, 3, 4, 6, 9]}, {[5, 6, 7, 8, 4, 9, 3, 10, 2, 1], [10, 9, 7, 5, 1, 2, 3, 4, 6, 8]}, {[6, 4, 3, 2, 5, 7, 1, 8, 9, 10], [7, 4, 3, 2, 5, 1, 6, 8, 9, 10]}, {[6, 4, 3, 2, 5, 7, 8, 1, 9, 10], [8, 4, 3, 2, 5, 1, 6, 7, 9, 10]}, {[6, 4, 3, 5, 2, 7, 1, 8, 9, 10], [7, 5, 3, 2, 4, 1, 6, 8, 9, 10]}, {[6, 4, 3, 5, 2, 7, 8, 1, 9, 10], [8, 5, 3, 2, 4, 1, 6, 7, 9, 10]}, {[6, 4, 3, 5, 7, 2, 1, 8, 9, 10], [7, 6, 3, 2, 4, 1, 5, 8, 9, 10]}, {[6, 4, 3, 5, 7, 8, 2, 1, 9, 10], [8, 7, 3, 2, 4, 1, 5, 6, 9, 10]}, {[6, 4, 3, 5, 7, 8, 9, 2, 1, 10], [9, 8, 3, 2, 4, 1, 5, 6, 7, 10]}, {[6, 4, 3, 5, 7, 8, 9, 10, 2, 1], [10, 9, 3, 2, 4, 1, 5, 6, 7, 8]}, {[6, 4, 5, 3, 7, 2, 8, 1, 9, 10], [8, 6, 4, 2, 3, 1, 5, 7, 9, 10]}, {[6, 4, 5, 3, 7, 8, 9, 2, 10, 1], [10, 8, 4, 2, 3, 1, 5, 6, 7, 9]}, {[6, 4, 5, 7, 3, 2, 8, 1, 9, 10], [8, 6, 5, 2, 3, 1, 4, 7, 9, 10]}, {[6, 4, 5, 7, 3, 8, 2, 1, 9, 10], [8, 7, 5, 2, 3, 1, 4, 6, 9, 10]}, {[6, 4, 5, 7, 3, 8, 9, 2, 1, 10], [9, 8, 5, 2, 3, 1, 4, 6, 7, 10]}, {[6, 4, 5, 7, 3, 8, 9, 10, 2, 1], [10, 9, 5, 2, 3, 1, 4, 6, 7, 8]}, {[6, 4, 5, 7, 8, 3, 9, 2, 1, 10], [9, 8, 6, 2, 3, 1, 4, 5, 7, 10]}, {[6, 4, 5, 7, 8, 3, 9, 10, 2, 1], [10, 9, 6, 2, 3, 1, 4, 5, 7, 8]}, {[6, 4, 5, 7, 8, 9, 3, 2, 10, 1], [10, 8, 7, 2, 3, 1, 4, 5, 6, 9]}, {[6, 4, 5, 7, 8, 9, 3, 10, 2, 1], [10, 9, 7, 2, 3, 1, 4, 5, 6, 8]}, {[6, 5, 3, 2, 4, 7, 1, 8, 9, 10], [7, 4, 3, 5, 2, 1, 6, 8, 9, 10]}, {[6, 5, 3, 2, 4, 7, 8, 1, 9, 10], [8, 4, 3, 5, 2, 1, 6, 7, 9, 10]}, {[6, 5, 3, 4, 7, 2, 8, 1, 9, 10], [8, 6, 3, 4, 2, 1, 5, 7, 9, 10]}, {[6, 5, 3, 4, 7, 8, 9, 2, 10, 1], [10, 8, 3, 4, 2, 1, 5, 6, 7, 9]}, {[6, 5, 4, 7, 2, 1, 3, 8, 9, 10], [6, 5, 7, 3, 2, 1, 4, 8, 9, 10]}, {[6, 5, 4, 7, 2, 3, 8, 1, 9, 10], [8, 5, 6, 3, 2, 1, 4, 7, 9, 10]}, {[6, 5, 4, 7, 3, 8, 1, 2, 9, 10], [7, 8, 5, 3, 2, 1, 4, 6, 9, 10]}, {[6, 5, 4, 7, 3, 8, 9, 1, 2, 10], [8, 9, 5, 3, 2, 1, 4, 6, 7, 10]}, {[6, 5, 4, 7, 3, 8, 9, 10, 1, 2], [9, 10, 5, 3, 2, 1, 4, 6, 7, 8]}, {[6, 5, 4, 7, 8, 2, 1, 3, 9, 10], [7, 6, 8, 3, 2, 1, 4, 5, 9, 10]}, {[6, 5, 4, 7, 8, 3, 9, 1, 2, 10], [8, 9, 6, 3, 2, 1, 4, 5, 7, 10]}, {[6, 5, 4, 7, 8, 3, 9, 10, 1, 2], [9, 10, 6, 3, 2, 1, 4, 5, 7, 8]}, {[6, 5, 4, 7, 8, 9, 2, 1, 3, 10], [8, 7, 9, 3, 2, 1, 4, 5, 6, 10]}, {[6, 5, 4, 7, 8, 9, 2, 3, 10, 1], [10, 7, 8, 3, 2, 1, 4, 5, 6, 9]}, {[6, 5, 4, 7, 8, 9, 3, 10, 1, 2], [9, 10, 7, 3, 2, 1, 4, 5, 6, 8]}, {[6, 5, 4, 7, 8, 9, 10, 2, 1, 3], [9, 8, 10, 3, 2, 1, 4, 5, 6, 7]}, {[6, 5, 7, 3, 2, 4, 1, 8, 9, 10], [7, 5, 4, 6, 2, 1, 3, 8, 9, 10]}, {[6, 5, 7, 3, 4, 2, 8, 1, 9, 10], [8, 6, 4, 5, 2, 1, 3, 7, 9, 10]}, {[6, 5, 7, 3, 4, 8, 2, 1, 9, 10], [8, 7, 4, 5, 2, 1, 3, 6, 9, 10]}, {[6, 5, 7, 3, 4, 8, 9, 2, 1, 10], [9, 8, 4, 5, 2, 1, 3, 6, 7, 10]}, {[6, 5, 7, 3, 4, 8, 9, 10, 2, 1], [10, 9, 4, 5, 2, 1, 3, 6, 7, 8]}, {[6, 5, 7, 4, 2, 3, 8, 1, 9, 10], [8, 5, 6, 4, 2, 1, 3, 7, 9, 10]}, {[6, 5, 7, 4, 3, 8, 1, 2, 9, 10], [7, 8, 5, 4, 2, 1, 3, 6, 9, 10]}, {[6, 5, 7, 4, 3, 8, 9, 1, 2, 10], [8, 9, 5, 4, 2, 1, 3, 6, 7, 10]}, {[6, 5, 7, 4, 3, 8, 9, 10, 1, 2], [9, 10, 5, 4, 2, 1, 3, 6, 7, 8]}, {[6, 5, 7, 4, 8, 2, 3, 1, 9, 10], [8, 6, 7, 4, 2, 1, 3, 5, 9, 10]}, {[6, 5, 7, 4, 8, 3, 1, 2, 9, 10], [7, 8, 6, 4, 2, 1, 3, 5, 9, 10]}, {[6, 5, 7, 4, 8, 9, 2, 3, 1, 10], [9, 7, 8, 4, 2, 1, 3, 5, 6, 10]}, {[6, 5, 7, 4, 8, 9, 3, 1, 2, 10], [8, 9, 7, 4, 2, 1, 3, 5, 6, 10]}, {[6, 5, 7, 4, 8, 9, 10, 2, 3, 1], [10, 8, 9, 4, 2, 1, 3, 5, 6, 7]}, {[6, 5, 7, 4, 8, 9, 10, 3, 1, 2], [9, 10, 8, 4, 2, 1, 3, 5, 6, 7]}, {[6, 5, 7, 8, 3, 2, 1, 4, 9, 10], [7, 6, 5, 8, 2, 1, 3, 4, 9, 10]}, {[6, 5, 7, 8, 3, 2, 4, 1, 9, 10], [8, 6, 5, 7, 2, 1, 3, 4, 9, 10]}, {[6, 5, 7, 8, 3, 4, 9, 2, 1, 10], [9, 8, 5, 6, 2, 1, 3, 4, 7, 10]}, {[6, 5, 7, 8, 3, 4, 9, 10, 2, 1], [10, 9, 5, 6, 2, 1, 3, 4, 7, 8]}, {[6, 5, 7, 8, 4, 2, 1, 3, 9, 10], [7, 6, 8, 5, 2, 1, 3, 4, 9, 10]}, {[6, 5, 7, 8, 4, 3, 9, 1, 2, 10], [8, 9, 6, 5, 2, 1, 3, 4, 7, 10]}, {[6, 5, 7, 8, 4, 3, 9, 10, 1, 2], [9, 10, 6, 5, 2, 1, 3, 4, 7, 8]}, {[6, 5, 7, 8, 4, 9, 2, 3, 1, 10], [9, 7, 8, 5, 2, 1, 3, 4, 6, 10]}, {[6, 5, 7, 8, 4, 9, 3, 1, 2, 10], [8, 9, 7, 5, 2, 1, 3, 4, 6, 10]}, {[6, 5, 7, 8, 4, 9, 10, 2, 3, 1], [10, 8, 9, 5, 2, 1, 3, 4, 6, 7]}, {[6, 5, 7, 8, 4, 9, 10, 3, 1, 2], [9, 10, 8, 5, 2, 1, 3, 4, 6, 7]}, {[6, 5, 7, 8, 9, 3, 2, 1, 4, 10], [8, 7, 6, 9, 2, 1, 3, 4, 5, 10]}, {[6, 5, 7, 8, 9, 3, 2, 4, 1, 10], [9, 7, 6, 8, 2, 1, 3, 4, 5, 10]}, {[6, 5, 7, 8, 9, 3, 4, 2, 10, 1], [10, 8, 6, 7, 2, 1, 3, 4, 5, 9]}, {[6, 5, 7, 8, 9, 3, 4, 10, 2, 1], [10, 9, 6, 7, 2, 1, 3, 4, 5, 8]}, {[6, 5, 7, 8, 9, 4, 2, 1, 3, 10], [8, 7, 9, 6, 2, 1, 3, 4, 5, 10]}, {[6, 5, 7, 8, 9, 4, 2, 3, 10, 1], [10, 7, 8, 6, 2, 1, 3, 4, 5, 9]}, {[6, 5, 7, 8, 9, 4, 3, 10, 1, 2], [9, 10, 7, 6, 2, 1, 3, 4, 5, 8]}, {[6, 5, 7, 8, 9, 4, 10, 2, 3, 1], [10, 8, 9, 6, 2, 1, 3, 4, 5, 7]}, {[6, 5, 7, 8, 9, 4, 10, 3, 1, 2], [9, 10, 8, 6, 2, 1, 3, 4, 5, 7]}, {[6, 5, 7, 8, 9, 10, 3, 2, 1, 4], [9, 8, 7, 10, 2, 1, 3, 4, 5, 6]}, {[6, 5, 7, 8, 9, 10, 3, 2, 4, 1], [10, 8, 7, 9, 2, 1, 3, 4, 5, 6]}, {[6, 5, 7, 8, 9, 10, 4, 2, 1, 3], [9, 8, 10, 7, 2, 1, 3, 4, 5, 6]}, {[6, 7, 4, 3, 2, 5, 8, 1, 9, 10], [8, 5, 4, 3, 6, 1, 2, 7, 9, 10]}, {[6, 7, 4, 3, 5, 2, 8, 1, 9, 10], [8, 6, 4, 3, 5, 1, 2, 7, 9, 10]}, {[6, 7, 4, 3, 5, 8, 2, 1, 9, 10], [8, 7, 4, 3, 5, 1, 2, 6, 9, 10]}, {[6, 7, 4, 3, 5, 8, 9, 2, 1, 10], [9, 8, 4, 3, 5, 1, 2, 6, 7, 10]}, {[6, 7, 4, 3, 5, 8, 9, 10, 2, 1], [10, 9, 4, 3, 5, 1, 2, 6, 7, 8]}, {[6, 7, 4, 5, 3, 8, 9, 2, 10, 1], [10, 8, 5, 3, 4, 1, 2, 6, 7, 9]}, {[6, 7, 4, 5, 8, 3, 9, 2, 1, 10], [9, 8, 6, 3, 4, 1, 2, 5, 7, 10]}, {[6, 7, 4, 5, 8, 3, 9, 10, 2, 1], [10, 9, 6, 3, 4, 1, 2, 5, 7, 8]}, {[6, 7, 4, 5, 8, 9, 3, 2, 10, 1], [10, 8, 7, 3, 4, 1, 2, 5, 6, 9]}, {[6, 7, 4, 5, 8, 9, 3, 10, 2, 1], [10, 9, 7, 3, 4, 1, 2, 5, 6, 8]}, {[6, 7, 5, 3, 2, 4, 8, 1, 9, 10], [8, 5, 4, 6, 3, 1, 2, 7, 9, 10]}, {[6, 7, 5, 3, 4, 8, 9, 2, 10, 1], [10, 8, 4, 5, 3, 1, 2, 6, 7, 9]}, {[6, 7, 5, 4, 8, 2, 1, 3, 9, 10], [7, 6, 8, 4, 3, 1, 2, 5, 9, 10]}, {[6, 7, 5, 4, 8, 3, 9, 1, 2, 10], [8, 9, 6, 4, 3, 1, 2, 5, 7, 10]}, {[6, 7, 5, 4, 8, 3, 9, 10, 1, 2], [9, 10, 6, 4, 3, 1, 2, 5, 7, 8]}, {[6, 7, 5, 4, 8, 9, 2, 1, 3, 10], [8, 7, 9, 4, 3, 1, 2, 5, 6, 10]}, {[6, 7, 5, 4, 8, 9, 2, 3, 10, 1], [10, 7, 8, 4, 3, 1, 2, 5, 6, 9]}, {[6, 7, 5, 4, 8, 9, 3, 10, 1, 2], [9, 10, 7, 4, 3, 1, 2, 5, 6, 8]}, {[6, 7, 5, 4, 8, 9, 10, 2, 1, 3], [9, 8, 10, 4, 3, 1, 2, 5, 6, 7]}, {[6, 7, 5, 8, 3, 2, 1, 4, 9, 10], [7, 6, 5, 8, 3, 1, 2, 4, 9, 10]}, {[6, 7, 5, 8, 3, 2, 4, 1, 9, 10], [8, 6, 5, 7, 3, 1, 2, 4, 9, 10]}, {[6, 7, 5, 8, 3, 4, 9, 2, 1, 10], [9, 8, 5, 6, 3, 1, 2, 4, 7, 10]}, {[6, 7, 5, 8, 3, 4, 9, 10, 2, 1], [10, 9, 5, 6, 3, 1, 2, 4, 7, 8]}, {[6, 7, 5, 8, 4, 2, 1, 3, 9, 10], [7, 6, 8, 5, 3, 1, 2, 4, 9, 10]}, {[6, 7, 5, 8, 4, 3, 9, 1, 2, 10], [8, 9, 6, 5, 3, 1, 2, 4, 7, 10]}, {[6, 7, 5, 8, 4, 3, 9, 10, 1, 2], [9, 10, 6, 5, 3, 1, 2, 4, 7, 8]}, {[6, 7, 5, 8, 4, 9, 2, 3, 1, 10], [9, 7, 8, 5, 3, 1, 2, 4, 6, 10]}, {[6, 7, 5, 8, 4, 9, 3, 1, 2, 10], [8, 9, 7, 5, 3, 1, 2, 4, 6, 10]}, {[6, 7, 5, 8, 4, 9, 10, 2, 3, 1], [10, 8, 9, 5, 3, 1, 2, 4, 6, 7]}, {[6, 7, 5, 8, 4, 9, 10, 3, 1, 2], [9, 10, 8, 5, 3, 1, 2, 4, 6, 7]}, {[6, 7, 5, 8, 9, 3, 2, 1, 4, 10], [8, 7, 6, 9, 3, 1, 2, 4, 5, 10]}, {[6, 7, 5, 8, 9, 3, 2, 4, 1, 10], [9, 7, 6, 8, 3, 1, 2, 4, 5, 10]}, {[6, 7, 5, 8, 9, 3, 4, 2, 10, 1], [10, 8, 6, 7, 3, 1, 2, 4, 5, 9]}, {[6, 7, 5, 8, 9, 3, 4, 10, 2, 1], [10, 9, 6, 7, 3, 1, 2, 4, 5, 8]}, {[6, 7, 5, 8, 9, 4, 2, 1, 3, 10], [8, 7, 9, 6, 3, 1, 2, 4, 5, 10]}, {[6, 7, 5, 8, 9, 4, 2, 3, 10, 1], [10, 7, 8, 6, 3, 1, 2, 4, 5, 9]}, {[6, 7, 5, 8, 9, 4, 3, 10, 1, 2], [9, 10, 7, 6, 3, 1, 2, 4, 5, 8]}, {[6, 7, 5, 8, 9, 4, 10, 2, 3, 1], [10, 8, 9, 6, 3, 1, 2, 4, 5, 7]}, {[6, 7, 5, 8, 9, 4, 10, 3, 1, 2], [9, 10, 8, 6, 3, 1, 2, 4, 5, 7]}, {[6, 7, 5, 8, 9, 10, 3, 2, 1, 4], [9, 8, 7, 10, 3, 1, 2, 4, 5, 6]}, {[6, 7, 5, 8, 9, 10, 3, 2, 4, 1], [10, 8, 7, 9, 3, 1, 2, 4, 5, 6]}, {[6, 7, 5, 8, 9, 10, 4, 2, 1, 3], [9, 8, 10, 7, 3, 1, 2, 4, 5, 6]}, {[6, 7, 8, 4, 3, 5, 9, 2, 1, 10], [9, 8, 5, 4, 6, 1, 2, 3, 7, 10]}, {[6, 7, 8, 4, 3, 5, 9, 10, 2, 1], [10, 9, 5, 4, 6, 1, 2, 3, 7, 8]}, {[6, 7, 8, 4, 5, 3, 9, 2, 10, 1], [10, 8, 6, 4, 5, 1, 2, 3, 7, 9]}, {[6, 7, 8, 4, 5, 9, 3, 2, 10, 1], [10, 8, 7, 4, 5, 1, 2, 3, 6, 9]}, {[6, 7, 8, 4, 5, 9, 3, 10, 2, 1], [10, 9, 7, 4, 5, 1, 2, 3, 6, 8]}, {[6, 7, 8, 5, 3, 4, 9, 2, 10, 1], [10, 8, 5, 6, 4, 1, 2, 3, 7, 9]}, {[6, 7, 8, 5, 4, 9, 2, 1, 3, 10], [8, 7, 9, 5, 4, 1, 2, 3, 6, 10]}, {[6, 7, 8, 5, 4, 9, 2, 3, 10, 1], [10, 7, 8, 5, 4, 1, 2, 3, 6, 9]}, {[6, 7, 8, 5, 4, 9, 3, 10, 1, 2], [9, 10, 7, 5, 4, 1, 2, 3, 6, 8]}, {[6, 7, 8, 5, 4, 9, 10, 2, 1, 3], [9, 8, 10, 5, 4, 1, 2, 3, 6, 7]}, {[6, 7, 8, 5, 9, 3, 2, 1, 4, 10], [8, 7, 6, 9, 4, 1, 2, 3, 5, 10]}, {[6, 7, 8, 5, 9, 3, 2, 4, 1, 10], [9, 7, 6, 8, 4, 1, 2, 3, 5, 10]}, {[6, 7, 8, 5, 9, 3, 4, 2, 10, 1], [10, 8, 6, 7, 4, 1, 2, 3, 5, 9]}, {[6, 7, 8, 5, 9, 3, 4, 10, 2, 1], [10, 9, 6, 7, 4, 1, 2, 3, 5, 8]}, {[6, 7, 8, 5, 9, 4, 2, 1, 3, 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9]}, { [7, 6, 8, 3, 4, 5, 2, 9, 1, 10], [7, 6, 8, 3, 4, 5, 2, 9, 10, 1], [9, 7, 4, 5, 6, 2, 1, 3, 8, 10], [10, 7, 4, 5, 6, 2, 1, 3, 8, 9]}, { [7, 6, 8, 4, 5, 2, 3, 9, 1, 10], [7, 6, 8, 4, 5, 2, 3, 9, 10, 1], [9, 6, 7, 4, 5, 2, 1, 3, 8, 10], [10, 6, 7, 4, 5, 2, 1, 3, 8, 9]}, { [7, 6, 8, 5, 2, 3, 4, 9, 1, 10], [7, 6, 8, 5, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 4, 2, 1, 3, 8, 10], [10, 5, 6, 7, 4, 2, 1, 3, 8, 9]}, { [7, 8, 4, 3, 2, 5, 6, 9, 1, 10], [7, 8, 4, 3, 2, 5, 6, 9, 10, 1], [9, 5, 4, 3, 6, 7, 1, 2, 8, 10], [10, 5, 4, 3, 6, 7, 1, 2, 8, 9]}, { [7, 8, 4, 3, 5, 6, 2, 9, 1, 10], [7, 8, 4, 3, 5, 6, 2, 9, 10, 1], [9, 7, 4, 3, 5, 6, 1, 2, 8, 10], [10, 7, 4, 3, 5, 6, 1, 2, 8, 9]}, { [7, 8, 4, 5, 3, 2, 6, 9, 1, 10], [7, 8, 4, 5, 3, 2, 6, 9, 10, 1], [9, 6, 5, 3, 4, 7, 1, 2, 8, 10], [10, 6, 5, 3, 4, 7, 1, 2, 8, 9]}, { [7, 8, 4, 5, 3, 6, 2, 9, 1, 10], [7, 8, 4, 5, 3, 6, 2, 9, 10, 1], [9, 7, 5, 3, 4, 6, 1, 2, 8, 10], [10, 7, 5, 3, 4, 6, 1, 2, 8, 9]}, { [7, 8, 5, 3, 4, 2, 6, 9, 1, 10], [7, 8, 5, 3, 4, 2, 6, 9, 10, 1], [9, 6, 4, 5, 3, 7, 1, 2, 8, 10], [10, 6, 4, 5, 3, 7, 1, 2, 8, 9]}, { [7, 8, 5, 3, 4, 6, 2, 9, 1, 10], [7, 8, 5, 3, 4, 6, 2, 9, 10, 1], [9, 7, 4, 5, 3, 6, 1, 2, 8, 10], [10, 7, 4, 5, 3, 6, 1, 2, 8, 9]}, { [7, 8, 5, 4, 2, 3, 6, 9, 1, 10], [7, 8, 5, 4, 2, 3, 6, 9, 10, 1], [9, 5, 6, 4, 3, 7, 1, 2, 8, 10], [10, 5, 6, 4, 3, 7, 1, 2, 8, 9]}, { [7, 8, 5, 4, 6, 2, 3, 9, 1, 10], [7, 8, 5, 4, 6, 2, 3, 9, 10, 1], [9, 6, 7, 4, 3, 5, 1, 2, 8, 10], [10, 6, 7, 4, 3, 5, 1, 2, 8, 9]}, { [7, 8, 5, 6, 3, 2, 4, 9, 1, 10], [7, 8, 5, 6, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 3, 4, 1, 2, 8, 10], [10, 6, 5, 7, 3, 4, 1, 2, 8, 9]}, { [7, 8, 6, 3, 2, 4, 5, 9, 1, 10], [7, 8, 6, 3, 2, 4, 5, 9, 10, 1], [9, 5, 4, 6, 7, 3, 1, 2, 8, 10], [10, 5, 4, 6, 7, 3, 1, 2, 8, 9]}, { [7, 8, 6, 3, 4, 2, 5, 9, 1, 10], [7, 8, 6, 3, 4, 2, 5, 9, 10, 1], [9, 6, 4, 5, 7, 3, 1, 2, 8, 10], [10, 6, 4, 5, 7, 3, 1, 2, 8, 9]}, { [7, 8, 6, 4, 2, 3, 5, 9, 1, 10], [7, 8, 6, 4, 2, 3, 5, 9, 10, 1], [9, 5, 6, 4, 7, 3, 1, 2, 8, 10], [10, 5, 6, 4, 7, 3, 1, 2, 8, 9]}, { [8, 4, 3, 2, 5, 6, 7, 9, 1, 10], [8, 4, 3, 2, 5, 6, 7, 9, 10, 1], [9, 4, 3, 2, 5, 6, 7, 1, 8, 10], [10, 4, 3, 2, 5, 6, 7, 1, 8, 9]}, { [8, 4, 3, 5, 6, 7, 2, 9, 1, 10], [8, 4, 3, 5, 6, 7, 2, 9, 10, 1], [9, 7, 3, 2, 4, 5, 6, 1, 8, 10], [10, 7, 3, 2, 4, 5, 6, 1, 8, 9]}, { [8, 4, 5, 3, 2, 6, 7, 9, 1, 10], [8, 4, 5, 3, 2, 6, 7, 9, 10, 1], [9, 5, 4, 2, 3, 6, 7, 1, 8, 10], [10, 5, 4, 2, 3, 6, 7, 1, 8, 9]}, { [8, 4, 5, 3, 6, 7, 2, 9, 1, 10], [8, 4, 5, 3, 6, 7, 2, 9, 10, 1], [9, 7, 4, 2, 3, 5, 6, 1, 8, 10], [10, 7, 4, 2, 3, 5, 6, 1, 8, 9]}, { [8, 4, 5, 6, 3, 2, 7, 9, 1, 10], [8, 4, 5, 6, 3, 2, 7, 9, 10, 1], [9, 6, 5, 2, 3, 4, 7, 1, 8, 10], [10, 6, 5, 2, 3, 4, 7, 1, 8, 9]}, { [8, 4, 5, 6, 3, 7, 2, 9, 1, 10], [8, 4, 5, 6, 3, 7, 2, 9, 10, 1], [9, 7, 5, 2, 3, 4, 6, 1, 8, 10], [10, 7, 5, 2, 3, 4, 6, 1, 8, 9]}, { [8, 5, 3, 4, 2, 6, 7, 9, 1, 10], [8, 5, 3, 4, 2, 6, 7, 9, 10, 1], [9, 5, 3, 4, 2, 6, 7, 1, 8, 10], [10, 5, 3, 4, 2, 6, 7, 1, 8, 9]}, { [8, 5, 3, 4, 6, 7, 2, 9, 1, 10], [8, 5, 3, 4, 6, 7, 2, 9, 10, 1], [9, 7, 3, 4, 2, 5, 6, 1, 8, 10], [10, 7, 3, 4, 2, 5, 6, 1, 8, 9]}, { [8, 5, 4, 2, 3, 6, 7, 9, 1, 10], [8, 5, 4, 2, 3, 6, 7, 9, 10, 1], [9, 4, 5, 3, 2, 6, 7, 1, 8, 10], [10, 4, 5, 3, 2, 6, 7, 1, 8, 9]}, { [8, 5, 4, 6, 7, 2, 3, 9, 1, 10], [8, 5, 4, 6, 7, 2, 3, 9, 10, 1], [9, 6, 7, 3, 2, 4, 5, 1, 8, 10], [10, 6, 7, 3, 2, 4, 5, 1, 8, 9]}, { [8, 5, 6, 3, 4, 2, 7, 9, 1, 10], [8, 5, 6, 3, 4, 2, 7, 9, 10, 1], [9, 6, 4, 5, 2, 3, 7, 1, 8, 10], [10, 6, 4, 5, 2, 3, 7, 1, 8, 9]}, { [8, 5, 6, 3, 4, 7, 2, 9, 1, 10], [8, 5, 6, 3, 4, 7, 2, 9, 10, 1], [9, 7, 4, 5, 2, 3, 6, 1, 8, 10], [10, 7, 4, 5, 2, 3, 6, 1, 8, 9]}, { [8, 5, 6, 4, 2, 3, 7, 9, 1, 10], [8, 5, 6, 4, 2, 3, 7, 9, 10, 1], [9, 5, 6, 4, 2, 3, 7, 1, 8, 10], [10, 5, 6, 4, 2, 3, 7, 1, 8, 9]}, { [8, 5, 6, 4, 7, 2, 3, 9, 1, 10], [8, 5, 6, 4, 7, 2, 3, 9, 10, 1], [9, 6, 7, 4, 2, 3, 5, 1, 8, 10], [10, 6, 7, 4, 2, 3, 5, 1, 8, 9]}, { [8, 5, 6, 7, 3, 2, 4, 9, 1, 10], [8, 5, 6, 7, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 2, 3, 4, 1, 8, 10], [10, 6, 5, 7, 2, 3, 4, 1, 8, 9]}, { [8, 6, 3, 4, 5, 2, 7, 9, 1, 10], [8, 6, 3, 4, 5, 2, 7, 9, 10, 1], [9, 6, 3, 4, 5, 2, 7, 1, 8, 10], [10, 6, 3, 4, 5, 2, 7, 1, 8, 9]}, { [8, 6, 3, 4, 5, 7, 2, 9, 1, 10], [8, 6, 3, 4, 5, 7, 2, 9, 10, 1], [9, 7, 3, 4, 5, 2, 6, 1, 8, 10], [10, 7, 3, 4, 5, 2, 6, 1, 8, 9]}, { [8, 6, 4, 5, 2, 3, 7, 9, 1, 10], [8, 6, 4, 5, 2, 3, 7, 9, 10, 1], [9, 5, 6, 3, 4, 2, 7, 1, 8, 10], [10, 5, 6, 3, 4, 2, 7, 1, 8, 9]}, { [8, 6, 4, 5, 7, 2, 3, 9, 1, 10], [8, 6, 4, 5, 7, 2, 3, 9, 10, 1], [9, 6, 7, 3, 4, 2, 5, 1, 8, 10], [10, 6, 7, 3, 4, 2, 5, 1, 8, 9]}, { [8, 6, 5, 2, 3, 4, 7, 9, 1, 10], [8, 6, 5, 2, 3, 4, 7, 9, 10, 1], [9, 4, 5, 6, 3, 2, 7, 1, 8, 10], [10, 4, 5, 6, 3, 2, 7, 1, 8, 9]}, { [8, 6, 5, 7, 2, 3, 4, 9, 1, 10], [8, 6, 5, 7, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 3, 2, 4, 1, 8, 10], [10, 5, 6, 7, 3, 2, 4, 1, 8, 9]}, { [8, 6, 7, 3, 2, 4, 5, 9, 1, 10], [8, 6, 7, 3, 2, 4, 5, 9, 10, 1], [9, 5, 4, 6, 7, 2, 3, 1, 8, 10], [10, 5, 4, 6, 7, 2, 3, 1, 8, 9]}, { [8, 6, 7, 3, 4, 2, 5, 9, 1, 10], [8, 6, 7, 3, 4, 2, 5, 9, 10, 1], [9, 6, 4, 5, 7, 2, 3, 1, 8, 10], [10, 6, 4, 5, 7, 2, 3, 1, 8, 9]}, { [8, 6, 7, 4, 2, 3, 5, 9, 1, 10], [8, 6, 7, 4, 2, 3, 5, 9, 10, 1], [9, 5, 6, 4, 7, 2, 3, 1, 8, 10], [10, 5, 6, 4, 7, 2, 3, 1, 8, 9]}, { [8, 7, 3, 2, 4, 5, 6, 9, 1, 10], [8, 7, 3, 2, 4, 5, 6, 9, 10, 1], [9, 4, 3, 5, 6, 7, 2, 1, 8, 10], [10, 4, 3, 5, 6, 7, 2, 1, 8, 9]}, { [8, 7, 3, 4, 2, 5, 6, 9, 1, 10], [8, 7, 3, 4, 2, 5, 6, 9, 10, 1], [9, 5, 3, 4, 6, 7, 2, 1, 8, 10], [10, 5, 3, 4, 6, 7, 2, 1, 8, 9]}, { [8, 7, 3, 4, 5, 2, 6, 9, 1, 10], [8, 7, 3, 4, 5, 2, 6, 9, 10, 1], [9, 6, 3, 4, 5, 7, 2, 1, 8, 10], [10, 6, 3, 4, 5, 7, 2, 1, 8, 9]}, { [8, 7, 4, 2, 3, 5, 6, 9, 1, 10], [8, 7, 4, 2, 3, 5, 6, 9, 10, 1], [9, 4, 5, 3, 6, 7, 2, 1, 8, 10], [10, 4, 5, 3, 6, 7, 2, 1, 8, 9]}, { [8, 7, 4, 5, 2, 3, 6, 9, 1, 10], [8, 7, 4, 5, 2, 3, 6, 9, 10, 1], [9, 5, 6, 3, 4, 7, 2, 1, 8, 10], [10, 5, 6, 3, 4, 7, 2, 1, 8, 9]}, { [8, 7, 5, 2, 3, 4, 6, 9, 1, 10], [8, 7, 5, 2, 3, 4, 6, 9, 10, 1], [9, 4, 5, 6, 3, 7, 2, 1, 8, 10], [10, 4, 5, 6, 3, 7, 2, 1, 8, 9]}} is given by the following expression / 373 1303 2 187 3 593 4 59 5 6\ n |- ------ n - ------- n + ----- n + ------ n + ------ n + 1/2949120 n | 4 \ 122880 1474560 65536 589824 983040 / / + | \ 41 2 29 3 4 367 5 31 6 7\ 1/330 n + ---- n + ----- n - 1/132 n - ----- n - ----- n - 1/83160 n | 5040 20790 83160 55440 / C(n) and in Maple input form: (-373/122880*n-1303/1474560*n^2+187/65536*n^3+593/589824*n^4+59/983040*n^5+1/ 2949120*n^6)*4^n+(1/330*n+41/5040*n^2+29/20790*n^3-1/132*n^4-367/83160*n^5-31/ 55440*n^6-1/83160*n^7)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 15 14 1/2 13 12 1/2 11 10 Pi m m 95 Pi m 31 m 25313 Pi m 367 m --------- - ----- + ------------ - ------ + --------------- - ------- 2949120 83160 1572864 55440 23592960 83160 1/2 9 8 1/2 7 6 1/2 5 4 2089 Pi m m 54887 Pi m 29 m 3169 Pi m 41 m + ------------- - --- + -------------- + ----- - ------------- + ----- 524288 132 23592960 20790 786432 5040 1/2 3 2 1119 Pi m m - ------------- + --- 327680 330 and in Maple input form: 1/2949120*Pi^(1/2)*m^15-1/83160*m^14+95/1572864*Pi^(1/2)*m^13-31/55440*m^12+ 25313/23592960*Pi^(1/2)*m^11-367/83160*m^10+2089/524288*Pi^(1/2)*m^9-1/132*m^8+ 54887/23592960*Pi^(1/2)*m^7+29/20790*m^6-3169/786432*Pi^(1/2)*m^5+41/5040*m^4-\ 1119/327680*Pi^(1/2)*m^3+1/330*m^2 For the, 35, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[5, 4, 6, 3, 7, 2, 8, 1, 9, 10], [8, 6, 4, 2, 1, 3, 5, 7, 9, 10]}, {[5, 4, 6, 3, 7, 8, 9, 2, 10, 1], [10, 8, 4, 2, 1, 3, 5, 6, 7, 9]}, {[5, 4, 6, 7, 3, 8, 9, 2, 10, 1], [10, 8, 5, 2, 1, 3, 4, 6, 7, 9]}, {[5, 4, 6, 7, 8, 3, 9, 2, 10, 1], [10, 8, 6, 2, 1, 3, 4, 5, 7, 9]}, {[5, 6, 4, 7, 3, 8, 9, 2, 10, 1], [10, 8, 5, 3, 1, 2, 4, 6, 7, 9]}, {[5, 6, 4, 7, 8, 3, 9, 2, 10, 1], [10, 8, 6, 3, 1, 2, 4, 5, 7, 9]}, {[5, 6, 7, 4, 8, 3, 9, 2, 10, 1], [10, 8, 6, 4, 1, 2, 3, 5, 7, 9]}, {[6, 4, 3, 5, 7, 2, 8, 1, 9, 10], [8, 6, 3, 2, 4, 1, 5, 7, 9, 10]}, {[6, 4, 3, 5, 7, 8, 9, 2, 10, 1], [10, 8, 3, 2, 4, 1, 5, 6, 7, 9]}, {[6, 4, 5, 7, 3, 8, 9, 2, 10, 1], [10, 8, 5, 2, 3, 1, 4, 6, 7, 9]}, {[6, 4, 5, 7, 8, 3, 9, 2, 10, 1], [10, 8, 6, 2, 3, 1, 4, 5, 7, 9]}, {[6, 5, 7, 3, 2, 4, 8, 1, 9, 10], [8, 5, 4, 6, 2, 1, 3, 7, 9, 10]}, {[6, 5, 7, 3, 4, 8, 9, 2, 10, 1], [10, 8, 4, 5, 2, 1, 3, 6, 7, 9]}, {[6, 5, 7, 4, 8, 2, 1, 3, 9, 10], [7, 6, 8, 4, 2, 1, 3, 5, 9, 10]}, {[6, 5, 7, 4, 8, 3, 9, 1, 2, 10], [8, 9, 6, 4, 2, 1, 3, 5, 7, 10]}, {[6, 5, 7, 4, 8, 3, 9, 10, 1, 2], [9, 10, 6, 4, 2, 1, 3, 5, 7, 8]}, {[6, 5, 7, 4, 8, 9, 2, 1, 3, 10], [8, 7, 9, 4, 2, 1, 3, 5, 6, 10]}, {[6, 5, 7, 4, 8, 9, 2, 3, 10, 1], [10, 7, 8, 4, 2, 1, 3, 5, 6, 9]}, {[6, 5, 7, 4, 8, 9, 3, 10, 1, 2], [9, 10, 7, 4, 2, 1, 3, 5, 6, 8]}, {[6, 5, 7, 4, 8, 9, 10, 2, 1, 3], [9, 8, 10, 4, 2, 1, 3, 5, 6, 7]}, {[6, 5, 7, 8, 3, 4, 9, 2, 10, 1], [10, 8, 5, 6, 2, 1, 3, 4, 7, 9]}, {[6, 5, 7, 8, 4, 9, 2, 1, 3, 10], [8, 7, 9, 5, 2, 1, 3, 4, 6, 10]}, {[6, 5, 7, 8, 4, 9, 2, 3, 10, 1], [10, 7, 8, 5, 2, 1, 3, 4, 6, 9]}, {[6, 5, 7, 8, 4, 9, 3, 10, 1, 2], [9, 10, 7, 5, 2, 1, 3, 4, 6, 8]}, {[6, 5, 7, 8, 4, 9, 10, 2, 1, 3], [9, 8, 10, 5, 2, 1, 3, 4, 6, 7]}, {[6, 5, 7, 8, 9, 3, 2, 4, 10, 1], [10, 7, 6, 8, 2, 1, 3, 4, 5, 9]}, {[6, 5, 7, 8, 9, 4, 10, 2, 1, 3], [9, 8, 10, 6, 2, 1, 3, 4, 5, 7]}, {[6, 7, 4, 3, 5, 8, 9, 2, 10, 1], [10, 8, 4, 3, 5, 1, 2, 6, 7, 9]}, {[6, 7, 4, 5, 8, 3, 9, 2, 10, 1], [10, 8, 6, 3, 4, 1, 2, 5, 7, 9]}, {[6, 7, 5, 8, 3, 4, 9, 2, 10, 1], [10, 8, 5, 6, 3, 1, 2, 4, 7, 9]}, {[6, 7, 5, 8, 4, 9, 2, 1, 3, 10], [8, 7, 9, 5, 3, 1, 2, 4, 6, 10]}, {[6, 7, 5, 8, 4, 9, 2, 3, 10, 1], [10, 7, 8, 5, 3, 1, 2, 4, 6, 9]}, {[6, 7, 5, 8, 4, 9, 3, 10, 1, 2], [9, 10, 7, 5, 3, 1, 2, 4, 6, 8]}, {[6, 7, 5, 8, 4, 9, 10, 2, 1, 3], [9, 8, 10, 5, 3, 1, 2, 4, 6, 7]}, {[6, 7, 5, 8, 9, 3, 2, 4, 10, 1], [10, 7, 6, 8, 3, 1, 2, 4, 5, 9]}, {[6, 7, 5, 8, 9, 4, 10, 2, 1, 3], [9, 8, 10, 6, 3, 1, 2, 4, 5, 7]}, {[6, 7, 8, 4, 3, 5, 9, 2, 10, 1], [10, 8, 5, 4, 6, 1, 2, 3, 7, 9]}, {[6, 7, 8, 5, 9, 3, 2, 4, 10, 1], [10, 7, 6, 8, 4, 1, 2, 3, 5, 9]}, {[6, 7, 8, 5, 9, 4, 10, 2, 1, 3], [9, 8, 10, 6, 4, 1, 2, 3, 5, 7]}, {[7, 4, 3, 5, 2, 6, 8, 1, 9, 10], [8, 5, 3, 2, 4, 6, 1, 7, 9, 10]}, {[7, 4, 3, 5, 6, 8, 9, 2, 10, 1], [10, 8, 3, 2, 4, 5, 1, 6, 7, 9]}, {[7, 4, 5, 3, 6, 8, 9, 2, 10, 1], [10, 8, 4, 2, 3, 5, 1, 6, 7, 9]}, {[7, 4, 5, 6, 8, 3, 9, 2, 10, 1], [10, 8, 6, 2, 3, 4, 1, 5, 7, 9]}, {[7, 5, 3, 2, 4, 6, 8, 1, 9, 10], [8, 4, 3, 5, 2, 6, 1, 7, 9, 10]}, {[7, 5, 3, 4, 6, 8, 9, 2, 10, 1], [10, 8, 3, 4, 2, 5, 1, 6, 7, 9]}, {[7, 5, 4, 6, 8, 2, 1, 3, 9, 10], [7, 6, 8, 3, 2, 4, 1, 5, 9, 10]}, {[7, 5, 4, 6, 8, 3, 9, 1, 2, 10], [8, 9, 6, 3, 2, 4, 1, 5, 7, 10]}, {[7, 5, 4, 6, 8, 3, 9, 10, 1, 2], [9, 10, 6, 3, 2, 4, 1, 5, 7, 8]}, {[7, 5, 4, 6, 8, 9, 2, 1, 3, 10], [8, 7, 9, 3, 2, 4, 1, 5, 6, 10]}, {[7, 5, 4, 6, 8, 9, 2, 3, 10, 1], [10, 7, 8, 3, 2, 4, 1, 5, 6, 9]}, {[7, 5, 4, 6, 8, 9, 3, 10, 1, 2], [9, 10, 7, 3, 2, 4, 1, 5, 6, 8]}, {[7, 5, 4, 6, 8, 9, 10, 2, 1, 3], [9, 8, 10, 3, 2, 4, 1, 5, 6, 7]}, {[7, 5, 6, 8, 3, 4, 9, 2, 10, 1], [10, 8, 5, 6, 2, 3, 1, 4, 7, 9]}, {[7, 5, 6, 8, 4, 9, 2, 1, 3, 10], [8, 7, 9, 5, 2, 3, 1, 4, 6, 10]}, {[7, 5, 6, 8, 4, 9, 2, 3, 10, 1], [10, 7, 8, 5, 2, 3, 1, 4, 6, 9]}, {[7, 5, 6, 8, 4, 9, 3, 10, 1, 2], [9, 10, 7, 5, 2, 3, 1, 4, 6, 8]}, {[7, 5, 6, 8, 4, 9, 10, 2, 1, 3], [9, 8, 10, 5, 2, 3, 1, 4, 6, 7]}, {[7, 5, 6, 8, 9, 3, 2, 4, 10, 1], [10, 7, 6, 8, 2, 3, 1, 4, 5, 9]}, {[7, 5, 6, 8, 9, 4, 10, 2, 1, 3], [9, 8, 10, 6, 2, 3, 1, 4, 5, 7]}, {[7, 6, 8, 3, 4, 5, 9, 2, 10, 1], [10, 8, 4, 5, 6, 2, 1, 3, 7, 9]}, {[7, 6, 8, 4, 3, 5, 9, 1, 2, 10], [8, 9, 5, 4, 6, 2, 1, 3, 7, 10]}, {[7, 6, 8, 4, 3, 5, 9, 10, 1, 2], [9, 10, 5, 4, 6, 2, 1, 3, 7, 8]}, {[7, 6, 8, 4, 5, 9, 2, 1, 3, 10], [8, 7, 9, 4, 5, 2, 1, 3, 6, 10]}, {[7, 6, 8, 4, 5, 9, 2, 3, 10, 1], [10, 7, 8, 4, 5, 2, 1, 3, 6, 9]}, {[7, 6, 8, 4, 5, 9, 3, 10, 1, 2], [9, 10, 7, 4, 5, 2, 1, 3, 6, 8]}, {[7, 6, 8, 4, 5, 9, 10, 2, 1, 3], [9, 8, 10, 4, 5, 2, 1, 3, 6, 7]}, {[7, 6, 8, 5, 9, 2, 1, 3, 4, 10], [7, 6, 8, 9, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 2, 3, 1, 4, 10], [8, 6, 7, 9, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 2, 3, 4, 10, 1], [10, 6, 7, 8, 4, 2, 1, 3, 5, 9]}, {[7, 6, 8, 5, 9, 3, 1, 2, 4, 10], [7, 8, 6, 9, 4, 2, 1, 3, 5, 10]}, {[7, 6, 8, 5, 9, 3, 4, 10, 1, 2], [9, 10, 6, 7, 4, 2, 1, 3, 5, 8]}, {[7, 6, 8, 5, 9, 4, 10, 1, 2, 3], [8, 9, 10, 6, 4, 2, 1, 3, 5, 7]}, {[7, 6, 8, 5, 9, 10, 2, 1, 3, 4], [8, 7, 9, 10, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 5, 9, 10, 2, 3, 1, 4], [9, 7, 8, 10, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 5, 9, 10, 3, 1, 2, 4], [8, 9, 7, 10, 4, 2, 1, 3, 5, 6]}, {[7, 6, 8, 9, 3, 2, 4, 1, 5, 10], [8, 6, 5, 7, 9, 2, 1, 3, 4, 10]}, {[7, 6, 8, 9, 3, 2, 4, 5, 10, 1], [10, 6, 5, 7, 8, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 3, 4, 2, 5, 10, 1], [10, 7, 5, 6, 8, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 4, 2, 3, 5, 10, 1], [10, 6, 7, 5, 8, 2, 1, 3, 4, 9]}, {[7, 6, 8, 9, 4, 3, 5, 10, 1, 2], [9, 10, 6, 5, 7, 2, 1, 3, 4, 8]}, {[7, 6, 8, 9, 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8, 1, 9]}, {[9, 4, 5, 3, 6, 2, 7, 8, 10, 1], [10, 6, 4, 2, 3, 5, 7, 8, 1, 9]}, {[9, 4, 5, 3, 6, 7, 2, 8, 10, 1], [10, 7, 4, 2, 3, 5, 6, 8, 1, 9]}, {[9, 4, 5, 6, 3, 7, 2, 8, 10, 1], [10, 7, 5, 2, 3, 4, 6, 8, 1, 9]}, {[9, 5, 3, 2, 4, 6, 7, 8, 10, 1], [10, 4, 3, 5, 2, 6, 7, 8, 1, 9]}, {[9, 5, 3, 4, 6, 2, 7, 8, 10, 1], [10, 6, 3, 4, 2, 5, 7, 8, 1, 9]}, {[9, 5, 3, 4, 6, 7, 2, 8, 10, 1], [10, 7, 3, 4, 2, 5, 6, 8, 1, 9]}, {[9, 5, 4, 6, 2, 3, 7, 8, 10, 1], [10, 5, 6, 3, 2, 4, 7, 8, 1, 9]}, {[9, 5, 4, 6, 3, 7, 8, 10, 1, 2], [9, 10, 5, 3, 2, 4, 6, 7, 1, 8]}, {[9, 5, 4, 6, 7, 2, 3, 8, 10, 1], [10, 6, 7, 3, 2, 4, 5, 8, 1, 9]}, {[9, 5, 4, 6, 7, 3, 8, 10, 1, 2], [9, 10, 6, 3, 2, 4, 5, 7, 1, 8]}, {[9, 5, 4, 6, 7, 8, 10, 2, 1, 3], [9, 8, 10, 3, 2, 4, 5, 6, 1, 7]}, {[9, 5, 6, 3, 2, 4, 7, 8, 10, 1], [10, 5, 4, 6, 2, 3, 7, 8, 1, 9]}, {[9, 5, 6, 3, 4, 7, 2, 8, 10, 1], [10, 7, 4, 5, 2, 3, 6, 8, 1, 9]}, {[9, 5, 6, 4, 7, 2, 3, 8, 10, 1], [10, 6, 7, 4, 2, 3, 5, 8, 1, 9]}, {[9, 5, 6, 4, 7, 3, 8, 10, 1, 2], [9, 10, 6, 4, 2, 3, 5, 7, 1, 8]}, {[9, 5, 6, 4, 7, 8, 10, 2, 1, 3], [9, 8, 10, 4, 2, 3, 5, 6, 1, 7]}, {[9, 5, 6, 7, 3, 2, 4, 8, 10, 1], [10, 6, 5, 7, 2, 3, 4, 8, 1, 9]}, {[9, 5, 6, 7, 4, 8, 10, 2, 1, 3], [9, 8, 10, 5, 2, 3, 4, 6, 1, 7]}, {[9, 6, 3, 2, 4, 5, 7, 8, 10, 1], [10, 4, 3, 5, 6, 2, 7, 8, 1, 9]}, {[9, 6, 3, 4, 2, 5, 7, 8, 10, 1], [10, 5, 3, 4, 6, 2, 7, 8, 1, 9]}, {[9, 6, 3, 4, 5, 7, 2, 8, 10, 1], [10, 7, 3, 4, 5, 2, 6, 8, 1, 9]}, {[9, 6, 4, 2, 3, 5, 7, 8, 10, 1], [10, 4, 5, 3, 6, 2, 7, 8, 1, 9]}, {[9, 6, 4, 3, 5, 7, 8, 10, 1, 2], [9, 10, 4, 3, 5, 2, 6, 7, 1, 8]}, {[9, 6, 4, 5, 7, 2, 3, 8, 10, 1], [10, 6, 7, 3, 4, 2, 5, 8, 1, 9]}, {[9, 6, 4, 5, 7, 3, 8, 10, 1, 2], [9, 10, 6, 3, 4, 2, 5, 7, 1, 8]}, {[9, 6, 4, 5, 7, 8, 10, 2, 1, 3], [9, 8, 10, 3, 4, 2, 5, 6, 1, 7]}, {[9, 6, 5, 7, 2, 3, 4, 8, 10, 1], [10, 5, 6, 7, 3, 2, 4, 8, 1, 9]}, {[9, 6, 5, 7, 3, 4, 8, 10, 1, 2], [9, 10, 5, 6, 3, 2, 4, 7, 1, 8]}, {[9, 6, 5, 7, 8, 10, 2, 3, 1, 4], [9, 7, 8, 10, 3, 2, 4, 5, 1, 6]}, {[9, 6, 7, 3, 2, 4, 5, 8, 10, 1], [10, 5, 4, 6, 7, 2, 3, 8, 1, 9]}, {[9, 6, 7, 3, 4, 2, 5, 8, 10, 1], [10, 6, 4, 5, 7, 2, 3, 8, 1, 9]}, {[9, 6, 7, 4, 2, 3, 5, 8, 10, 1], [10, 5, 6, 4, 7, 2, 3, 8, 1, 9]}, {[9, 6, 7, 4, 3, 5, 8, 10, 1, 2], [9, 10, 5, 4, 6, 2, 3, 7, 1, 8]}, {[9, 6, 7, 4, 5, 8, 10, 2, 1, 3], [9, 8, 10, 4, 5, 2, 3, 6, 1, 7]}, {[9, 6, 7, 5, 8, 10, 2, 3, 1, 4], [9, 7, 8, 10, 4, 2, 3, 5, 1, 6]}, {[9, 6, 7, 8, 10, 3, 2, 4, 1, 5], [9, 7, 6, 8, 10, 2, 3, 4, 1, 5]}, {[9, 7, 3, 2, 4, 5, 6, 8, 10, 1], [10, 4, 3, 5, 6, 7, 2, 8, 1, 9]}, {[9, 7, 3, 4, 2, 5, 6, 8, 10, 1], [10, 5, 3, 4, 6, 7, 2, 8, 1, 9]}, {[9, 7, 3, 4, 5, 2, 6, 8, 10, 1], [10, 6, 3, 4, 5, 7, 2, 8, 1, 9]}, {[9, 7, 4, 2, 3, 5, 6, 8, 10, 1], [10, 4, 5, 3, 6, 7, 2, 8, 1, 9]}, {[9, 7, 4, 3, 5, 6, 8, 10, 1, 2], [9, 10, 4, 3, 5, 6, 2, 7, 1, 8]}, {[9, 7, 4, 5, 2, 3, 6, 8, 10, 1], [10, 5, 6, 3, 4, 7, 2, 8, 1, 9]}, {[9, 7, 4, 5, 3, 6, 8, 10, 1, 2], [9, 10, 5, 3, 4, 6, 2, 7, 1, 8]}, {[9, 7, 4, 5, 6, 8, 10, 2, 1, 3], [9, 8, 10, 3, 4, 5, 2, 6, 1, 7]}, {[9, 7, 5, 2, 3, 4, 6, 8, 10, 1], [10, 4, 5, 6, 3, 7, 2, 8, 1, 9]}, {[9, 7, 5, 3, 4, 6, 8, 10, 1, 2], [9, 10, 4, 5, 3, 6, 2, 7, 1, 8]}, {[9, 7, 5, 6, 8, 10, 2, 3, 1, 4], [9, 7, 8, 10, 3, 4, 2, 5, 1, 6]}, { [5, 4, 6, 3, 7, 2, 8, 9, 1, 10], [5, 4, 6, 3, 7, 2, 8, 9, 10, 1], [9, 6, 4, 2, 1, 3, 5, 7, 8, 10], [10, 6, 4, 2, 1, 3, 5, 7, 8, 9]}, { [5, 4, 6, 3, 7, 8, 2, 9, 1, 10], [5, 4, 6, 3, 7, 8, 2, 9, 10, 1], [9, 7, 4, 2, 1, 3, 5, 6, 8, 10], [10, 7, 4, 2, 1, 3, 5, 6, 8, 9]}, { [5, 4, 6, 7, 3, 8, 2, 9, 1, 10], [5, 4, 6, 7, 3, 8, 2, 9, 10, 1], [9, 7, 5, 2, 1, 3, 4, 6, 8, 10], [10, 7, 5, 2, 1, 3, 4, 6, 8, 9]}, { [5, 6, 4, 7, 3, 8, 2, 9, 1, 10], [5, 6, 4, 7, 3, 8, 2, 9, 10, 1], [9, 7, 5, 3, 1, 2, 4, 6, 8, 10], [10, 7, 5, 3, 1, 2, 4, 6, 8, 9]}, { [6, 4, 3, 5, 7, 2, 8, 9, 1, 10], [6, 4, 3, 5, 7, 2, 8, 9, 10, 1], [9, 6, 3, 2, 4, 1, 5, 7, 8, 10], [10, 6, 3, 2, 4, 1, 5, 7, 8, 9]}, { [6, 4, 3, 5, 7, 8, 2, 9, 1, 10], [6, 4, 3, 5, 7, 8, 2, 9, 10, 1], [9, 7, 3, 2, 4, 1, 5, 6, 8, 10], [10, 7, 3, 2, 4, 1, 5, 6, 8, 9]}, { [6, 4, 5, 7, 3, 8, 2, 9, 1, 10], [6, 4, 5, 7, 3, 8, 2, 9, 10, 1], [9, 7, 5, 2, 3, 1, 4, 6, 8, 10], [10, 7, 5, 2, 3, 1, 4, 6, 8, 9]}, { [6, 5, 7, 3, 2, 4, 8, 9, 1, 10], [6, 5, 7, 3, 2, 4, 8, 9, 10, 1], [9, 5, 4, 6, 2, 1, 3, 7, 8, 10], [10, 5, 4, 6, 2, 1, 3, 7, 8, 9]}, { [6, 5, 7, 3, 4, 8, 2, 9, 1, 10], [6, 5, 7, 3, 4, 8, 2, 9, 10, 1], [9, 7, 4, 5, 2, 1, 3, 6, 8, 10], [10, 7, 4, 5, 2, 1, 3, 6, 8, 9]}, { [6, 5, 7, 4, 8, 2, 3, 9, 1, 10], [6, 5, 7, 4, 8, 2, 3, 9, 10, 1], [9, 6, 7, 4, 2, 1, 3, 5, 8, 10], [10, 6, 7, 4, 2, 1, 3, 5, 8, 9]}, { [6, 5, 7, 8, 3, 2, 4, 9, 1, 10], [6, 5, 7, 8, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 2, 1, 3, 4, 8, 10], [10, 6, 5, 7, 2, 1, 3, 4, 8, 9]}, { [6, 7, 4, 3, 5, 8, 2, 9, 1, 10], [6, 7, 4, 3, 5, 8, 2, 9, 10, 1], [9, 7, 4, 3, 5, 1, 2, 6, 8, 10], [10, 7, 4, 3, 5, 1, 2, 6, 8, 9]}, { [6, 7, 5, 8, 3, 2, 4, 9, 1, 10], [6, 7, 5, 8, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 3, 1, 2, 4, 8, 10], [10, 6, 5, 7, 3, 1, 2, 4, 8, 9]}, { [7, 4, 3, 5, 2, 6, 8, 9, 1, 10], [7, 4, 3, 5, 2, 6, 8, 9, 10, 1], [9, 5, 3, 2, 4, 6, 1, 7, 8, 10], [10, 5, 3, 2, 4, 6, 1, 7, 8, 9]}, { [7, 4, 3, 5, 6, 8, 2, 9, 1, 10], [7, 4, 3, 5, 6, 8, 2, 9, 10, 1], [9, 7, 3, 2, 4, 5, 1, 6, 8, 10], [10, 7, 3, 2, 4, 5, 1, 6, 8, 9]}, { [7, 4, 5, 3, 6, 8, 2, 9, 1, 10], [7, 4, 5, 3, 6, 8, 2, 9, 10, 1], [9, 7, 4, 2, 3, 5, 1, 6, 8, 10], [10, 7, 4, 2, 3, 5, 1, 6, 8, 9]}, { [7, 5, 3, 2, 4, 6, 8, 9, 1, 10], [7, 5, 3, 2, 4, 6, 8, 9, 10, 1], [9, 4, 3, 5, 2, 6, 1, 7, 8, 10], [10, 4, 3, 5, 2, 6, 1, 7, 8, 9]}, { [7, 5, 3, 4, 6, 8, 2, 9, 1, 10], [7, 5, 3, 4, 6, 8, 2, 9, 10, 1], [9, 7, 3, 4, 2, 5, 1, 6, 8, 10], [10, 7, 3, 4, 2, 5, 1, 6, 8, 9]}, { [7, 5, 4, 6, 8, 2, 3, 9, 1, 10], [7, 5, 4, 6, 8, 2, 3, 9, 10, 1], [9, 6, 7, 3, 2, 4, 1, 5, 8, 10], [10, 6, 7, 3, 2, 4, 1, 5, 8, 9]}, { [7, 5, 6, 8, 3, 2, 4, 9, 1, 10], [7, 5, 6, 8, 3, 2, 4, 9, 10, 1], [9, 6, 5, 7, 2, 3, 1, 4, 8, 10], [10, 6, 5, 7, 2, 3, 1, 4, 8, 9]}, { [7, 6, 8, 3, 2, 4, 5, 9, 1, 10], [7, 6, 8, 3, 2, 4, 5, 9, 10, 1], [9, 5, 4, 6, 7, 2, 1, 3, 8, 10], [10, 5, 4, 6, 7, 2, 1, 3, 8, 9]}, { [7, 6, 8, 3, 4, 2, 5, 9, 1, 10], [7, 6, 8, 3, 4, 2, 5, 9, 10, 1], [9, 6, 4, 5, 7, 2, 1, 3, 8, 10], [10, 6, 4, 5, 7, 2, 1, 3, 8, 9]}, { [7, 6, 8, 4, 2, 3, 5, 9, 1, 10], [7, 6, 8, 4, 2, 3, 5, 9, 10, 1], [9, 5, 6, 4, 7, 2, 1, 3, 8, 10], [10, 5, 6, 4, 7, 2, 1, 3, 8, 9]}, { [7, 8, 4, 3, 5, 2, 6, 9, 1, 10], [7, 8, 4, 3, 5, 2, 6, 9, 10, 1], [9, 6, 4, 3, 5, 7, 1, 2, 8, 10], [10, 6, 4, 3, 5, 7, 1, 2, 8, 9]}, { [7, 8, 5, 3, 2, 4, 6, 9, 1, 10], [7, 8, 5, 3, 2, 4, 6, 9, 10, 1], [9, 5, 4, 6, 3, 7, 1, 2, 8, 10], [10, 5, 4, 6, 3, 7, 1, 2, 8, 9]}, { [8, 4, 3, 5, 2, 6, 7, 9, 1, 10], [8, 4, 3, 5, 2, 6, 7, 9, 10, 1], [9, 5, 3, 2, 4, 6, 7, 1, 8, 10], [10, 5, 3, 2, 4, 6, 7, 1, 8, 9]}, { [8, 4, 3, 5, 6, 2, 7, 9, 1, 10], [8, 4, 3, 5, 6, 2, 7, 9, 10, 1], [9, 6, 3, 2, 4, 5, 7, 1, 8, 10], [10, 6, 3, 2, 4, 5, 7, 1, 8, 9]}, { [8, 4, 5, 3, 6, 2, 7, 9, 1, 10], [8, 4, 5, 3, 6, 2, 7, 9, 10, 1], [9, 6, 4, 2, 3, 5, 7, 1, 8, 10], [10, 6, 4, 2, 3, 5, 7, 1, 8, 9]}, { [8, 5, 3, 2, 4, 6, 7, 9, 1, 10], [8, 5, 3, 2, 4, 6, 7, 9, 10, 1], [9, 4, 3, 5, 2, 6, 7, 1, 8, 10], [10, 4, 3, 5, 2, 6, 7, 1, 8, 9]}, { [8, 5, 3, 4, 6, 2, 7, 9, 1, 10], [8, 5, 3, 4, 6, 2, 7, 9, 10, 1], [9, 6, 3, 4, 2, 5, 7, 1, 8, 10], [10, 6, 3, 4, 2, 5, 7, 1, 8, 9]}, { [8, 5, 4, 6, 2, 3, 7, 9, 1, 10], [8, 5, 4, 6, 2, 3, 7, 9, 10, 1], [9, 5, 6, 3, 2, 4, 7, 1, 8, 10], [10, 5, 6, 3, 2, 4, 7, 1, 8, 9]}, { [8, 5, 6, 3, 2, 4, 7, 9, 1, 10], [8, 5, 6, 3, 2, 4, 7, 9, 10, 1], [9, 5, 4, 6, 2, 3, 7, 1, 8, 10], [10, 5, 4, 6, 2, 3, 7, 1, 8, 9]}, { [8, 6, 3, 2, 4, 5, 7, 9, 1, 10], [8, 6, 3, 2, 4, 5, 7, 9, 10, 1], [9, 4, 3, 5, 6, 2, 7, 1, 8, 10], [10, 4, 3, 5, 6, 2, 7, 1, 8, 9]}, { [8, 6, 3, 4, 2, 5, 7, 9, 1, 10], [8, 6, 3, 4, 2, 5, 7, 9, 10, 1], [9, 5, 3, 4, 6, 2, 7, 1, 8, 10], [10, 5, 3, 4, 6, 2, 7, 1, 8, 9]}, { [8, 6, 4, 2, 3, 5, 7, 9, 1, 10], [8, 6, 4, 2, 3, 5, 7, 9, 10, 1], [9, 4, 5, 3, 6, 2, 7, 1, 8, 10], [10, 4, 5, 3, 6, 2, 7, 1, 8, 9]}} is given by the following expression / 179 1783 2 127 3 209 4 43 5 6\ n |------ n - ------- n - ------ n + ------- n + ------- n + 1/5898240 n | 4 \245760 2949120 393216 1179648 1966080 / / 2 43 3 19 4 5 6 + |-1/1320 n - 1/960 n + ----- n + ----- n - 7/19008 n - 1/6336 n \ 38016 15840 7\ - 1/190080 n | C(n) / and in Maple input form: (179/245760*n-1783/2949120*n^2-127/393216*n^3+209/1179648*n^4+43/1966080*n^5+1/ 5898240*n^6)*4^n+(-1/1320*n-1/960*n^2+43/38016*n^3+19/15840*n^4-7/19008*n^5-1/ 6336*n^6-1/190080*n^7)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 15 14 1/2 13 12 1/2 11 10 Pi m m 347 Pi m m 9521 Pi m 7 m --------- - ------ + ------------- - ---- + -------------- - ----- 5898240 190080 15728640 6336 47185920 19008 1/2 9 8 1/2 7 6 1/2 5 4 389 Pi m 19 m 45673 Pi m 43 m 379 Pi m m - ------------ + ----- - -------------- + ----- + ------------ - --- 3145728 15840 47185920 38016 7864320 960 1/2 3 2 537 Pi m m + ------------ - ---- 655360 1320 and in Maple input form: 1/5898240*Pi^(1/2)*m^15-1/190080*m^14+347/15728640*Pi^(1/2)*m^13-1/6336*m^12+ 9521/47185920*Pi^(1/2)*m^11-7/19008*m^10-389/3145728*Pi^(1/2)*m^9+19/15840*m^8-\ 45673/47185920*Pi^(1/2)*m^7+43/38016*m^6+379/7864320*Pi^(1/2)*m^5-1/960*m^4+537 /655360*Pi^(1/2)*m^3-1/1320*m^2 For the, 36, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[4, 3, 2, 1, 5, 6, 7, 8, 9, 10]}, {[5, 6, 4, 3, 1, 2, 7, 8, 9, 10]}, {[6, 4, 5, 2, 3, 1, 7, 8, 9, 10]}, {[6, 7, 8, 5, 4, 1, 2, 3, 9, 10]}, {[7, 8, 5, 6, 3, 4, 1, 2, 9, 10]}, {[7, 8, 9, 10, 6, 5, 1, 2, 3, 4]}, {[8, 5, 6, 7, 2, 3, 4, 1, 9, 10]}, {[8, 9, 10, 6, 7, 4, 5, 1, 2, 3]}, {[9, 10, 6, 7, 8, 3, 4, 5, 1, 2]}, {[10, 6, 7, 8, 9, 2, 3, 4, 5, 1]}, {[4, 5, 3, 2, 1, 6, 7, 8, 9, 10], [5, 4, 3, 1, 2, 6, 7, 8, 9, 10]}, {[4, 5, 6, 3, 2, 1, 7, 8, 9, 10], [6, 5, 4, 1, 2, 3, 7, 8, 9, 10]}, {[4, 5, 6, 7, 3, 2, 1, 8, 9, 10], [7, 6, 5, 1, 2, 3, 4, 8, 9, 10]}, {[4, 5, 6, 7, 8, 3, 2, 1, 9, 10], [8, 7, 6, 1, 2, 3, 4, 5, 9, 10]}, {[4, 5, 6, 7, 8, 9, 3, 2, 1, 10], [9, 8, 7, 1, 2, 3, 4, 5, 6, 10]}, {[4, 5, 6, 7, 8, 9, 10, 3, 2, 1], [10, 9, 8, 1, 2, 3, 4, 5, 6, 7]}, {[5, 3, 4, 2, 1, 6, 7, 8, 9, 10], [5, 4, 2, 3, 1, 6, 7, 8, 9, 10]}, {[5, 6, 3, 4, 2, 1, 7, 8, 9, 10], [6, 5, 3, 4, 1, 2, 7, 8, 9, 10]}, {[5, 6, 4, 2, 3, 1, 7, 8, 9, 10], [6, 4, 5, 3, 1, 2, 7, 8, 9, 10]}, {[5, 6, 7, 3, 4, 2, 1, 8, 9, 10], [7, 6, 4, 5, 1, 2, 3, 8, 9, 10]}, {[5, 6, 7, 4, 2, 3, 1, 8, 9, 10], [7, 5, 6, 4, 1, 2, 3, 8, 9, 10]}, {[5, 6, 7, 4, 3, 1, 2, 8, 9, 10], [6, 7, 5, 4, 1, 2, 3, 8, 9, 10]}, {[5, 6, 7, 8, 3, 4, 2, 1, 9, 10], [8, 7, 5, 6, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 4, 2, 3, 1, 9, 10], [8, 6, 7, 5, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 4, 3, 1, 2, 9, 10], [7, 8, 6, 5, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 9, 3, 4, 2, 1, 10], [9, 8, 6, 7, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 4, 2, 3, 1, 10], [9, 7, 8, 6, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 4, 3, 1, 2, 10], [8, 9, 7, 6, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 10, 3, 4, 2, 1], [10, 9, 7, 8, 1, 2, 3, 4, 5, 6]}, {[5, 6, 7, 8, 9, 10, 4, 2, 3, 1], [10, 8, 9, 7, 1, 2, 3, 4, 5, 6]}, {[5, 6, 7, 8, 9, 10, 4, 3, 1, 2], [9, 10, 8, 7, 1, 2, 3, 4, 5, 6]}, {[6, 3, 4, 5, 2, 1, 7, 8, 9, 10], [6, 5, 2, 3, 4, 1, 7, 8, 9, 10]}, {[6, 7, 3, 4, 5, 2, 1, 8, 9, 10], [7, 6, 3, 4, 5, 1, 2, 8, 9, 10]}, {[6, 7, 4, 5, 2, 3, 1, 8, 9, 10], [7, 5, 6, 3, 4, 1, 2, 8, 9, 10]}, {[6, 7, 4, 5, 3, 1, 2, 8, 9, 10], [6, 7, 5, 3, 4, 1, 2, 8, 9, 10]}, {[6, 7, 5, 2, 3, 4, 1, 8, 9, 10], [7, 4, 5, 6, 3, 1, 2, 8, 9, 10]}, {[6, 7, 8, 3, 4, 5, 2, 1, 9, 10], [8, 7, 4, 5, 6, 1, 2, 3, 9, 10]}, {[6, 7, 8, 4, 5, 2, 3, 1, 9, 10], [8, 6, 7, 4, 5, 1, 2, 3, 9, 10]}, {[6, 7, 8, 4, 5, 3, 1, 2, 9, 10], [7, 8, 6, 4, 5, 1, 2, 3, 9, 10]}, {[6, 7, 8, 5, 2, 3, 4, 1, 9, 10], [8, 5, 6, 7, 4, 1, 2, 3, 9, 10]}, {[6, 7, 8, 5, 3, 4, 1, 2, 9, 10], [7, 8, 5, 6, 4, 1, 2, 3, 9, 10]}, {[6, 7, 8, 9, 3, 4, 5, 2, 1, 10], [9, 8, 5, 6, 7, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 4, 5, 2, 3, 1, 10], [9, 7, 8, 5, 6, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 4, 5, 3, 1, 2, 10], [8, 9, 7, 5, 6, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 5, 2, 3, 4, 1, 10], [9, 6, 7, 8, 5, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 5, 3, 4, 1, 2, 10], [8, 9, 6, 7, 5, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 5, 4, 1, 2, 3, 10], [7, 8, 9, 6, 5, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 10, 3, 4, 5, 2, 1], [10, 9, 6, 7, 8, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 4, 5, 2, 3, 1], [10, 8, 9, 6, 7, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 4, 5, 3, 1, 2], [9, 10, 8, 6, 7, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 5, 2, 3, 4, 1], [10, 7, 8, 9, 6, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 5, 3, 4, 1, 2], [9, 10, 7, 8, 6, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 5, 4, 1, 2, 3], [8, 9, 10, 7, 6, 1, 2, 3, 4, 5]}, {[7, 3, 4, 5, 6, 2, 1, 8, 9, 10], [7, 6, 2, 3, 4, 5, 1, 8, 9, 10]}, {[7, 4, 5, 6, 2, 3, 1, 8, 9, 10], [7, 5, 6, 2, 3, 4, 1, 8, 9, 10]}, {[7, 8, 3, 4, 5, 6, 2, 1, 9, 10], [8, 7, 3, 4, 5, 6, 1, 2, 9, 10]}, {[7, 8, 4, 5, 6, 2, 3, 1, 9, 10], [8, 6, 7, 3, 4, 5, 1, 2, 9, 10]}, {[7, 8, 4, 5, 6, 3, 1, 2, 9, 10], [7, 8, 6, 3, 4, 5, 1, 2, 9, 10]}, {[7, 8, 5, 6, 2, 3, 4, 1, 9, 10], [8, 5, 6, 7, 3, 4, 1, 2, 9, 10]}, {[7, 8, 6, 2, 3, 4, 5, 1, 9, 10], [8, 4, 5, 6, 7, 3, 1, 2, 9, 10]}, {[7, 8, 9, 3, 4, 5, 6, 2, 1, 10], [9, 8, 4, 5, 6, 7, 1, 2, 3, 10]}, {[7, 8, 9, 4, 5, 6, 2, 3, 1, 10], [9, 7, 8, 4, 5, 6, 1, 2, 3, 10]}, {[7, 8, 9, 4, 5, 6, 3, 1, 2, 10], [8, 9, 7, 4, 5, 6, 1, 2, 3, 10]}, {[7, 8, 9, 5, 6, 2, 3, 4, 1, 10], [9, 6, 7, 8, 4, 5, 1, 2, 3, 10]}, {[7, 8, 9, 5, 6, 3, 4, 1, 2, 10], [8, 9, 6, 7, 4, 5, 1, 2, 3, 10]}, {[7, 8, 9, 5, 6, 4, 1, 2, 3, 10], [7, 8, 9, 6, 4, 5, 1, 2, 3, 10]}, {[7, 8, 9, 6, 2, 3, 4, 5, 1, 10], [9, 5, 6, 7, 8, 4, 1, 2, 3, 10]}, {[7, 8, 9, 6, 3, 4, 5, 1, 2, 10], [8, 9, 5, 6, 7, 4, 1, 2, 3, 10]}, {[7, 8, 9, 10, 3, 4, 5, 6, 2, 1], [10, 9, 5, 6, 7, 8, 1, 2, 3, 4]}, {[7, 8, 9, 10, 4, 5, 6, 2, 3, 1], [10, 8, 9, 5, 6, 7, 1, 2, 3, 4]}, {[7, 8, 9, 10, 4, 5, 6, 3, 1, 2], [9, 10, 8, 5, 6, 7, 1, 2, 3, 4]}, {[7, 8, 9, 10, 5, 6, 2, 3, 4, 1], [10, 7, 8, 9, 5, 6, 1, 2, 3, 4]}, {[7, 8, 9, 10, 5, 6, 3, 4, 1, 2], [9, 10, 7, 8, 5, 6, 1, 2, 3, 4]}, {[7, 8, 9, 10, 5, 6, 4, 1, 2, 3], [8, 9, 10, 7, 5, 6, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 3, 4, 5, 1, 2], [9, 10, 6, 7, 8, 5, 1, 2, 3, 4]}, {[7, 8, 9, 10, 6, 4, 5, 1, 2, 3], [8, 9, 10, 6, 7, 5, 1, 2, 3, 4]}, {[8, 3, 4, 5, 6, 7, 2, 1, 9, 10], [8, 7, 2, 3, 4, 5, 6, 1, 9, 10]}, {[8, 4, 5, 6, 7, 2, 3, 1, 9, 10], [8, 6, 7, 2, 3, 4, 5, 1, 9, 10]}, {[8, 9, 3, 4, 5, 6, 7, 2, 1, 10], [9, 8, 3, 4, 5, 6, 7, 1, 2, 10]}, {[8, 9, 4, 5, 6, 7, 2, 3, 1, 10], [9, 7, 8, 3, 4, 5, 6, 1, 2, 10]}, {[8, 9, 4, 5, 6, 7, 3, 1, 2, 10], [8, 9, 7, 3, 4, 5, 6, 1, 2, 10]}, {[8, 9, 5, 6, 7, 2, 3, 4, 1, 10], [9, 6, 7, 8, 3, 4, 5, 1, 2, 10]}, {[8, 9, 5, 6, 7, 3, 4, 1, 2, 10], [8, 9, 6, 7, 3, 4, 5, 1, 2, 10]}, {[8, 9, 6, 7, 2, 3, 4, 5, 1, 10], [9, 5, 6, 7, 8, 3, 4, 1, 2, 10]}, {[8, 9, 7, 2, 3, 4, 5, 6, 1, 10], [9, 4, 5, 6, 7, 8, 3, 1, 2, 10]}, {[8, 9, 10, 3, 4, 5, 6, 7, 2, 1], [10, 9, 4, 5, 6, 7, 8, 1, 2, 3]}, {[8, 9, 10, 4, 5, 6, 7, 2, 3, 1], [10, 8, 9, 4, 5, 6, 7, 1, 2, 3]}, {[8, 9, 10, 4, 5, 6, 7, 3, 1, 2], [9, 10, 8, 4, 5, 6, 7, 1, 2, 3]}, {[8, 9, 10, 5, 6, 7, 2, 3, 4, 1], [10, 7, 8, 9, 4, 5, 6, 1, 2, 3]}, {[8, 9, 10, 5, 6, 7, 3, 4, 1, 2], [9, 10, 7, 8, 4, 5, 6, 1, 2, 3]}, {[8, 9, 10, 5, 6, 7, 4, 1, 2, 3], [8, 9, 10, 7, 4, 5, 6, 1, 2, 3]}, {[8, 9, 10, 6, 7, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 4, 5, 1, 2, 3]}, {[8, 9, 10, 6, 7, 3, 4, 5, 1, 2], [9, 10, 6, 7, 8, 4, 5, 1, 2, 3]}, {[8, 9, 10, 7, 2, 3, 4, 5, 6, 1], [10, 5, 6, 7, 8, 9, 4, 1, 2, 3]}, {[8, 9, 10, 7, 3, 4, 5, 6, 1, 2], [9, 10, 5, 6, 7, 8, 4, 1, 2, 3]}, {[9, 3, 4, 5, 6, 7, 8, 2, 1, 10], [9, 8, 2, 3, 4, 5, 6, 7, 1, 10]}, {[9, 4, 5, 6, 7, 8, 2, 3, 1, 10], [9, 7, 8, 2, 3, 4, 5, 6, 1, 10]}, {[9, 5, 6, 7, 8, 2, 3, 4, 1, 10], [9, 6, 7, 8, 2, 3, 4, 5, 1, 10]}, {[9, 10, 3, 4, 5, 6, 7, 8, 2, 1], [10, 9, 3, 4, 5, 6, 7, 8, 1, 2]}, {[9, 10, 4, 5, 6, 7, 8, 2, 3, 1], [10, 8, 9, 3, 4, 5, 6, 7, 1, 2]}, {[9, 10, 4, 5, 6, 7, 8, 3, 1, 2], [9, 10, 8, 3, 4, 5, 6, 7, 1, 2]}, {[9, 10, 5, 6, 7, 8, 2, 3, 4, 1], [10, 7, 8, 9, 3, 4, 5, 6, 1, 2]}, {[9, 10, 5, 6, 7, 8, 3, 4, 1, 2], [9, 10, 7, 8, 3, 4, 5, 6, 1, 2]}, {[9, 10, 6, 7, 8, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 3, 4, 5, 1, 2]}, {[9, 10, 7, 8, 2, 3, 4, 5, 6, 1], [10, 5, 6, 7, 8, 9, 3, 4, 1, 2]}, {[9, 10, 8, 2, 3, 4, 5, 6, 7, 1], [10, 4, 5, 6, 7, 8, 9, 3, 1, 2]}, {[10, 3, 4, 5, 6, 7, 8, 9, 2, 1], [10, 9, 2, 3, 4, 5, 6, 7, 8, 1]}, {[10, 4, 5, 6, 7, 8, 9, 2, 3, 1], [10, 8, 9, 2, 3, 4, 5, 6, 7, 1]}, {[10, 5, 6, 7, 8, 9, 2, 3, 4, 1], [10, 7, 8, 9, 2, 3, 4, 5, 6, 1]}} is given by the following expression / 1457 13609 2 1885 3 185 4 5\ n / |- 1/2 - ---- n - ----- n - ----- n - ----- n - 5/49152 n | 4 + |1/2 \ 1536 24576 16384 24576 / \ 118739 13687 2 68017 3 77135 4 42227 5 1327 6 + ------ n + ----- n + ----- n + ------ n + ------ n + ------ n 55440 4320 33264 133056 665280 665280 7\ + 1/133056 n | C(n) / and in Maple input form: (-1/2-1457/1536*n-13609/24576*n^2-1885/16384*n^3-185/24576*n^4-5/49152*n^5)*4^n +(1/2+118739/55440*n+13687/4320*n^2+68017/33264*n^3+77135/133056*n^4+42227/ 665280*n^5+1327/665280*n^6+1/133056*n^7)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 14 1/2 13 12 1/2 11 10 1/2 9 m 5 Pi m 1327 m 3005 Pi m 42227 m 8095 Pi m ------ - ----------- + -------- - -------------- + --------- - ------------- 133056 49152 665280 393216 665280 65536 8 1/2 7 6 1/2 5 4 77135 m 268639 Pi m 68017 m 308977 Pi m 13687 m + -------- - --------------- + -------- - --------------- + -------- 133056 393216 33264 196608 4320 1/2 3 2 1/2 6419 Pi m 118739 m 9 Pi m - ------------- + --------- - --------- + 1/2 4096 55440 16 and in Maple input form: 1/133056*m^14-5/49152*Pi^(1/2)*m^13+1327/665280*m^12-3005/393216*Pi^(1/2)*m^11+ 42227/665280*m^10-8095/65536*Pi^(1/2)*m^9+77135/133056*m^8-268639/393216*Pi^(1/ 2)*m^7+68017/33264*m^6-308977/196608*Pi^(1/2)*m^5+13687/4320*m^4-6419/4096*Pi^( 1/2)*m^3+118739/55440*m^2-9/16*Pi^(1/2)*m+1/2 For the, 37, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[5, 3, 2, 4, 1, 6, 7, 8, 9, 10]}, {[6, 3, 2, 4, 5, 1, 7, 8, 9, 10]}, {[6, 7, 4, 3, 5, 1, 2, 8, 9, 10]}, {[7, 3, 2, 4, 5, 6, 1, 8, 9, 10]}, {[7, 4, 5, 2, 3, 6, 1, 8, 9, 10]}, {[7, 8, 4, 3, 5, 6, 1, 2, 9, 10]}, {[7, 8, 9, 5, 4, 6, 1, 2, 3, 10]}, {[8, 3, 2, 4, 5, 6, 7, 1, 9, 10]}, {[8, 4, 5, 2, 3, 6, 7, 1, 9, 10]}, {[8, 9, 4, 3, 5, 6, 7, 1, 2, 10]}, {[8, 9, 5, 6, 3, 4, 7, 1, 2, 10]}, {[8, 9, 10, 5, 4, 6, 7, 1, 2, 3]}, {[9, 3, 2, 4, 5, 6, 7, 8, 1, 10]}, {[9, 4, 5, 2, 3, 6, 7, 8, 1, 10]}, {[9, 5, 6, 7, 2, 3, 4, 8, 1, 10]}, {[9, 10, 4, 3, 5, 6, 7, 8, 1, 2]}, {[9, 10, 5, 6, 3, 4, 7, 8, 1, 2]}, {[10, 3, 2, 4, 5, 6, 7, 8, 9, 1]}, {[10, 4, 5, 2, 3, 6, 7, 8, 9, 1]}, {[10, 5, 6, 7, 2, 3, 4, 8, 9, 1]}, {[4, 3, 2, 5, 1, 6, 7, 8, 9, 10], [5, 3, 2, 1, 4, 6, 7, 8, 9, 10]}, {[4, 3, 2, 5, 6, 1, 7, 8, 9, 10], [6, 3, 2, 1, 4, 5, 7, 8, 9, 10]}, {[4, 3, 2, 5, 6, 7, 1, 8, 9, 10], [7, 3, 2, 1, 4, 5, 6, 8, 9, 10]}, {[4, 3, 2, 5, 6, 7, 8, 1, 9, 10], [8, 3, 2, 1, 4, 5, 6, 7, 9, 10]}, {[4, 3, 5, 2, 1, 6, 7, 8, 9, 10], [5, 4, 2, 1, 3, 6, 7, 8, 9, 10]}, {[4, 3, 5, 6, 2, 1, 7, 8, 9, 10], [6, 5, 2, 1, 3, 4, 7, 8, 9, 10]}, {[4, 3, 5, 6, 7, 2, 1, 8, 9, 10], [7, 6, 2, 1, 3, 4, 5, 8, 9, 10]}, {[4, 3, 5, 6, 7, 8, 2, 1, 9, 10], [8, 7, 2, 1, 3, 4, 5, 6, 9, 10]}, {[4, 3, 5, 6, 7, 8, 9, 2, 1, 10], [9, 8, 2, 1, 3, 4, 5, 6, 7, 10]}, {[4, 3, 5, 6, 7, 8, 9, 10, 2, 1], [10, 9, 2, 1, 3, 4, 5, 6, 7, 8]}, {[4, 5, 3, 2, 6, 1, 7, 8, 9, 10], [6, 4, 3, 1, 2, 5, 7, 8, 9, 10]}, {[4, 5, 3, 2, 6, 7, 1, 8, 9, 10], [7, 4, 3, 1, 2, 5, 6, 8, 9, 10]}, {[4, 5, 3, 2, 6, 7, 8, 1, 9, 10], [8, 4, 3, 1, 2, 5, 6, 7, 9, 10]}, {[4, 5, 3, 6, 2, 1, 7, 8, 9, 10], [6, 5, 3, 1, 2, 4, 7, 8, 9, 10]}, {[4, 5, 3, 6, 7, 2, 1, 8, 9, 10], [7, 6, 3, 1, 2, 4, 5, 8, 9, 10]}, {[4, 5, 3, 6, 7, 8, 2, 1, 9, 10], [8, 7, 3, 1, 2, 4, 5, 6, 9, 10]}, {[4, 5, 3, 6, 7, 8, 9, 2, 1, 10], [9, 8, 3, 1, 2, 4, 5, 6, 7, 10]}, {[4, 5, 3, 6, 7, 8, 9, 10, 2, 1], [10, 9, 3, 1, 2, 4, 5, 6, 7, 8]}, {[4, 5, 6, 3, 2, 7, 1, 8, 9, 10], [7, 5, 4, 1, 2, 3, 6, 8, 9, 10]}, {[4, 5, 6, 3, 2, 7, 8, 1, 9, 10], [8, 5, 4, 1, 2, 3, 6, 7, 9, 10]}, {[4, 5, 6, 3, 7, 2, 1, 8, 9, 10], [7, 6, 4, 1, 2, 3, 5, 8, 9, 10]}, {[4, 5, 6, 3, 7, 8, 2, 1, 9, 10], [8, 7, 4, 1, 2, 3, 5, 6, 9, 10]}, {[4, 5, 6, 3, 7, 8, 9, 2, 1, 10], [9, 8, 4, 1, 2, 3, 5, 6, 7, 10]}, {[4, 5, 6, 3, 7, 8, 9, 10, 2, 1], [10, 9, 4, 1, 2, 3, 5, 6, 7, 8]}, {[4, 5, 6, 7, 3, 2, 8, 1, 9, 10], [8, 6, 5, 1, 2, 3, 4, 7, 9, 10]}, {[4, 5, 6, 7, 3, 8, 2, 1, 9, 10], [8, 7, 5, 1, 2, 3, 4, 6, 9, 10]}, {[4, 5, 6, 7, 3, 8, 9, 2, 1, 10], [9, 8, 5, 1, 2, 3, 4, 6, 7, 10]}, {[4, 5, 6, 7, 3, 8, 9, 10, 2, 1], [10, 9, 5, 1, 2, 3, 4, 6, 7, 8]}, {[4, 5, 6, 7, 8, 3, 9, 2, 1, 10], [9, 8, 6, 1, 2, 3, 4, 5, 7, 10]}, {[4, 5, 6, 7, 8, 3, 9, 10, 2, 1], [10, 9, 6, 1, 2, 3, 4, 5, 7, 8]}, {[4, 5, 6, 7, 8, 9, 3, 2, 10, 1], [10, 8, 7, 1, 2, 3, 4, 5, 6, 9]}, {[4, 5, 6, 7, 8, 9, 3, 10, 2, 1], [10, 9, 7, 1, 2, 3, 4, 5, 6, 8]}, {[5, 3, 4, 2, 6, 1, 7, 8, 9, 10], [6, 4, 2, 3, 1, 5, 7, 8, 9, 10]}, {[5, 3, 4, 2, 6, 7, 1, 8, 9, 10], [7, 4, 2, 3, 1, 5, 6, 8, 9, 10]}, {[5, 3, 4, 2, 6, 7, 8, 1, 9, 10], [8, 4, 2, 3, 1, 5, 6, 7, 9, 10]}, {[5, 3, 4, 6, 2, 1, 7, 8, 9, 10], [6, 5, 2, 3, 1, 4, 7, 8, 9, 10]}, {[5, 3, 4, 6, 7, 2, 1, 8, 9, 10], [7, 6, 2, 3, 1, 4, 5, 8, 9, 10]}, {[5, 3, 4, 6, 7, 8, 2, 1, 9, 10], [8, 7, 2, 3, 1, 4, 5, 6, 9, 10]}, {[5, 3, 4, 6, 7, 8, 9, 2, 1, 10], [9, 8, 2, 3, 1, 4, 5, 6, 7, 10]}, {[5, 3, 4, 6, 7, 8, 9, 10, 2, 1], [10, 9, 2, 3, 1, 4, 5, 6, 7, 8]}, {[5, 4, 2, 3, 6, 1, 7, 8, 9, 10], [6, 3, 4, 2, 1, 5, 7, 8, 9, 10]}, {[5, 4, 2, 3, 6, 7, 1, 8, 9, 10], [7, 3, 4, 2, 1, 5, 6, 8, 9, 10]}, {[5, 4, 2, 3, 6, 7, 8, 1, 9, 10], [8, 3, 4, 2, 1, 5, 6, 7, 9, 10]}, {[5, 4, 3, 6, 1, 2, 7, 8, 9, 10], [5, 6, 3, 2, 1, 4, 7, 8, 9, 10]}, {[5, 4, 3, 6, 7, 1, 2, 8, 9, 10], [6, 7, 3, 2, 1, 4, 5, 8, 9, 10]}, {[5, 4, 3, 6, 7, 8, 1, 2, 9, 10], [7, 8, 3, 2, 1, 4, 5, 6, 9, 10]}, {[5, 4, 3, 6, 7, 8, 9, 1, 2, 10], [8, 9, 3, 2, 1, 4, 5, 6, 7, 10]}, {[5, 4, 3, 6, 7, 8, 9, 10, 1, 2], [9, 10, 3, 2, 1, 4, 5, 6, 7, 8]}, {[5, 4, 6, 2, 3, 1, 7, 8, 9, 10], [6, 4, 5, 2, 1, 3, 7, 8, 9, 10]}, {[5, 4, 6, 3, 1, 2, 7, 8, 9, 10], [5, 6, 4, 2, 1, 3, 7, 8, 9, 10]}, {[5, 4, 6, 7, 2, 3, 1, 8, 9, 10], [7, 5, 6, 2, 1, 3, 4, 8, 9, 10]}, {[5, 4, 6, 7, 3, 1, 2, 8, 9, 10], [6, 7, 5, 2, 1, 3, 4, 8, 9, 10]}, {[5, 4, 6, 7, 8, 2, 3, 1, 9, 10], [8, 6, 7, 2, 1, 3, 4, 5, 9, 10]}, {[5, 4, 6, 7, 8, 3, 1, 2, 9, 10], [7, 8, 6, 2, 1, 3, 4, 5, 9, 10]}, {[5, 4, 6, 7, 8, 9, 2, 3, 1, 10], [9, 7, 8, 2, 1, 3, 4, 5, 6, 10]}, {[5, 4, 6, 7, 8, 9, 3, 1, 2, 10], [8, 9, 7, 2, 1, 3, 4, 5, 6, 10]}, {[5, 4, 6, 7, 8, 9, 10, 2, 3, 1], [10, 8, 9, 2, 1, 3, 4, 5, 6, 7]}, {[5, 4, 6, 7, 8, 9, 10, 3, 1, 2], [9, 10, 8, 2, 1, 3, 4, 5, 6, 7]}, {[5, 6, 3, 2, 4, 1, 7, 8, 9, 10], [6, 4, 3, 5, 1, 2, 7, 8, 9, 10]}, {[5, 6, 3, 4, 2, 7, 1, 8, 9, 10], [7, 5, 3, 4, 1, 2, 6, 8, 9, 10]}, {[5, 6, 3, 4, 2, 7, 8, 1, 9, 10], [8, 5, 3, 4, 1, 2, 6, 7, 9, 10]}, {[5, 6, 3, 4, 7, 2, 1, 8, 9, 10], [7, 6, 3, 4, 1, 2, 5, 8, 9, 10]}, {[5, 6, 3, 4, 7, 8, 2, 1, 9, 10], [8, 7, 3, 4, 1, 2, 5, 6, 9, 10]}, {[5, 6, 3, 4, 7, 8, 9, 2, 1, 10], [9, 8, 3, 4, 1, 2, 5, 6, 7, 10]}, {[5, 6, 3, 4, 7, 8, 9, 10, 2, 1], [10, 9, 3, 4, 1, 2, 5, 6, 7, 8]}, {[5, 6, 4, 2, 3, 7, 1, 8, 9, 10], [7, 4, 5, 3, 1, 2, 6, 8, 9, 10]}, {[5, 6, 4, 2, 3, 7, 8, 1, 9, 10], [8, 4, 5, 3, 1, 2, 6, 7, 9, 10]}, {[5, 6, 4, 3, 7, 1, 2, 8, 9, 10], [6, 7, 4, 3, 1, 2, 5, 8, 9, 10]}, {[5, 6, 4, 3, 7, 8, 1, 2, 9, 10], [7, 8, 4, 3, 1, 2, 5, 6, 9, 10]}, {[5, 6, 4, 3, 7, 8, 9, 1, 2, 10], [8, 9, 4, 3, 1, 2, 5, 6, 7, 10]}, {[5, 6, 4, 3, 7, 8, 9, 10, 1, 2], [9, 10, 4, 3, 1, 2, 5, 6, 7, 8]}, {[5, 6, 4, 7, 2, 3, 1, 8, 9, 10], [7, 5, 6, 3, 1, 2, 4, 8, 9, 10]}, {[5, 6, 4, 7, 3, 1, 2, 8, 9, 10], [6, 7, 5, 3, 1, 2, 4, 8, 9, 10]}, {[5, 6, 4, 7, 8, 2, 3, 1, 9, 10], [8, 6, 7, 3, 1, 2, 4, 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7, 1], [10, 6, 7, 8, 4, 5, 9, 1, 2, 3]}, {[8, 9, 10, 5, 6, 3, 4, 7, 1, 2], [9, 10, 6, 7, 4, 5, 8, 1, 2, 3]}, {[8, 9, 10, 5, 6, 4, 7, 1, 2, 3], [8, 9, 10, 6, 4, 5, 7, 1, 2, 3]}, {[8, 9, 10, 5, 6, 7, 2, 3, 1, 4], [9, 7, 8, 10, 4, 5, 6, 1, 2, 3]}, {[8, 9, 10, 6, 2, 3, 4, 5, 1, 7], [9, 5, 6, 7, 8, 4, 10, 1, 2, 3]}, {[8, 9, 10, 6, 2, 3, 4, 5, 7, 1], [10, 5, 6, 7, 8, 4, 9, 1, 2, 3]}, {[8, 9, 10, 6, 3, 4, 5, 7, 1, 2], [9, 10, 5, 6, 7, 4, 8, 1, 2, 3]}, {[8, 9, 10, 6, 7, 2, 3, 4, 1, 5], [9, 6, 7, 8, 10, 4, 5, 1, 2, 3]}, {[8, 9, 10, 7, 2, 3, 4, 5, 1, 6], [9, 5, 6, 7, 8, 10, 4, 1, 2, 3]}, {[9, 3, 4, 2, 5, 6, 7, 8, 1, 10], [9, 4, 2, 3, 5, 6, 7, 8, 1, 10]}, {[9, 3, 4, 5, 2, 6, 7, 8, 1, 10], [9, 5, 2, 3, 4, 6, 7, 8, 1, 10]}, {[9, 3, 4, 5, 6, 2, 7, 8, 1, 10], [9, 6, 2, 3, 4, 5, 7, 8, 1, 10]}, {[9, 3, 4, 5, 6, 7, 2, 8, 1, 10], [9, 7, 2, 3, 4, 5, 6, 8, 1, 10]}, {[9, 3, 4, 5, 6, 7, 8, 2, 10, 1], [10, 8, 2, 3, 4, 5, 6, 7, 1, 9]}, {[9, 3, 4, 5, 6, 7, 8, 10, 2, 1], [10, 9, 2, 3, 4, 5, 6, 7, 1, 8]}, {[9, 4, 5, 6, 2, 3, 7, 8, 1, 10], [9, 5, 6, 2, 3, 4, 7, 8, 1, 10]}, {[9, 4, 5, 6, 7, 2, 3, 8, 1, 10], [9, 6, 7, 2, 3, 4, 5, 8, 1, 10]}, {[9, 4, 5, 6, 7, 8, 2, 3, 10, 1], [10, 7, 8, 2, 3, 4, 5, 6, 1, 9]}, {[9, 4, 5, 6, 7, 8, 3, 10, 1, 2], [9, 10, 7, 2, 3, 4, 5, 6, 1, 8]}, {[9, 4, 5, 6, 7, 8, 10, 2, 3, 1], [10, 8, 9, 2, 3, 4, 5, 6, 1, 7]}, {[9, 4, 5, 6, 7, 8, 10, 3, 1, 2], [9, 10, 8, 2, 3, 4, 5, 6, 1, 7]}, {[9, 5, 6, 7, 8, 2, 3, 4, 10, 1], [10, 6, 7, 8, 2, 3, 4, 5, 1, 9]}, {[9, 5, 6, 7, 8, 3, 4, 10, 1, 2], [9, 10, 6, 7, 2, 3, 4, 5, 1, 8]}, {[9, 5, 6, 7, 8, 10, 2, 3, 4, 1], [10, 7, 8, 9, 2, 3, 4, 5, 1, 6]}, {[9, 5, 6, 7, 8, 10, 3, 4, 1, 2], [9, 10, 7, 8, 2, 3, 4, 5, 1, 6]}, {[9, 6, 7, 8, 2, 3, 4, 5, 10, 1], [10, 5, 6, 7, 8, 2, 3, 4, 1, 9]}, {[9, 6, 7, 8, 3, 4, 5, 10, 1, 2], [9, 10, 5, 6, 7, 2, 3, 4, 1, 8]}, {[9, 6, 7, 8, 10, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 2, 3, 4, 1, 5]}, {[9, 6, 7, 8, 10, 3, 4, 5, 1, 2], [9, 10, 6, 7, 8, 2, 3, 4, 1, 5]}, {[9, 7, 8, 2, 3, 4, 5, 6, 10, 1], [10, 4, 5, 6, 7, 8, 2, 3, 1, 9]}, {[9, 7, 8, 3, 4, 5, 6, 10, 1, 2], [9, 10, 4, 5, 6, 7, 2, 3, 1, 8]}, {[9, 7, 8, 10, 2, 3, 4, 5, 6, 1], [10, 5, 6, 7, 8, 9, 2, 3, 1, 4]}, {[9, 7, 8, 10, 3, 4, 5, 6, 1, 2], [9, 10, 5, 6, 7, 8, 2, 3, 1, 4]}, {[9, 8, 2, 3, 4, 5, 6, 7, 10, 1], [10, 3, 4, 5, 6, 7, 8, 2, 1, 9]}, {[9, 8, 3, 4, 5, 6, 7, 10, 1, 2], [9, 10, 3, 4, 5, 6, 7, 2, 1, 8]}, {[9, 8, 10, 2, 3, 4, 5, 6, 7, 1], [10, 4, 5, 6, 7, 8, 9, 2, 1, 3]}, {[9, 8, 10, 3, 4, 5, 6, 7, 1, 2], [9, 10, 4, 5, 6, 7, 8, 2, 1, 3]}, {[9, 10, 3, 2, 4, 5, 6, 7, 8, 1], [10, 4, 3, 5, 6, 7, 8, 9, 1, 2]}, {[9, 10, 3, 4, 2, 5, 6, 7, 8, 1], [10, 5, 3, 4, 6, 7, 8, 9, 1, 2]}, {[9, 10, 3, 4, 5, 2, 6, 7, 8, 1], [10, 6, 3, 4, 5, 7, 8, 9, 1, 2]}, {[9, 10, 3, 4, 5, 6, 2, 7, 8, 1], [10, 7, 3, 4, 5, 6, 8, 9, 1, 2]}, {[9, 10, 3, 4, 5, 6, 7, 2, 8, 1], [10, 8, 3, 4, 5, 6, 7, 9, 1, 2]}, {[9, 10, 4, 2, 3, 5, 6, 7, 8, 1], [10, 4, 5, 3, 6, 7, 8, 9, 1, 2]}, {[9, 10, 4, 5, 2, 3, 6, 7, 8, 1], [10, 5, 6, 3, 4, 7, 8, 9, 1, 2]}, {[9, 10, 4, 5, 3, 6, 7, 8, 1, 2], [9, 10, 5, 3, 4, 6, 7, 8, 1, 2]}, {[9, 10, 4, 5, 6, 2, 3, 7, 8, 1], [10, 6, 7, 3, 4, 5, 8, 9, 1, 2]}, {[9, 10, 4, 5, 6, 3, 7, 8, 1, 2], [9, 10, 6, 3, 4, 5, 7, 8, 1, 2]}, {[9, 10, 4, 5, 6, 7, 2, 3, 8, 1], [10, 7, 8, 3, 4, 5, 6, 9, 1, 2]}, {[9, 10, 4, 5, 6, 7, 3, 8, 1, 2], [9, 10, 7, 3, 4, 5, 6, 8, 1, 2]}, {[9, 10, 5, 2, 3, 4, 6, 7, 8, 1], [10, 4, 5, 6, 3, 7, 8, 9, 1, 2]}, {[9, 10, 5, 6, 2, 3, 4, 7, 8, 1], [10, 5, 6, 7, 3, 4, 8, 9, 1, 2]}, {[9, 10, 5, 6, 7, 2, 3, 4, 8, 1], [10, 6, 7, 8, 3, 4, 5, 9, 1, 2]}, {[9, 10, 5, 6, 7, 3, 4, 8, 1, 2], [9, 10, 6, 7, 3, 4, 5, 8, 1, 2]}, {[9, 10, 6, 2, 3, 4, 5, 7, 8, 1], [10, 4, 5, 6, 7, 3, 8, 9, 1, 2]}, {[9, 10, 6, 7, 2, 3, 4, 5, 8, 1], [10, 5, 6, 7, 8, 3, 4, 9, 1, 2]}, {[9, 10, 7, 2, 3, 4, 5, 6, 8, 1], [10, 4, 5, 6, 7, 8, 3, 9, 1, 2]}, {[10, 3, 4, 2, 5, 6, 7, 8, 9, 1], [10, 4, 2, 3, 5, 6, 7, 8, 9, 1]}, {[10, 3, 4, 5, 2, 6, 7, 8, 9, 1], [10, 5, 2, 3, 4, 6, 7, 8, 9, 1]}, {[10, 3, 4, 5, 6, 2, 7, 8, 9, 1], [10, 6, 2, 3, 4, 5, 7, 8, 9, 1]}, {[10, 3, 4, 5, 6, 7, 2, 8, 9, 1], [10, 7, 2, 3, 4, 5, 6, 8, 9, 1]}, {[10, 3, 4, 5, 6, 7, 8, 2, 9, 1], [10, 8, 2, 3, 4, 5, 6, 7, 9, 1]}, {[10, 4, 5, 6, 2, 3, 7, 8, 9, 1], [10, 5, 6, 2, 3, 4, 7, 8, 9, 1]}, {[10, 4, 5, 6, 7, 2, 3, 8, 9, 1], [10, 6, 7, 2, 3, 4, 5, 8, 9, 1]}, {[10, 4, 5, 6, 7, 8, 2, 3, 9, 1], [10, 7, 8, 2, 3, 4, 5, 6, 9, 1]}, {[10, 5, 6, 7, 8, 2, 3, 4, 9, 1], [10, 6, 7, 8, 2, 3, 4, 5, 9, 1]}, { [4, 3, 2, 5, 6, 7, 8, 9, 1, 10], [4, 3, 2, 5, 6, 7, 8, 9, 10, 1], [9, 3, 2, 1, 4, 5, 6, 7, 8, 10], [10, 3, 2, 1, 4, 5, 6, 7, 8, 9]}, { [4, 5, 3, 2, 6, 7, 8, 9, 1, 10], [4, 5, 3, 2, 6, 7, 8, 9, 10, 1], [9, 4, 3, 1, 2, 5, 6, 7, 8, 10], [10, 4, 3, 1, 2, 5, 6, 7, 8, 9]}, { [4, 5, 6, 3, 2, 7, 8, 9, 1, 10], [4, 5, 6, 3, 2, 7, 8, 9, 10, 1], [9, 5, 4, 1, 2, 3, 6, 7, 8, 10], [10, 5, 4, 1, 2, 3, 6, 7, 8, 9]}, { [4, 5, 6, 7, 3, 2, 8, 9, 1, 10], [4, 5, 6, 7, 3, 2, 8, 9, 10, 1], [9, 6, 5, 1, 2, 3, 4, 7, 8, 10], [10, 6, 5, 1, 2, 3, 4, 7, 8, 9]}, { [4, 5, 6, 7, 8, 3, 2, 9, 1, 10], [4, 5, 6, 7, 8, 3, 2, 9, 10, 1], [9, 7, 6, 1, 2, 3, 4, 5, 8, 10], [10, 7, 6, 1, 2, 3, 4, 5, 8, 9]}, { [5, 3, 4, 2, 6, 7, 8, 9, 1, 10], [5, 3, 4, 2, 6, 7, 8, 9, 10, 1], [9, 4, 2, 3, 1, 5, 6, 7, 8, 10], [10, 4, 2, 3, 1, 5, 6, 7, 8, 9]}, { [5, 4, 2, 3, 6, 7, 8, 9, 1, 10], [5, 4, 2, 3, 6, 7, 8, 9, 10, 1], [9, 3, 4, 2, 1, 5, 6, 7, 8, 10], [10, 3, 4, 2, 1, 5, 6, 7, 8, 9]}, { [5, 6, 3, 4, 2, 7, 8, 9, 1, 10], [5, 6, 3, 4, 2, 7, 8, 9, 10, 1], [9, 5, 3, 4, 1, 2, 6, 7, 8, 10], [10, 5, 3, 4, 1, 2, 6, 7, 8, 9]}, { [5, 6, 4, 2, 3, 7, 8, 9, 1, 10], [5, 6, 4, 2, 3, 7, 8, 9, 10, 1], [9, 4, 5, 3, 1, 2, 6, 7, 8, 10], [10, 4, 5, 3, 1, 2, 6, 7, 8, 9]}, { [5, 6, 7, 3, 4, 2, 8, 9, 1, 10], [5, 6, 7, 3, 4, 2, 8, 9, 10, 1], [9, 6, 4, 5, 1, 2, 3, 7, 8, 10], [10, 6, 4, 5, 1, 2, 3, 7, 8, 9]}, { [5, 6, 7, 4, 2, 3, 8, 9, 1, 10], [5, 6, 7, 4, 2, 3, 8, 9, 10, 1], [9, 5, 6, 4, 1, 2, 3, 7, 8, 10], [10, 5, 6, 4, 1, 2, 3, 7, 8, 9]}, { [5, 6, 7, 8, 3, 4, 2, 9, 1, 10], [5, 6, 7, 8, 3, 4, 2, 9, 10, 1], [9, 7, 5, 6, 1, 2, 3, 4, 8, 10], [10, 7, 5, 6, 1, 2, 3, 4, 8, 9]}, { [5, 6, 7, 8, 4, 2, 3, 9, 1, 10], [5, 6, 7, 8, 4, 2, 3, 9, 10, 1], [9, 6, 7, 5, 1, 2, 3, 4, 8, 10], [10, 6, 7, 5, 1, 2, 3, 4, 8, 9]}, { [6, 3, 4, 5, 2, 7, 8, 9, 1, 10], [6, 3, 4, 5, 2, 7, 8, 9, 10, 1], [9, 5, 2, 3, 4, 1, 6, 7, 8, 10], [10, 5, 2, 3, 4, 1, 6, 7, 8, 9]}, { [6, 4, 5, 2, 3, 7, 8, 9, 1, 10], [6, 4, 5, 2, 3, 7, 8, 9, 10, 1], [9, 4, 5, 2, 3, 1, 6, 7, 8, 10], [10, 4, 5, 2, 3, 1, 6, 7, 8, 9]}, { [6, 5, 2, 3, 4, 7, 8, 9, 1, 10], [6, 5, 2, 3, 4, 7, 8, 9, 10, 1], [9, 3, 4, 5, 2, 1, 6, 7, 8, 10], [10, 3, 4, 5, 2, 1, 6, 7, 8, 9]}, { [6, 7, 3, 4, 5, 2, 8, 9, 1, 10], [6, 7, 3, 4, 5, 2, 8, 9, 10, 1], [9, 6, 3, 4, 5, 1, 2, 7, 8, 10], [10, 6, 3, 4, 5, 1, 2, 7, 8, 9]}, { [6, 7, 4, 5, 2, 3, 8, 9, 1, 10], [6, 7, 4, 5, 2, 3, 8, 9, 10, 1], [9, 5, 6, 3, 4, 1, 2, 7, 8, 10], [10, 5, 6, 3, 4, 1, 2, 7, 8, 9]}, { [6, 7, 5, 2, 3, 4, 8, 9, 1, 10], [6, 7, 5, 2, 3, 4, 8, 9, 10, 1], [9, 4, 5, 6, 3, 1, 2, 7, 8, 10], [10, 4, 5, 6, 3, 1, 2, 7, 8, 9]}, { [6, 7, 8, 3, 4, 5, 2, 9, 1, 10], [6, 7, 8, 3, 4, 5, 2, 9, 10, 1], [9, 7, 4, 5, 6, 1, 2, 3, 8, 10], [10, 7, 4, 5, 6, 1, 2, 3, 8, 9]}, { [6, 7, 8, 4, 5, 2, 3, 9, 1, 10], [6, 7, 8, 4, 5, 2, 3, 9, 10, 1], [9, 6, 7, 4, 5, 1, 2, 3, 8, 10], [10, 6, 7, 4, 5, 1, 2, 3, 8, 9]}, { [6, 7, 8, 5, 2, 3, 4, 9, 1, 10], [6, 7, 8, 5, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 4, 1, 2, 3, 8, 10], [10, 5, 6, 7, 4, 1, 2, 3, 8, 9]}, { [7, 3, 4, 5, 6, 2, 8, 9, 1, 10], [7, 3, 4, 5, 6, 2, 8, 9, 10, 1], [9, 6, 2, 3, 4, 5, 1, 7, 8, 10], [10, 6, 2, 3, 4, 5, 1, 7, 8, 9]}, { [7, 4, 5, 6, 2, 3, 8, 9, 1, 10], [7, 4, 5, 6, 2, 3, 8, 9, 10, 1], [9, 5, 6, 2, 3, 4, 1, 7, 8, 10], [10, 5, 6, 2, 3, 4, 1, 7, 8, 9]}, { [7, 5, 6, 2, 3, 4, 8, 9, 1, 10], [7, 5, 6, 2, 3, 4, 8, 9, 10, 1], [9, 4, 5, 6, 2, 3, 1, 7, 8, 10], [10, 4, 5, 6, 2, 3, 1, 7, 8, 9]}, { [7, 6, 2, 3, 4, 5, 8, 9, 1, 10], [7, 6, 2, 3, 4, 5, 8, 9, 10, 1], [9, 3, 4, 5, 6, 2, 1, 7, 8, 10], [10, 3, 4, 5, 6, 2, 1, 7, 8, 9]}, { [7, 8, 3, 4, 5, 6, 2, 9, 1, 10], [7, 8, 3, 4, 5, 6, 2, 9, 10, 1], [9, 7, 3, 4, 5, 6, 1, 2, 8, 10], [10, 7, 3, 4, 5, 6, 1, 2, 8, 9]}, { [7, 8, 4, 5, 6, 2, 3, 9, 1, 10], [7, 8, 4, 5, 6, 2, 3, 9, 10, 1], [9, 6, 7, 3, 4, 5, 1, 2, 8, 10], [10, 6, 7, 3, 4, 5, 1, 2, 8, 9]}, { [7, 8, 5, 6, 2, 3, 4, 9, 1, 10], [7, 8, 5, 6, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 3, 4, 1, 2, 8, 10], [10, 5, 6, 7, 3, 4, 1, 2, 8, 9]}, { [7, 8, 6, 2, 3, 4, 5, 9, 1, 10], [7, 8, 6, 2, 3, 4, 5, 9, 10, 1], [9, 4, 5, 6, 7, 3, 1, 2, 8, 10], [10, 4, 5, 6, 7, 3, 1, 2, 8, 9]}, { [8, 3, 4, 5, 6, 7, 2, 9, 1, 10], [8, 3, 4, 5, 6, 7, 2, 9, 10, 1], [9, 7, 2, 3, 4, 5, 6, 1, 8, 10], [10, 7, 2, 3, 4, 5, 6, 1, 8, 9]}, { [8, 4, 5, 6, 7, 2, 3, 9, 1, 10], [8, 4, 5, 6, 7, 2, 3, 9, 10, 1], [9, 6, 7, 2, 3, 4, 5, 1, 8, 10], [10, 6, 7, 2, 3, 4, 5, 1, 8, 9]}, { [8, 5, 6, 7, 2, 3, 4, 9, 1, 10], [8, 5, 6, 7, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 2, 3, 4, 1, 8, 10], [10, 5, 6, 7, 2, 3, 4, 1, 8, 9]}, { [8, 6, 7, 2, 3, 4, 5, 9, 1, 10], [8, 6, 7, 2, 3, 4, 5, 9, 10, 1], [9, 4, 5, 6, 7, 2, 3, 1, 8, 10], [10, 4, 5, 6, 7, 2, 3, 1, 8, 9]}, { [8, 7, 2, 3, 4, 5, 6, 9, 1, 10], [8, 7, 2, 3, 4, 5, 6, 9, 10, 1], [9, 3, 4, 5, 6, 7, 2, 1, 8, 10], [10, 3, 4, 5, 6, 7, 2, 1, 8, 9]}} is given by the following expression / 419 493 2 357 3 17 4 5\ n / |- ----- n - ---- n - ----- n - ---- n - 3/81920 n | 4 + |9/220 n \ 10240 8192 16384 8192 / \ 1591 2 129161 3 20297 4 9941 5 47 6 7\ + ----- n + ------ n + ------ n + ------ n + ----- n + 1/332640 n | 10080 665280 221760 665280 73920 / C(n) and in Maple input form: (-419/10240*n-493/8192*n^2-357/16384*n^3-17/8192*n^4-3/81920*n^5)*4^n+(9/220*n+ 1591/10080*n^2+129161/665280*n^3+20297/221760*n^4+9941/665280*n^5+47/73920*n^6+ 1/332640*n^7)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 14 1/2 13 12 1/2 11 10 1/2 9 m 3 Pi m 47 m 1387 Pi m 9941 m 1581 Pi m ------ - ----------- + ------ - -------------- + -------- - ------------- 332640 81920 73920 655360 665280 65536 8 1/2 7 6 1/2 5 4 20297 m 11101 Pi m 129161 m 35593 Pi m 1591 m + -------- - -------------- + --------- - -------------- + ------- 221760 131072 665280 327680 10080 1/2 3 2 3771 Pi m 9 m - ------------- + ---- 81920 220 and in Maple input form: 1/332640*m^14-3/81920*Pi^(1/2)*m^13+47/73920*m^12-1387/655360*Pi^(1/2)*m^11+ 9941/665280*m^10-1581/65536*Pi^(1/2)*m^9+20297/221760*m^8-11101/131072*Pi^(1/2) *m^7+129161/665280*m^6-35593/327680*Pi^(1/2)*m^5+1591/10080*m^4-3771/81920*Pi^( 1/2)*m^3+9/220*m^2 For the, 38, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[5, 4, 6, 2, 1, 3, 7, 8, 9, 10]}, {[6, 5, 7, 8, 2, 1, 3, 4, 9, 10]}, {[6, 7, 5, 8, 3, 1, 2, 4, 9, 10]}, {[7, 5, 6, 8, 2, 3, 1, 4, 9, 10]}, {[7, 6, 8, 9, 10, 2, 1, 3, 4, 5]}, {[7, 8, 6, 9, 10, 3, 1, 2, 4, 5]}, {[7, 8, 9, 6, 10, 4, 1, 2, 3, 5]}, {[8, 6, 7, 9, 10, 2, 3, 1, 4, 5]}, {[8, 9, 6, 7, 10, 3, 4, 1, 2, 5]}, {[9, 6, 7, 8, 10, 2, 3, 4, 1, 5]}, {[4, 3, 5, 2, 6, 1, 7, 8, 9, 10], [6, 4, 2, 1, 3, 5, 7, 8, 9, 10]}, {[4, 3, 5, 2, 6, 7, 1, 8, 9, 10], [7, 4, 2, 1, 3, 5, 6, 8, 9, 10]}, {[4, 3, 5, 2, 6, 7, 8, 1, 9, 10], [8, 4, 2, 1, 3, 5, 6, 7, 9, 10]}, {[4, 3, 5, 6, 2, 7, 1, 8, 9, 10], [7, 5, 2, 1, 3, 4, 6, 8, 9, 10]}, {[4, 3, 5, 6, 2, 7, 8, 1, 9, 10], [8, 5, 2, 1, 3, 4, 6, 7, 9, 10]}, {[4, 3, 5, 6, 7, 2, 8, 1, 9, 10], [8, 6, 2, 1, 3, 4, 5, 7, 9, 10]}, {[4, 3, 5, 6, 7, 8, 9, 2, 10, 1], [10, 8, 2, 1, 3, 4, 5, 6, 7, 9]}, {[4, 5, 3, 6, 2, 7, 1, 8, 9, 10], [7, 5, 3, 1, 2, 4, 6, 8, 9, 10]}, {[4, 5, 3, 6, 2, 7, 8, 1, 9, 10], [8, 5, 3, 1, 2, 4, 6, 7, 9, 10]}, {[4, 5, 3, 6, 7, 2, 8, 1, 9, 10], [8, 6, 3, 1, 2, 4, 5, 7, 9, 10]}, {[4, 5, 3, 6, 7, 8, 9, 2, 10, 1], [10, 8, 3, 1, 2, 4, 5, 6, 7, 9]}, {[4, 5, 6, 3, 7, 2, 8, 1, 9, 10], [8, 6, 4, 1, 2, 3, 5, 7, 9, 10]}, {[4, 5, 6, 3, 7, 8, 9, 2, 10, 1], [10, 8, 4, 1, 2, 3, 5, 6, 7, 9]}, {[4, 5, 6, 7, 3, 8, 9, 2, 10, 1], [10, 8, 5, 1, 2, 3, 4, 6, 7, 9]}, {[4, 5, 6, 7, 8, 3, 9, 2, 10, 1], [10, 8, 6, 1, 2, 3, 4, 5, 7, 9]}, {[5, 3, 2, 4, 6, 1, 7, 8, 9, 10], [6, 3, 2, 4, 1, 5, 7, 8, 9, 10]}, {[5, 3, 2, 4, 6, 7, 1, 8, 9, 10], [7, 3, 2, 4, 1, 5, 6, 8, 9, 10]}, {[5, 3, 2, 4, 6, 7, 8, 1, 9, 10], [8, 3, 2, 4, 1, 5, 6, 7, 9, 10]}, {[5, 3, 4, 6, 2, 7, 1, 8, 9, 10], [7, 5, 2, 3, 1, 4, 6, 8, 9, 10]}, {[5, 3, 4, 6, 2, 7, 8, 1, 9, 10], [8, 5, 2, 3, 1, 4, 6, 7, 9, 10]}, {[5, 3, 4, 6, 7, 2, 8, 1, 9, 10], [8, 6, 2, 3, 1, 4, 5, 7, 9, 10]}, {[5, 3, 4, 6, 7, 8, 9, 2, 10, 1], [10, 8, 2, 3, 1, 4, 5, 6, 7, 9]}, {[5, 4, 6, 2, 3, 7, 1, 8, 9, 10], [7, 4, 5, 2, 1, 3, 6, 8, 9, 10]}, {[5, 4, 6, 2, 3, 7, 8, 1, 9, 10], [8, 4, 5, 2, 1, 3, 6, 7, 9, 10]}, {[5, 4, 6, 3, 7, 1, 2, 8, 9, 10], [6, 7, 4, 2, 1, 3, 5, 8, 9, 10]}, {[5, 4, 6, 3, 7, 8, 1, 2, 9, 10], [7, 8, 4, 2, 1, 3, 5, 6, 9, 10]}, {[5, 4, 6, 3, 7, 8, 9, 1, 2, 10], [8, 9, 4, 2, 1, 3, 5, 6, 7, 10]}, {[5, 4, 6, 3, 7, 8, 9, 10, 1, 2], [9, 10, 4, 2, 1, 3, 5, 6, 7, 8]}, {[5, 4, 6, 7, 2, 1, 3, 8, 9, 10], [6, 5, 7, 2, 1, 3, 4, 8, 9, 10]}, {[5, 4, 6, 7, 2, 3, 8, 1, 9, 10], [8, 5, 6, 2, 1, 3, 4, 7, 9, 10]}, {[5, 4, 6, 7, 3, 8, 1, 2, 9, 10], [7, 8, 5, 2, 1, 3, 4, 6, 9, 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[9, 5, 6, 2, 3, 1, 4, 7, 8, 10], [10, 5, 6, 2, 3, 1, 4, 7, 8, 9]}, { [6, 4, 5, 7, 8, 2, 3, 9, 1, 10], [6, 4, 5, 7, 8, 2, 3, 9, 10, 1], [9, 6, 7, 2, 3, 1, 4, 5, 8, 10], [10, 6, 7, 2, 3, 1, 4, 5, 8, 9]}, { [6, 5, 7, 2, 3, 4, 8, 9, 1, 10], [6, 5, 7, 2, 3, 4, 8, 9, 10, 1], [9, 4, 5, 6, 2, 1, 3, 7, 8, 10], [10, 4, 5, 6, 2, 1, 3, 7, 8, 9]}, { [6, 5, 7, 8, 2, 3, 4, 9, 1, 10], [6, 5, 7, 8, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 2, 1, 3, 4, 8, 10], [10, 5, 6, 7, 2, 1, 3, 4, 8, 9]}, { [6, 7, 3, 2, 4, 5, 8, 9, 1, 10], [6, 7, 3, 2, 4, 5, 8, 9, 10, 1], [9, 4, 3, 5, 6, 1, 2, 7, 8, 10], [10, 4, 3, 5, 6, 1, 2, 7, 8, 9]}, { [6, 7, 3, 4, 2, 5, 8, 9, 1, 10], [6, 7, 3, 4, 2, 5, 8, 9, 10, 1], [9, 5, 3, 4, 6, 1, 2, 7, 8, 10], [10, 5, 3, 4, 6, 1, 2, 7, 8, 9]}, { [6, 7, 3, 4, 5, 8, 2, 9, 1, 10], [6, 7, 3, 4, 5, 8, 2, 9, 10, 1], [9, 7, 3, 4, 5, 1, 2, 6, 8, 10], [10, 7, 3, 4, 5, 1, 2, 6, 8, 9]}, { [6, 7, 4, 2, 3, 5, 8, 9, 1, 10], [6, 7, 4, 2, 3, 5, 8, 9, 10, 1], [9, 4, 5, 3, 6, 1, 2, 7, 8, 10], [10, 4, 5, 3, 6, 1, 2, 7, 8, 9]}, { [6, 7, 4, 5, 8, 2, 3, 9, 1, 10], [6, 7, 4, 5, 8, 2, 3, 9, 10, 1], [9, 6, 7, 3, 4, 1, 2, 5, 8, 10], [10, 6, 7, 3, 4, 1, 2, 5, 8, 9]}, { [6, 7, 5, 8, 2, 3, 4, 9, 1, 10], [6, 7, 5, 8, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 3, 1, 2, 4, 8, 10], [10, 5, 6, 7, 3, 1, 2, 4, 8, 9]}, { [6, 7, 8, 3, 2, 4, 5, 9, 1, 10], [6, 7, 8, 3, 2, 4, 5, 9, 10, 1], [9, 5, 4, 6, 7, 1, 2, 3, 8, 10], [10, 5, 4, 6, 7, 1, 2, 3, 8, 9]}, { [6, 7, 8, 3, 4, 2, 5, 9, 1, 10], [6, 7, 8, 3, 4, 2, 5, 9, 10, 1], [9, 6, 4, 5, 7, 1, 2, 3, 8, 10], [10, 6, 4, 5, 7, 1, 2, 3, 8, 9]}, { [6, 7, 8, 4, 2, 3, 5, 9, 1, 10], [6, 7, 8, 4, 2, 3, 5, 9, 10, 1], [9, 5, 6, 4, 7, 1, 2, 3, 8, 10], [10, 5, 6, 4, 7, 1, 2, 3, 8, 9]}, { [7, 3, 2, 4, 5, 6, 8, 9, 1, 10], [7, 3, 2, 4, 5, 6, 8, 9, 10, 1], [9, 3, 2, 4, 5, 6, 1, 7, 8, 10], [10, 3, 2, 4, 5, 6, 1, 7, 8, 9]}, { [7, 3, 4, 2, 5, 6, 8, 9, 1, 10], [7, 3, 4, 2, 5, 6, 8, 9, 10, 1], [9, 4, 2, 3, 5, 6, 1, 7, 8, 10], [10, 4, 2, 3, 5, 6, 1, 7, 8, 9]}, { [7, 3, 4, 5, 2, 6, 8, 9, 1, 10], [7, 3, 4, 5, 2, 6, 8, 9, 10, 1], [9, 5, 2, 3, 4, 6, 1, 7, 8, 10], [10, 5, 2, 3, 4, 6, 1, 7, 8, 9]}, { [7, 3, 4, 5, 6, 8, 2, 9, 1, 10], [7, 3, 4, 5, 6, 8, 2, 9, 10, 1], [9, 7, 2, 3, 4, 5, 1, 6, 8, 10], [10, 7, 2, 3, 4, 5, 1, 6, 8, 9]}, { [7, 4, 2, 3, 5, 6, 8, 9, 1, 10], [7, 4, 2, 3, 5, 6, 8, 9, 10, 1], [9, 3, 4, 2, 5, 6, 1, 7, 8, 10], [10, 3, 4, 2, 5, 6, 1, 7, 8, 9]}, { [7, 4, 5, 2, 3, 6, 8, 9, 1, 10], [7, 4, 5, 2, 3, 6, 8, 9, 10, 1], [9, 4, 5, 2, 3, 6, 1, 7, 8, 10], [10, 4, 5, 2, 3, 6, 1, 7, 8, 9]}, { [7, 4, 5, 6, 8, 2, 3, 9, 1, 10], [7, 4, 5, 6, 8, 2, 3, 9, 10, 1], [9, 6, 7, 2, 3, 4, 1, 5, 8, 10], [10, 6, 7, 2, 3, 4, 1, 5, 8, 9]}, { [7, 5, 2, 3, 4, 6, 8, 9, 1, 10], [7, 5, 2, 3, 4, 6, 8, 9, 10, 1], [9, 3, 4, 5, 2, 6, 1, 7, 8, 10], [10, 3, 4, 5, 2, 6, 1, 7, 8, 9]}, { [7, 5, 6, 8, 2, 3, 4, 9, 1, 10], [7, 5, 6, 8, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 2, 3, 1, 4, 8, 10], [10, 5, 6, 7, 2, 3, 1, 4, 8, 9]}, { [7, 6, 8, 2, 3, 4, 5, 9, 1, 10], [7, 6, 8, 2, 3, 4, 5, 9, 10, 1], [9, 4, 5, 6, 7, 2, 1, 3, 8, 10], [10, 4, 5, 6, 7, 2, 1, 3, 8, 9]}, { [7, 8, 3, 2, 4, 5, 6, 9, 1, 10], [7, 8, 3, 2, 4, 5, 6, 9, 10, 1], [9, 4, 3, 5, 6, 7, 1, 2, 8, 10], [10, 4, 3, 5, 6, 7, 1, 2, 8, 9]}, { [7, 8, 3, 4, 2, 5, 6, 9, 1, 10], [7, 8, 3, 4, 2, 5, 6, 9, 10, 1], [9, 5, 3, 4, 6, 7, 1, 2, 8, 10], [10, 5, 3, 4, 6, 7, 1, 2, 8, 9]}, { [7, 8, 3, 4, 5, 2, 6, 9, 1, 10], [7, 8, 3, 4, 5, 2, 6, 9, 10, 1], [9, 6, 3, 4, 5, 7, 1, 2, 8, 10], [10, 6, 3, 4, 5, 7, 1, 2, 8, 9]}, { [7, 8, 4, 2, 3, 5, 6, 9, 1, 10], [7, 8, 4, 2, 3, 5, 6, 9, 10, 1], [9, 4, 5, 3, 6, 7, 1, 2, 8, 10], [10, 4, 5, 3, 6, 7, 1, 2, 8, 9]}, { [7, 8, 4, 5, 2, 3, 6, 9, 1, 10], [7, 8, 4, 5, 2, 3, 6, 9, 10, 1], [9, 5, 6, 3, 4, 7, 1, 2, 8, 10], [10, 5, 6, 3, 4, 7, 1, 2, 8, 9]}, { [7, 8, 5, 2, 3, 4, 6, 9, 1, 10], [7, 8, 5, 2, 3, 4, 6, 9, 10, 1], [9, 4, 5, 6, 3, 7, 1, 2, 8, 10], [10, 4, 5, 6, 3, 7, 1, 2, 8, 9]}, { [8, 3, 2, 4, 5, 6, 7, 9, 1, 10], [8, 3, 2, 4, 5, 6, 7, 9, 10, 1], [9, 3, 2, 4, 5, 6, 7, 1, 8, 10], [10, 3, 2, 4, 5, 6, 7, 1, 8, 9]}, { [8, 3, 4, 2, 5, 6, 7, 9, 1, 10], [8, 3, 4, 2, 5, 6, 7, 9, 10, 1], [9, 4, 2, 3, 5, 6, 7, 1, 8, 10], [10, 4, 2, 3, 5, 6, 7, 1, 8, 9]}, { [8, 3, 4, 5, 2, 6, 7, 9, 1, 10], [8, 3, 4, 5, 2, 6, 7, 9, 10, 1], [9, 5, 2, 3, 4, 6, 7, 1, 8, 10], [10, 5, 2, 3, 4, 6, 7, 1, 8, 9]}, { [8, 3, 4, 5, 6, 2, 7, 9, 1, 10], [8, 3, 4, 5, 6, 2, 7, 9, 10, 1], [9, 6, 2, 3, 4, 5, 7, 1, 8, 10], [10, 6, 2, 3, 4, 5, 7, 1, 8, 9]}, { [8, 4, 2, 3, 5, 6, 7, 9, 1, 10], [8, 4, 2, 3, 5, 6, 7, 9, 10, 1], [9, 3, 4, 2, 5, 6, 7, 1, 8, 10], [10, 3, 4, 2, 5, 6, 7, 1, 8, 9]}, { [8, 4, 5, 2, 3, 6, 7, 9, 1, 10], [8, 4, 5, 2, 3, 6, 7, 9, 10, 1], [9, 4, 5, 2, 3, 6, 7, 1, 8, 10], [10, 4, 5, 2, 3, 6, 7, 1, 8, 9]}, { [8, 4, 5, 6, 2, 3, 7, 9, 1, 10], [8, 4, 5, 6, 2, 3, 7, 9, 10, 1], [9, 5, 6, 2, 3, 4, 7, 1, 8, 10], [10, 5, 6, 2, 3, 4, 7, 1, 8, 9]}, { [8, 5, 2, 3, 4, 6, 7, 9, 1, 10], [8, 5, 2, 3, 4, 6, 7, 9, 10, 1], [9, 3, 4, 5, 2, 6, 7, 1, 8, 10], [10, 3, 4, 5, 2, 6, 7, 1, 8, 9]}, { [8, 5, 6, 2, 3, 4, 7, 9, 1, 10], [8, 5, 6, 2, 3, 4, 7, 9, 10, 1], [9, 4, 5, 6, 2, 3, 7, 1, 8, 10], [10, 4, 5, 6, 2, 3, 7, 1, 8, 9]}, { [8, 6, 2, 3, 4, 5, 7, 9, 1, 10], [8, 6, 2, 3, 4, 5, 7, 9, 10, 1], [9, 3, 4, 5, 6, 2, 7, 1, 8, 10], [10, 3, 4, 5, 6, 2, 7, 1, 8, 9]}} is given by the following expression / 23 2 43 3 4 5\ n / |---- n - 1/3072 n - ----- n - 1/1536 n - 1/61440 n | 4 + |-1/220 n \5120 12288 / \ 103 2 577 3 79 4 1223 5 6 7\ - ----- n + ------ n + ---- n + ------ n + 3/12320 n + 1/665280 n | 10080 665280 7920 332640 / C(n) and in Maple input form: (23/5120*n-1/3072*n^2-43/12288*n^3-1/1536*n^4-1/61440*n^5)*4^n+(-1/220*n-103/ 10080*n^2+577/665280*n^3+79/7920*n^4+1223/332640*n^5+3/12320*n^6+1/665280*n^7)* C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 14 1/2 13 12 1/2 11 10 1/2 9 8 m Pi m 3 m 329 Pi m 1223 m 13 Pi m 79 m ------ - --------- + ----- - ------------- + -------- - ----------- + ----- 665280 61440 12320 491520 332640 3072 7920 1/2 7 6 1/2 5 4 1/2 3 2 419 Pi m 577 m 169 Pi m 103 m 207 Pi m m - ------------ + ------ + ------------ - ------ + ------------ - --- 98304 665280 40960 10080 40960 220 and in Maple input form: 1/665280*m^14-1/61440*Pi^(1/2)*m^13+3/12320*m^12-329/491520*Pi^(1/2)*m^11+1223/ 332640*m^10-13/3072*Pi^(1/2)*m^9+79/7920*m^8-419/98304*Pi^(1/2)*m^7+577/665280* m^6+169/40960*Pi^(1/2)*m^5-103/10080*m^4+207/40960*Pi^(1/2)*m^3-1/220*m^2 For the, 39, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[3, 2, 1, 4, 5, 6, 7, 8, 9, 10]}, {[4, 2, 3, 1, 5, 6, 7, 8, 9, 10]}, {[4, 5, 3, 1, 2, 6, 7, 8, 9, 10]}, {[5, 2, 3, 4, 1, 6, 7, 8, 9, 10]}, {[5, 6, 3, 4, 1, 2, 7, 8, 9, 10]}, {[5, 6, 7, 4, 1, 2, 3, 8, 9, 10]}, {[6, 2, 3, 4, 5, 1, 7, 8, 9, 10]}, {[6, 7, 3, 4, 5, 1, 2, 8, 9, 10]}, {[6, 7, 8, 4, 5, 1, 2, 3, 9, 10]}, {[6, 7, 8, 9, 5, 1, 2, 3, 4, 10]}, {[7, 2, 3, 4, 5, 6, 1, 8, 9, 10]}, {[7, 8, 3, 4, 5, 6, 1, 2, 9, 10]}, {[7, 8, 9, 4, 5, 6, 1, 2, 3, 10]}, {[7, 8, 9, 10, 5, 6, 1, 2, 3, 4]}, {[8, 2, 3, 4, 5, 6, 7, 1, 9, 10]}, {[8, 9, 3, 4, 5, 6, 7, 1, 2, 10]}, {[8, 9, 10, 4, 5, 6, 7, 1, 2, 3]}, {[9, 2, 3, 4, 5, 6, 7, 8, 1, 10]}, {[9, 10, 3, 4, 5, 6, 7, 8, 1, 2]}, {[10, 2, 3, 4, 5, 6, 7, 8, 9, 1]}, {[3, 4, 2, 1, 5, 6, 7, 8, 9, 10], [4, 3, 1, 2, 5, 6, 7, 8, 9, 10]}, {[3, 4, 5, 2, 1, 6, 7, 8, 9, 10], [5, 4, 1, 2, 3, 6, 7, 8, 9, 10]}, {[3, 4, 5, 6, 2, 1, 7, 8, 9, 10], [6, 5, 1, 2, 3, 4, 7, 8, 9, 10]}, {[3, 4, 5, 6, 7, 2, 1, 8, 9, 10], [7, 6, 1, 2, 3, 4, 5, 8, 9, 10]}, {[3, 4, 5, 6, 7, 8, 2, 1, 9, 10], [8, 7, 1, 2, 3, 4, 5, 6, 9, 10]}, {[3, 4, 5, 6, 7, 8, 9, 2, 1, 10], [9, 8, 1, 2, 3, 4, 5, 6, 7, 10]}, {[3, 4, 5, 6, 7, 8, 9, 10, 2, 1], [10, 9, 1, 2, 3, 4, 5, 6, 7, 8]}, {[4, 5, 2, 3, 1, 6, 7, 8, 9, 10], [5, 3, 4, 1, 2, 6, 7, 8, 9, 10]}, {[4, 5, 6, 2, 3, 1, 7, 8, 9, 10], [6, 4, 5, 1, 2, 3, 7, 8, 9, 10]}, {[4, 5, 6, 3, 1, 2, 7, 8, 9, 10], [5, 6, 4, 1, 2, 3, 7, 8, 9, 10]}, {[4, 5, 6, 7, 2, 3, 1, 8, 9, 10], [7, 5, 6, 1, 2, 3, 4, 8, 9, 10]}, {[4, 5, 6, 7, 3, 1, 2, 8, 9, 10], [6, 7, 5, 1, 2, 3, 4, 8, 9, 10]}, {[4, 5, 6, 7, 8, 2, 3, 1, 9, 10], [8, 6, 7, 1, 2, 3, 4, 5, 9, 10]}, {[4, 5, 6, 7, 8, 3, 1, 2, 9, 10], [7, 8, 6, 1, 2, 3, 4, 5, 9, 10]}, {[4, 5, 6, 7, 8, 9, 2, 3, 1, 10], [9, 7, 8, 1, 2, 3, 4, 5, 6, 10]}, {[4, 5, 6, 7, 8, 9, 3, 1, 2, 10], [8, 9, 7, 1, 2, 3, 4, 5, 6, 10]}, {[4, 5, 6, 7, 8, 9, 10, 2, 3, 1], [10, 8, 9, 1, 2, 3, 4, 5, 6, 7]}, {[4, 5, 6, 7, 8, 9, 10, 3, 1, 2], [9, 10, 8, 1, 2, 3, 4, 5, 6, 7]}, {[5, 6, 2, 3, 4, 1, 7, 8, 9, 10], [6, 3, 4, 5, 1, 2, 7, 8, 9, 10]}, {[5, 6, 7, 2, 3, 4, 1, 8, 9, 10], [7, 4, 5, 6, 1, 2, 3, 8, 9, 10]}, {[5, 6, 7, 3, 4, 1, 2, 8, 9, 10], [6, 7, 4, 5, 1, 2, 3, 8, 9, 10]}, {[5, 6, 7, 8, 2, 3, 4, 1, 9, 10], [8, 5, 6, 7, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 3, 4, 1, 2, 9, 10], [7, 8, 5, 6, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 4, 1, 2, 3, 9, 10], [6, 7, 8, 5, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 9, 2, 3, 4, 1, 10], [9, 6, 7, 8, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 3, 4, 1, 2, 10], [8, 9, 6, 7, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 4, 1, 2, 3, 10], [7, 8, 9, 6, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 10, 2, 3, 4, 1], [10, 7, 8, 9, 1, 2, 3, 4, 5, 6]}, {[5, 6, 7, 8, 9, 10, 3, 4, 1, 2], [9, 10, 7, 8, 1, 2, 3, 4, 5, 6]}, {[5, 6, 7, 8, 9, 10, 4, 1, 2, 3], [8, 9, 10, 7, 1, 2, 3, 4, 5, 6]}, {[6, 7, 2, 3, 4, 5, 1, 8, 9, 10], [7, 3, 4, 5, 6, 1, 2, 8, 9, 10]}, {[6, 7, 8, 2, 3, 4, 5, 1, 9, 10], [8, 4, 5, 6, 7, 1, 2, 3, 9, 10]}, {[6, 7, 8, 3, 4, 5, 1, 2, 9, 10], [7, 8, 4, 5, 6, 1, 2, 3, 9, 10]}, {[6, 7, 8, 9, 2, 3, 4, 5, 1, 10], [9, 5, 6, 7, 8, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 3, 4, 5, 1, 2, 10], [8, 9, 5, 6, 7, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 4, 5, 1, 2, 3, 10], [7, 8, 9, 5, 6, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 10, 2, 3, 4, 5, 1], [10, 6, 7, 8, 9, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 3, 4, 5, 1, 2], [9, 10, 6, 7, 8, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 4, 5, 1, 2, 3], [8, 9, 10, 6, 7, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 5, 1, 2, 3, 4], [7, 8, 9, 10, 6, 1, 2, 3, 4, 5]}, {[7, 8, 2, 3, 4, 5, 6, 1, 9, 10], [8, 3, 4, 5, 6, 7, 1, 2, 9, 10]}, {[7, 8, 9, 2, 3, 4, 5, 6, 1, 10], [9, 4, 5, 6, 7, 8, 1, 2, 3, 10]}, {[7, 8, 9, 3, 4, 5, 6, 1, 2, 10], [8, 9, 4, 5, 6, 7, 1, 2, 3, 10]}, {[7, 8, 9, 10, 2, 3, 4, 5, 6, 1], [10, 5, 6, 7, 8, 9, 1, 2, 3, 4]}, {[7, 8, 9, 10, 3, 4, 5, 6, 1, 2], [9, 10, 5, 6, 7, 8, 1, 2, 3, 4]}, {[7, 8, 9, 10, 4, 5, 6, 1, 2, 3], [8, 9, 10, 5, 6, 7, 1, 2, 3, 4]}, {[8, 9, 2, 3, 4, 5, 6, 7, 1, 10], [9, 3, 4, 5, 6, 7, 8, 1, 2, 10]}, {[8, 9, 10, 2, 3, 4, 5, 6, 7, 1], [10, 4, 5, 6, 7, 8, 9, 1, 2, 3]}, {[8, 9, 10, 3, 4, 5, 6, 7, 1, 2], [9, 10, 4, 5, 6, 7, 8, 1, 2, 3]}, {[9, 10, 2, 3, 4, 5, 6, 7, 8, 1], [10, 3, 4, 5, 6, 7, 8, 9, 1, 2]}} is given by the following expression / 25231 765 2 1307 3 4 5\ n |1/2 + ----- n + ---- n + ----- n + 1/512 n + 1/122880 n | 4 + \ 30720 2048 24576 / / 10153 81181 2 2107 3 9529 4 5 6\ |- 1/2 - ----- n - ----- n - ---- n - ----- n - 5/224 n - 1/3024 n | \ 5040 30240 1440 30240 / C(n) and in Maple input form: (1/2+25231/30720*n+765/2048*n^2+1307/24576*n^3+1/512*n^4+1/122880*n^5)*4^n+(-1/ 2-10153/5040*n-81181/30240*n^2-2107/1440*n^3-9529/30240*n^4-5/224*n^5-1/3024*n^ 6)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 13 12 1/2 11 10 1/2 9 8 Pi m m 643 Pi m 5 m 1361 Pi m 9529 m --------- - ---- + ------------- - ----- + ------------- - ------- 122880 3024 327680 224 24576 30240 1/2 7 6 1/2 5 4 1/2 3 28401 Pi m 2107 m 305123 Pi m 81181 m 116653 Pi m + -------------- - ------- + --------------- - -------- + --------------- 65536 1440 245760 30240 81920 2 1/2 10153 m 9 Pi m - -------- + --------- - 1/2 5040 16 and in Maple input form: 1/122880*Pi^(1/2)*m^13-1/3024*m^12+643/327680*Pi^(1/2)*m^11-5/224*m^10+1361/ 24576*Pi^(1/2)*m^9-9529/30240*m^8+28401/65536*Pi^(1/2)*m^7-2107/1440*m^6+305123 /245760*Pi^(1/2)*m^5-81181/30240*m^4+116653/81920*Pi^(1/2)*m^3-10153/5040*m^2+9 /16*Pi^(1/2)*m-1/2 For the, 40, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[3, 2, 4, 1, 5, 6, 7, 8, 9, 10], [4, 2, 1, 3, 5, 6, 7, 8, 9, 10]}, {[3, 2, 4, 5, 1, 6, 7, 8, 9, 10], [5, 2, 1, 3, 4, 6, 7, 8, 9, 10]}, {[3, 2, 4, 5, 6, 1, 7, 8, 9, 10], [6, 2, 1, 3, 4, 5, 7, 8, 9, 10]}, {[3, 2, 4, 5, 6, 7, 1, 8, 9, 10], [7, 2, 1, 3, 4, 5, 6, 8, 9, 10]}, {[3, 2, 4, 5, 6, 7, 8, 1, 9, 10], [8, 2, 1, 3, 4, 5, 6, 7, 9, 10]}, {[3, 4, 2, 5, 1, 6, 7, 8, 9, 10], [5, 3, 1, 2, 4, 6, 7, 8, 9, 10]}, {[3, 4, 2, 5, 6, 1, 7, 8, 9, 10], [6, 3, 1, 2, 4, 5, 7, 8, 9, 10]}, {[3, 4, 2, 5, 6, 7, 1, 8, 9, 10], [7, 3, 1, 2, 4, 5, 6, 8, 9, 10]}, {[3, 4, 2, 5, 6, 7, 8, 1, 9, 10], [8, 3, 1, 2, 4, 5, 6, 7, 9, 10]}, {[3, 4, 5, 2, 6, 1, 7, 8, 9, 10], [6, 4, 1, 2, 3, 5, 7, 8, 9, 10]}, {[3, 4, 5, 2, 6, 7, 1, 8, 9, 10], [7, 4, 1, 2, 3, 5, 6, 8, 9, 10]}, {[3, 4, 5, 2, 6, 7, 8, 1, 9, 10], [8, 4, 1, 2, 3, 5, 6, 7, 9, 10]}, {[3, 4, 5, 6, 2, 7, 1, 8, 9, 10], [7, 5, 1, 2, 3, 4, 6, 8, 9, 10]}, {[3, 4, 5, 6, 2, 7, 8, 1, 9, 10], [8, 5, 1, 2, 3, 4, 6, 7, 9, 10]}, {[3, 4, 5, 6, 7, 2, 8, 1, 9, 10], [8, 6, 1, 2, 3, 4, 5, 7, 9, 10]}, {[3, 4, 5, 6, 7, 8, 9, 2, 10, 1], [10, 8, 1, 2, 3, 4, 5, 6, 7, 9]}, {[4, 2, 3, 5, 1, 6, 7, 8, 9, 10], [5, 2, 3, 1, 4, 6, 7, 8, 9, 10]}, {[4, 2, 3, 5, 6, 1, 7, 8, 9, 10], [6, 2, 3, 1, 4, 5, 7, 8, 9, 10]}, {[4, 2, 3, 5, 6, 7, 1, 8, 9, 10], [7, 2, 3, 1, 4, 5, 6, 8, 9, 10]}, {[4, 2, 3, 5, 6, 7, 8, 1, 9, 10], [8, 2, 3, 1, 4, 5, 6, 7, 9, 10]}, {[4, 3, 5, 1, 2, 6, 7, 8, 9, 10], [4, 5, 2, 1, 3, 6, 7, 8, 9, 10]}, {[4, 3, 5, 6, 1, 2, 7, 8, 9, 10], [5, 6, 2, 1, 3, 4, 7, 8, 9, 10]}, {[4, 3, 5, 6, 7, 1, 2, 8, 9, 10], [6, 7, 2, 1, 3, 4, 5, 8, 9, 10]}, {[4, 3, 5, 6, 7, 8, 1, 2, 9, 10], [7, 8, 2, 1, 3, 4, 5, 6, 9, 10]}, {[4, 3, 5, 6, 7, 8, 9, 1, 2, 10], [8, 9, 2, 1, 3, 4, 5, 6, 7, 10]}, {[4, 3, 5, 6, 7, 8, 9, 10, 1, 2], [9, 10, 2, 1, 3, 4, 5, 6, 7, 8]}, {[4, 5, 2, 3, 6, 1, 7, 8, 9, 10], [6, 3, 4, 1, 2, 5, 7, 8, 9, 10]}, {[4, 5, 2, 3, 6, 7, 1, 8, 9, 10], [7, 3, 4, 1, 2, 5, 6, 8, 9, 10]}, {[4, 5, 2, 3, 6, 7, 8, 1, 9, 10], [8, 3, 4, 1, 2, 5, 6, 7, 9, 10]}, {[4, 5, 3, 6, 1, 2, 7, 8, 9, 10], [5, 6, 3, 1, 2, 4, 7, 8, 9, 10]}, {[4, 5, 3, 6, 7, 1, 2, 8, 9, 10], [6, 7, 3, 1, 2, 4, 5, 8, 9, 10]}, {[4, 5, 3, 6, 7, 8, 1, 2, 9, 10], [7, 8, 3, 1, 2, 4, 5, 6, 9, 10]}, {[4, 5, 3, 6, 7, 8, 9, 1, 2, 10], [8, 9, 3, 1, 2, 4, 5, 6, 7, 10]}, {[4, 5, 3, 6, 7, 8, 9, 10, 1, 2], [9, 10, 3, 1, 2, 4, 5, 6, 7, 8]}, {[4, 5, 6, 2, 1, 3, 7, 8, 9, 10], [5, 4, 6, 1, 2, 3, 7, 8, 9, 10]}, {[4, 5, 6, 2, 3, 7, 1, 8, 9, 10], [7, 4, 5, 1, 2, 3, 6, 8, 9, 10]}, {[4, 5, 6, 2, 3, 7, 8, 1, 9, 10], [8, 4, 5, 1, 2, 3, 6, 7, 9, 10]}, {[4, 5, 6, 3, 7, 1, 2, 8, 9, 10], [6, 7, 4, 1, 2, 3, 5, 8, 9, 10]}, {[4, 5, 6, 3, 7, 8, 1, 2, 9, 10], [7, 8, 4, 1, 2, 3, 5, 6, 9, 10]}, {[4, 5, 6, 3, 7, 8, 9, 1, 2, 10], [8, 9, 4, 1, 2, 3, 5, 6, 7, 10]}, {[4, 5, 6, 3, 7, 8, 9, 10, 1, 2], [9, 10, 4, 1, 2, 3, 5, 6, 7, 8]}, {[4, 5, 6, 7, 2, 1, 3, 8, 9, 10], [6, 5, 7, 1, 2, 3, 4, 8, 9, 10]}, {[4, 5, 6, 7, 2, 3, 8, 1, 9, 10], [8, 5, 6, 1, 2, 3, 4, 7, 9, 10]}, {[4, 5, 6, 7, 3, 8, 1, 2, 9, 10], [7, 8, 5, 1, 2, 3, 4, 6, 9, 10]}, {[4, 5, 6, 7, 3, 8, 9, 1, 2, 10], [8, 9, 5, 1, 2, 3, 4, 6, 7, 10]}, {[4, 5, 6, 7, 3, 8, 9, 10, 1, 2], [9, 10, 5, 1, 2, 3, 4, 6, 7, 8]}, {[4, 5, 6, 7, 8, 2, 1, 3, 9, 10], [7, 6, 8, 1, 2, 3, 4, 5, 9, 10]}, {[4, 5, 6, 7, 8, 3, 9, 1, 2, 10], [8, 9, 6, 1, 2, 3, 4, 5, 7, 10]}, {[4, 5, 6, 7, 8, 3, 9, 10, 1, 2], [9, 10, 6, 1, 2, 3, 4, 5, 7, 8]}, {[4, 5, 6, 7, 8, 9, 2, 1, 3, 10], [8, 7, 9, 1, 2, 3, 4, 5, 6, 10]}, {[4, 5, 6, 7, 8, 9, 2, 3, 10, 1], [10, 7, 8, 1, 2, 3, 4, 5, 6, 9]}, {[4, 5, 6, 7, 8, 9, 3, 10, 1, 2], [9, 10, 7, 1, 2, 3, 4, 5, 6, 8]}, {[4, 5, 6, 7, 8, 9, 10, 2, 1, 3], [9, 8, 10, 1, 2, 3, 4, 5, 6, 7]}, {[5, 2, 3, 4, 6, 1, 7, 8, 9, 10], [6, 2, 3, 4, 1, 5, 7, 8, 9, 10]}, {[5, 2, 3, 4, 6, 7, 1, 8, 9, 10], [7, 2, 3, 4, 1, 5, 6, 8, 9, 10]}, {[5, 2, 3, 4, 6, 7, 8, 1, 9, 10], [8, 2, 3, 4, 1, 5, 6, 7, 9, 10]}, {[5, 3, 4, 6, 1, 2, 7, 8, 9, 10], [5, 6, 2, 3, 1, 4, 7, 8, 9, 10]}, {[5, 3, 4, 6, 7, 1, 2, 8, 9, 10], [6, 7, 2, 3, 1, 4, 5, 8, 9, 10]}, {[5, 3, 4, 6, 7, 8, 1, 2, 9, 10], [7, 8, 2, 3, 1, 4, 5, 6, 9, 10]}, {[5, 3, 4, 6, 7, 8, 9, 1, 2, 10], [8, 9, 2, 3, 1, 4, 5, 6, 7, 10]}, {[5, 3, 4, 6, 7, 8, 9, 10, 1, 2], [9, 10, 2, 3, 1, 4, 5, 6, 7, 8]}, {[5, 4, 6, 7, 1, 2, 3, 8, 9, 10], [5, 6, 7, 2, 1, 3, 4, 8, 9, 10]}, {[5, 4, 6, 7, 8, 1, 2, 3, 9, 10], [6, 7, 8, 2, 1, 3, 4, 5, 9, 10]}, {[5, 4, 6, 7, 8, 9, 1, 2, 3, 10], [7, 8, 9, 2, 1, 3, 4, 5, 6, 10]}, {[5, 4, 6, 7, 8, 9, 10, 1, 2, 3], [8, 9, 10, 2, 1, 3, 4, 5, 6, 7]}, {[5, 6, 2, 3, 4, 7, 1, 8, 9, 10], [7, 3, 4, 5, 1, 2, 6, 8, 9, 10]}, {[5, 6, 2, 3, 4, 7, 8, 1, 9, 10], [8, 3, 4, 5, 1, 2, 6, 7, 9, 10]}, {[5, 6, 3, 4, 7, 1, 2, 8, 9, 10], [6, 7, 3, 4, 1, 2, 5, 8, 9, 10]}, {[5, 6, 3, 4, 7, 8, 1, 2, 9, 10], [7, 8, 3, 4, 1, 2, 5, 6, 9, 10]}, {[5, 6, 3, 4, 7, 8, 9, 1, 2, 10], [8, 9, 3, 4, 1, 2, 5, 6, 7, 10]}, {[5, 6, 3, 4, 7, 8, 9, 10, 1, 2], [9, 10, 3, 4, 1, 2, 5, 6, 7, 8]}, {[5, 6, 4, 7, 1, 2, 3, 8, 9, 10], [5, 6, 7, 3, 1, 2, 4, 8, 9, 10]}, {[5, 6, 4, 7, 8, 1, 2, 3, 9, 10], [6, 7, 8, 3, 1, 2, 4, 5, 9, 10]}, {[5, 6, 4, 7, 8, 9, 1, 2, 3, 10], [7, 8, 9, 3, 1, 2, 4, 5, 6, 10]}, {[5, 6, 4, 7, 8, 9, 10, 1, 2, 3], [8, 9, 10, 3, 1, 2, 4, 5, 6, 7]}, {[5, 6, 7, 2, 3, 1, 4, 8, 9, 10], [6, 4, 5, 7, 1, 2, 3, 8, 9, 10]}, {[5, 6, 7, 2, 3, 4, 8, 1, 9, 10], [8, 4, 5, 6, 1, 2, 3, 7, 9, 10]}, {[5, 6, 7, 3, 4, 8, 1, 2, 9, 10], [7, 8, 4, 5, 1, 2, 3, 6, 9, 10]}, {[5, 6, 7, 3, 4, 8, 9, 1, 2, 10], [8, 9, 4, 5, 1, 2, 3, 6, 7, 10]}, {[5, 6, 7, 3, 4, 8, 9, 10, 1, 2], [9, 10, 4, 5, 1, 2, 3, 6, 7, 8]}, {[5, 6, 7, 4, 8, 1, 2, 3, 9, 10], [6, 7, 8, 4, 1, 2, 3, 5, 9, 10]}, {[5, 6, 7, 4, 8, 9, 1, 2, 3, 10], [7, 8, 9, 4, 1, 2, 3, 5, 6, 10]}, {[5, 6, 7, 4, 8, 9, 10, 1, 2, 3], [8, 9, 10, 4, 1, 2, 3, 5, 6, 7]}, {[5, 6, 7, 8, 2, 1, 3, 4, 9, 10], [6, 5, 7, 8, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 2, 3, 1, 4, 9, 10], [7, 5, 6, 8, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 3, 1, 2, 4, 9, 10], [6, 7, 5, 8, 1, 2, 3, 4, 9, 10]}, {[5, 6, 7, 8, 3, 4, 9, 1, 2, 10], [8, 9, 5, 6, 1, 2, 3, 4, 7, 10]}, {[5, 6, 7, 8, 3, 4, 9, 10, 1, 2], [9, 10, 5, 6, 1, 2, 3, 4, 7, 8]}, {[5, 6, 7, 8, 4, 9, 1, 2, 3, 10], [7, 8, 9, 5, 1, 2, 3, 4, 6, 10]}, {[5, 6, 7, 8, 4, 9, 10, 1, 2, 3], [8, 9, 10, 5, 1, 2, 3, 4, 6, 7]}, {[5, 6, 7, 8, 9, 2, 1, 3, 4, 10], [7, 6, 8, 9, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 2, 3, 1, 4, 10], [8, 6, 7, 9, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 2, 3, 4, 10, 1], [10, 6, 7, 8, 1, 2, 3, 4, 5, 9]}, {[5, 6, 7, 8, 9, 3, 1, 2, 4, 10], [7, 8, 6, 9, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 3, 4, 10, 1, 2], [9, 10, 6, 7, 1, 2, 3, 4, 5, 8]}, {[5, 6, 7, 8, 9, 4, 10, 1, 2, 3], [8, 9, 10, 6, 1, 2, 3, 4, 5, 7]}, {[5, 6, 7, 8, 9, 10, 2, 1, 3, 4], [8, 7, 9, 10, 1, 2, 3, 4, 5, 6]}, {[5, 6, 7, 8, 9, 10, 2, 3, 1, 4], [9, 7, 8, 10, 1, 2, 3, 4, 5, 6]}, {[5, 6, 7, 8, 9, 10, 3, 1, 2, 4], [8, 9, 7, 10, 1, 2, 3, 4, 5, 6]}, {[6, 2, 3, 4, 5, 7, 1, 8, 9, 10], [7, 2, 3, 4, 5, 1, 6, 8, 9, 10]}, {[6, 2, 3, 4, 5, 7, 8, 1, 9, 10], [8, 2, 3, 4, 5, 1, 6, 7, 9, 10]}, {[6, 3, 4, 5, 7, 1, 2, 8, 9, 10], [6, 7, 2, 3, 4, 1, 5, 8, 9, 10]}, {[6, 3, 4, 5, 7, 8, 1, 2, 9, 10], [7, 8, 2, 3, 4, 1, 5, 6, 9, 10]}, {[6, 3, 4, 5, 7, 8, 9, 1, 2, 10], [8, 9, 2, 3, 4, 1, 5, 6, 7, 10]}, {[6, 3, 4, 5, 7, 8, 9, 10, 1, 2], [9, 10, 2, 3, 4, 1, 5, 6, 7, 8]}, {[6, 4, 5, 7, 8, 1, 2, 3, 9, 10], [6, 7, 8, 2, 3, 1, 4, 5, 9, 10]}, {[6, 4, 5, 7, 8, 9, 1, 2, 3, 10], [7, 8, 9, 2, 3, 1, 4, 5, 6, 10]}, {[6, 4, 5, 7, 8, 9, 10, 1, 2, 3], [8, 9, 10, 2, 3, 1, 4, 5, 6, 7]}, {[6, 5, 7, 8, 9, 1, 2, 3, 4, 10], [6, 7, 8, 9, 2, 1, 3, 4, 5, 10]}, {[6, 5, 7, 8, 9, 10, 1, 2, 3, 4], [7, 8, 9, 10, 2, 1, 3, 4, 5, 6]}, {[6, 7, 2, 3, 4, 5, 8, 1, 9, 10], [8, 3, 4, 5, 6, 1, 2, 7, 9, 10]}, {[6, 7, 3, 4, 5, 8, 1, 2, 9, 10], [7, 8, 3, 4, 5, 1, 2, 6, 9, 10]}, {[6, 7, 3, 4, 5, 8, 9, 1, 2, 10], [8, 9, 3, 4, 5, 1, 2, 6, 7, 10]}, {[6, 7, 3, 4, 5, 8, 9, 10, 1, 2], [9, 10, 3, 4, 5, 1, 2, 6, 7, 8]}, {[6, 7, 4, 5, 8, 1, 2, 3, 9, 10], [6, 7, 8, 3, 4, 1, 2, 5, 9, 10]}, {[6, 7, 4, 5, 8, 9, 1, 2, 3, 10], [7, 8, 9, 3, 4, 1, 2, 5, 6, 10]}, {[6, 7, 4, 5, 8, 9, 10, 1, 2, 3], [8, 9, 10, 3, 4, 1, 2, 5, 6, 7]}, {[6, 7, 5, 8, 9, 1, 2, 3, 4, 10], [6, 7, 8, 9, 3, 1, 2, 4, 5, 10]}, {[6, 7, 5, 8, 9, 10, 1, 2, 3, 4], [7, 8, 9, 10, 3, 1, 2, 4, 5, 6]}, {[6, 7, 8, 2, 3, 4, 1, 5, 9, 10], [7, 4, 5, 6, 8, 1, 2, 3, 9, 10]}, {[6, 7, 8, 3, 4, 5, 9, 1, 2, 10], [8, 9, 4, 5, 6, 1, 2, 3, 7, 10]}, {[6, 7, 8, 3, 4, 5, 9, 10, 1, 2], [9, 10, 4, 5, 6, 1, 2, 3, 7, 8]}, {[6, 7, 8, 4, 5, 9, 1, 2, 3, 10], [7, 8, 9, 4, 5, 1, 2, 3, 6, 10]}, {[6, 7, 8, 4, 5, 9, 10, 1, 2, 3], [8, 9, 10, 4, 5, 1, 2, 3, 6, 7]}, {[6, 7, 8, 5, 9, 1, 2, 3, 4, 10], [6, 7, 8, 9, 4, 1, 2, 3, 5, 10]}, {[6, 7, 8, 5, 9, 10, 1, 2, 3, 4], [7, 8, 9, 10, 4, 1, 2, 3, 5, 6]}, {[6, 7, 8, 9, 2, 3, 1, 4, 5, 10], [7, 5, 6, 8, 9, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 2, 3, 4, 1, 5, 10], [8, 5, 6, 7, 9, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 2, 3, 4, 5, 10, 1], [10, 5, 6, 7, 8, 1, 2, 3, 4, 9]}, {[6, 7, 8, 9, 3, 4, 1, 2, 5, 10], [7, 8, 5, 6, 9, 1, 2, 3, 4, 10]}, {[6, 7, 8, 9, 3, 4, 5, 10, 1, 2], [9, 10, 5, 6, 7, 1, 2, 3, 4, 8]}, {[6, 7, 8, 9, 4, 5, 10, 1, 2, 3], [8, 9, 10, 5, 6, 1, 2, 3, 4, 7]}, {[6, 7, 8, 9, 5, 10, 1, 2, 3, 4], [7, 8, 9, 10, 5, 1, 2, 3, 4, 6]}, {[6, 7, 8, 9, 10, 2, 1, 3, 4, 5], [7, 6, 8, 9, 10, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 2, 3, 1, 4, 5], [8, 6, 7, 9, 10, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 2, 3, 4, 1, 5], [9, 6, 7, 8, 10, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 3, 1, 2, 4, 5], [7, 8, 6, 9, 10, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 3, 4, 1, 2, 5], [8, 9, 6, 7, 10, 1, 2, 3, 4, 5]}, {[6, 7, 8, 9, 10, 4, 1, 2, 3, 5], [7, 8, 9, 6, 10, 1, 2, 3, 4, 5]}, {[7, 2, 3, 4, 5, 6, 8, 1, 9, 10], [8, 2, 3, 4, 5, 6, 1, 7, 9, 10]}, {[7, 3, 4, 5, 6, 8, 1, 2, 9, 10], [7, 8, 2, 3, 4, 5, 1, 6, 9, 10]}, {[7, 3, 4, 5, 6, 8, 9, 1, 2, 10], [8, 9, 2, 3, 4, 5, 1, 6, 7, 10]}, {[7, 3, 4, 5, 6, 8, 9, 10, 1, 2], [9, 10, 2, 3, 4, 5, 1, 6, 7, 8]}, {[7, 4, 5, 6, 8, 9, 1, 2, 3, 10], [7, 8, 9, 2, 3, 4, 1, 5, 6, 10]}, {[7, 4, 5, 6, 8, 9, 10, 1, 2, 3], [8, 9, 10, 2, 3, 4, 1, 5, 6, 7]}, {[7, 5, 6, 8, 9, 10, 1, 2, 3, 4], [7, 8, 9, 10, 2, 3, 1, 4, 5, 6]}, {[7, 8, 3, 4, 5, 6, 9, 1, 2, 10], [8, 9, 3, 4, 5, 6, 1, 2, 7, 10]}, {[7, 8, 3, 4, 5, 6, 9, 10, 1, 2], [9, 10, 3, 4, 5, 6, 1, 2, 7, 8]}, {[7, 8, 4, 5, 6, 9, 1, 2, 3, 10], [7, 8, 9, 3, 4, 5, 1, 2, 6, 10]}, {[7, 8, 4, 5, 6, 9, 10, 1, 2, 3], [8, 9, 10, 3, 4, 5, 1, 2, 6, 7]}, {[7, 8, 5, 6, 9, 10, 1, 2, 3, 4], [7, 8, 9, 10, 3, 4, 1, 2, 5, 6]}, {[7, 8, 9, 2, 3, 4, 5, 1, 6, 10], [8, 4, 5, 6, 7, 9, 1, 2, 3, 10]}, {[7, 8, 9, 2, 3, 4, 5, 6, 10, 1], [10, 4, 5, 6, 7, 8, 1, 2, 3, 9]}, {[7, 8, 9, 3, 4, 5, 6, 10, 1, 2], [9, 10, 4, 5, 6, 7, 1, 2, 3, 8]}, {[7, 8, 9, 4, 5, 6, 10, 1, 2, 3], [8, 9, 10, 4, 5, 6, 1, 2, 3, 7]}, {[7, 8, 9, 5, 6, 10, 1, 2, 3, 4], [7, 8, 9, 10, 4, 5, 1, 2, 3, 6]}, {[7, 8, 9, 10, 2, 3, 4, 1, 5, 6], [8, 5, 6, 7, 9, 10, 1, 2, 3, 4]}, {[7, 8, 9, 10, 2, 3, 4, 5, 1, 6], [9, 5, 6, 7, 8, 10, 1, 2, 3, 4]}, {[7, 8, 9, 10, 3, 4, 5, 1, 2, 6], [8, 9, 5, 6, 7, 10, 1, 2, 3, 4]}, {[8, 3, 4, 5, 6, 7, 9, 1, 2, 10], [8, 9, 2, 3, 4, 5, 6, 1, 7, 10]}, {[8, 3, 4, 5, 6, 7, 9, 10, 1, 2], [9, 10, 2, 3, 4, 5, 6, 1, 7, 8]}, {[8, 4, 5, 6, 7, 9, 10, 1, 2, 3], [8, 9, 10, 2, 3, 4, 5, 1, 6, 7]}, {[8, 9, 2, 3, 4, 5, 6, 7, 10, 1], [10, 3, 4, 5, 6, 7, 8, 1, 2, 9]}, {[8, 9, 3, 4, 5, 6, 7, 10, 1, 2], [9, 10, 3, 4, 5, 6, 7, 1, 2, 8]}, {[8, 9, 4, 5, 6, 7, 10, 1, 2, 3], [8, 9, 10, 3, 4, 5, 6, 1, 2, 7]}, {[8, 9, 10, 2, 3, 4, 5, 6, 1, 7], [9, 4, 5, 6, 7, 8, 10, 1, 2, 3]}, {[9, 2, 3, 4, 5, 6, 7, 8, 10, 1], [10, 2, 3, 4, 5, 6, 7, 8, 1, 9]}, {[9, 3, 4, 5, 6, 7, 8, 10, 1, 2], [9, 10, 2, 3, 4, 5, 6, 7, 1, 8]}, { [3, 2, 4, 5, 6, 7, 8, 9, 1, 10], [3, 2, 4, 5, 6, 7, 8, 9, 10, 1], [9, 2, 1, 3, 4, 5, 6, 7, 8, 10], [10, 2, 1, 3, 4, 5, 6, 7, 8, 9]}, { [3, 4, 2, 5, 6, 7, 8, 9, 1, 10], [3, 4, 2, 5, 6, 7, 8, 9, 10, 1], [9, 3, 1, 2, 4, 5, 6, 7, 8, 10], [10, 3, 1, 2, 4, 5, 6, 7, 8, 9]}, { [3, 4, 5, 2, 6, 7, 8, 9, 1, 10], [3, 4, 5, 2, 6, 7, 8, 9, 10, 1], [9, 4, 1, 2, 3, 5, 6, 7, 8, 10], [10, 4, 1, 2, 3, 5, 6, 7, 8, 9]}, { [3, 4, 5, 6, 2, 7, 8, 9, 1, 10], [3, 4, 5, 6, 2, 7, 8, 9, 10, 1], [9, 5, 1, 2, 3, 4, 6, 7, 8, 10], [10, 5, 1, 2, 3, 4, 6, 7, 8, 9]}, { [3, 4, 5, 6, 7, 2, 8, 9, 1, 10], [3, 4, 5, 6, 7, 2, 8, 9, 10, 1], [9, 6, 1, 2, 3, 4, 5, 7, 8, 10], [10, 6, 1, 2, 3, 4, 5, 7, 8, 9]}, { [3, 4, 5, 6, 7, 8, 2, 9, 1, 10], [3, 4, 5, 6, 7, 8, 2, 9, 10, 1], [9, 7, 1, 2, 3, 4, 5, 6, 8, 10], [10, 7, 1, 2, 3, 4, 5, 6, 8, 9]}, { [4, 2, 3, 5, 6, 7, 8, 9, 1, 10], [4, 2, 3, 5, 6, 7, 8, 9, 10, 1], [9, 2, 3, 1, 4, 5, 6, 7, 8, 10], [10, 2, 3, 1, 4, 5, 6, 7, 8, 9]}, { [4, 5, 2, 3, 6, 7, 8, 9, 1, 10], [4, 5, 2, 3, 6, 7, 8, 9, 10, 1], [9, 3, 4, 1, 2, 5, 6, 7, 8, 10], [10, 3, 4, 1, 2, 5, 6, 7, 8, 9]}, { [4, 5, 6, 2, 3, 7, 8, 9, 1, 10], [4, 5, 6, 2, 3, 7, 8, 9, 10, 1], [9, 4, 5, 1, 2, 3, 6, 7, 8, 10], [10, 4, 5, 1, 2, 3, 6, 7, 8, 9]}, { [4, 5, 6, 7, 2, 3, 8, 9, 1, 10], [4, 5, 6, 7, 2, 3, 8, 9, 10, 1], [9, 5, 6, 1, 2, 3, 4, 7, 8, 10], [10, 5, 6, 1, 2, 3, 4, 7, 8, 9]}, { [4, 5, 6, 7, 8, 2, 3, 9, 1, 10], [4, 5, 6, 7, 8, 2, 3, 9, 10, 1], [9, 6, 7, 1, 2, 3, 4, 5, 8, 10], [10, 6, 7, 1, 2, 3, 4, 5, 8, 9]}, { [5, 2, 3, 4, 6, 7, 8, 9, 1, 10], [5, 2, 3, 4, 6, 7, 8, 9, 10, 1], [9, 2, 3, 4, 1, 5, 6, 7, 8, 10], [10, 2, 3, 4, 1, 5, 6, 7, 8, 9]}, { [5, 6, 2, 3, 4, 7, 8, 9, 1, 10], [5, 6, 2, 3, 4, 7, 8, 9, 10, 1], [9, 3, 4, 5, 1, 2, 6, 7, 8, 10], [10, 3, 4, 5, 1, 2, 6, 7, 8, 9]}, { [5, 6, 7, 2, 3, 4, 8, 9, 1, 10], [5, 6, 7, 2, 3, 4, 8, 9, 10, 1], [9, 4, 5, 6, 1, 2, 3, 7, 8, 10], [10, 4, 5, 6, 1, 2, 3, 7, 8, 9]}, { [5, 6, 7, 8, 2, 3, 4, 9, 1, 10], [5, 6, 7, 8, 2, 3, 4, 9, 10, 1], [9, 5, 6, 7, 1, 2, 3, 4, 8, 10], [10, 5, 6, 7, 1, 2, 3, 4, 8, 9]}, { [6, 2, 3, 4, 5, 7, 8, 9, 1, 10], [6, 2, 3, 4, 5, 7, 8, 9, 10, 1], [9, 2, 3, 4, 5, 1, 6, 7, 8, 10], [10, 2, 3, 4, 5, 1, 6, 7, 8, 9]}, { [6, 7, 2, 3, 4, 5, 8, 9, 1, 10], [6, 7, 2, 3, 4, 5, 8, 9, 10, 1], [9, 3, 4, 5, 6, 1, 2, 7, 8, 10], [10, 3, 4, 5, 6, 1, 2, 7, 8, 9]}, { [6, 7, 8, 2, 3, 4, 5, 9, 1, 10], [6, 7, 8, 2, 3, 4, 5, 9, 10, 1], [9, 4, 5, 6, 7, 1, 2, 3, 8, 10], [10, 4, 5, 6, 7, 1, 2, 3, 8, 9]}, { [7, 2, 3, 4, 5, 6, 8, 9, 1, 10], [7, 2, 3, 4, 5, 6, 8, 9, 10, 1], [9, 2, 3, 4, 5, 6, 1, 7, 8, 10], [10, 2, 3, 4, 5, 6, 1, 7, 8, 9]}, { [7, 8, 2, 3, 4, 5, 6, 9, 1, 10], [7, 8, 2, 3, 4, 5, 6, 9, 10, 1], [9, 3, 4, 5, 6, 7, 1, 2, 8, 10], [10, 3, 4, 5, 6, 7, 1, 2, 8, 9]}, { [8, 2, 3, 4, 5, 6, 7, 9, 1, 10], [8, 2, 3, 4, 5, 6, 7, 9, 10, 1], [9, 2, 3, 4, 5, 6, 7, 1, 8, 10], [10, 2, 3, 4, 5, 6, 7, 1, 8, 9]}} is given by the following expression / 511 1463 2 727 3 19 4 5\ n |----- n + ----- n + ----- n + ----- n + 1/245760 n | 4 \10240 24576 49152 24576 / / 599 2 431 3 481 4 17 5 6\ + |-1/20 n - ---- n - ---- n - ---- n - ---- n - 1/6720 n | C(n) \ 3360 2240 6720 2240 / and in Maple input form: (511/10240*n+1463/24576*n^2+727/49152*n^3+19/24576*n^4+1/245760*n^5)*4^n+(-1/20 *n-599/3360*n^2-431/2240*n^3-481/6720*n^4-17/2240*n^5-1/6720*n^6)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 13 12 1/2 11 10 1/2 9 8 Pi m m 1529 Pi m 17 m 3079 Pi m 481 m --------- - ---- + -------------- - ------ + ------------- - ------ 245760 6720 1966080 2240 196608 6720 1/2 7 6 1/2 5 4 1/2 3 2 29951 Pi m 431 m 38297 Pi m 599 m 4599 Pi m m + -------------- - ------ + -------------- - ------ + ------------- - ---- 393216 2240 327680 3360 81920 20 and in Maple input form: 1/245760*Pi^(1/2)*m^13-1/6720*m^12+1529/1966080*Pi^(1/2)*m^11-17/2240*m^10+3079 /196608*Pi^(1/2)*m^9-481/6720*m^8+29951/393216*Pi^(1/2)*m^7-431/2240*m^6+38297/ 327680*Pi^(1/2)*m^5-599/3360*m^4+4599/81920*Pi^(1/2)*m^3-1/20*m^2 For the, 41, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[2, 1, 3, 4, 5, 6, 7, 8, 9, 10]}, {[3, 4, 1, 2, 5, 6, 7, 8, 9, 10]}, {[4, 5, 6, 1, 2, 3, 7, 8, 9, 10]}, {[5, 6, 7, 8, 1, 2, 3, 4, 9, 10]}, {[6, 7, 8, 9, 10, 1, 2, 3, 4, 5]}, {[2, 3, 1, 4, 5, 6, 7, 8, 9, 10], [3, 1, 2, 4, 5, 6, 7, 8, 9, 10]}, {[2, 3, 4, 1, 5, 6, 7, 8, 9, 10], [4, 1, 2, 3, 5, 6, 7, 8, 9, 10]}, {[2, 3, 4, 5, 1, 6, 7, 8, 9, 10], [5, 1, 2, 3, 4, 6, 7, 8, 9, 10]}, {[2, 3, 4, 5, 6, 1, 7, 8, 9, 10], [6, 1, 2, 3, 4, 5, 7, 8, 9, 10]}, {[2, 3, 4, 5, 6, 7, 1, 8, 9, 10], [7, 1, 2, 3, 4, 5, 6, 8, 9, 10]}, {[2, 3, 4, 5, 6, 7, 8, 1, 9, 10], [8, 1, 2, 3, 4, 5, 6, 7, 9, 10]}, {[3, 4, 5, 1, 2, 6, 7, 8, 9, 10], [4, 5, 1, 2, 3, 6, 7, 8, 9, 10]}, {[3, 4, 5, 6, 1, 2, 7, 8, 9, 10], [5, 6, 1, 2, 3, 4, 7, 8, 9, 10]}, {[3, 4, 5, 6, 7, 1, 2, 8, 9, 10], [6, 7, 1, 2, 3, 4, 5, 8, 9, 10]}, {[3, 4, 5, 6, 7, 8, 1, 2, 9, 10], [7, 8, 1, 2, 3, 4, 5, 6, 9, 10]}, {[3, 4, 5, 6, 7, 8, 9, 1, 2, 10], [8, 9, 1, 2, 3, 4, 5, 6, 7, 10]}, {[3, 4, 5, 6, 7, 8, 9, 10, 1, 2], [9, 10, 1, 2, 3, 4, 5, 6, 7, 8]}, {[4, 5, 6, 7, 1, 2, 3, 8, 9, 10], [5, 6, 7, 1, 2, 3, 4, 8, 9, 10]}, {[4, 5, 6, 7, 8, 1, 2, 3, 9, 10], [6, 7, 8, 1, 2, 3, 4, 5, 9, 10]}, {[4, 5, 6, 7, 8, 9, 1, 2, 3, 10], [7, 8, 9, 1, 2, 3, 4, 5, 6, 10]}, {[4, 5, 6, 7, 8, 9, 10, 1, 2, 3], [8, 9, 10, 1, 2, 3, 4, 5, 6, 7]}, {[5, 6, 7, 8, 9, 1, 2, 3, 4, 10], [6, 7, 8, 9, 1, 2, 3, 4, 5, 10]}, {[5, 6, 7, 8, 9, 10, 1, 2, 3, 4], [7, 8, 9, 10, 1, 2, 3, 4, 5, 6]}, { [2, 3, 4, 5, 6, 7, 8, 9, 1, 10], [2, 3, 4, 5, 6, 7, 8, 9, 10, 1], [9, 1, 2, 3, 4, 5, 6, 7, 8, 10], [10, 1, 2, 3, 4, 5, 6, 7, 8, 9]}} is given by the following expression / 4433 3127 2 145 3 4\ n |- 1/2 - ---- n - ----- n - ---- n - 5/12288 n | 4 + \ 6144 12288 6144 / / 9649 10057 2 1087 3 65 4 5 6\ |1/2 + ---- n + ----- n + ---- n + --- n + 1/140 n + 1/30240 n | C(n) \ 5040 4320 1008 378 / and in Maple input form: (-1/2-4433/6144*n-3127/12288*n^2-145/6144*n^3-5/12288*n^4)*4^n+(1/2+9649/5040*n +10057/4320*n^2+1087/1008*n^3+65/378*n^4+1/140*n^5+1/30240*n^6)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 12 1/2 11 10 1/2 9 8 1/2 7 6 m 5 Pi m m 2365 Pi m 65 m 13813 Pi m 1087 m ----- - ----------- + --- - ------------- + ----- - -------------- + ------- 30240 12288 140 98304 378 49152 1008 1/2 5 4 1/2 3 2 1/2 99071 Pi m 10057 m 21491 Pi m 9649 m 9 Pi m - -------------- + -------- - -------------- + ------- - --------- + 1/2 98304 4320 16384 5040 16 and in Maple input form: 1/30240*m^12-5/12288*Pi^(1/2)*m^11+1/140*m^10-2365/98304*Pi^(1/2)*m^9+65/378*m^ 8-13813/49152*Pi^(1/2)*m^7+1087/1008*m^6-99071/98304*Pi^(1/2)*m^5+10057/4320*m^ 4-21491/16384*Pi^(1/2)*m^3+9649/5040*m^2-9/16*Pi^(1/2)*m+1/2 For the, 42, -th most abundant set of patterns we have The "total number of occurrences in all 132-avoiding n-permutations" of the following patterns: {{[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}} is given by the following expression / 6127 6011 2 39 3 4\ n |9/2 + ---- n + ----- n + ---- n + 1/12288 n | 4 \ 2048 12288 2048 / / 7689 7249 2 1859 3 143 4 11 5\ + |- 9/2 - ---- n - ---- n - ---- n - --- n - ---- n | C(n) \ 560 672 672 672 3360 / and in Maple input form: (9/2+6127/2048*n+6011/12288*n^2+39/2048*n^3+1/12288*n^4)*4^n+(-9/2-7689/560*n-\ 7249/672*n^2-1859/672*n^3-143/672*n^4-11/3360*n^5)*C(n) The asymptotics of the AVERAGE (i.e. the above expression divided by C(n), i\ s: 1/2 11 10 1/2 9 8 1/2 7 6 Pi m 11 m 627 Pi m 143 m 25097 Pi m 1859 m --------- - ------ + ------------ - ------ + -------------- - ------- 12288 3360 32768 672 49152 672 1/2 5 4 1/2 3 2 1/2 116065 Pi m 7249 m 128871 Pi m 7689 m 81 Pi m + --------------- - ------- + --------------- - ------- + ---------- - 9/2 32768 672 16384 560 16 and in Maple input form: 1/12288*Pi^(1/2)*m^11-11/3360*m^10+627/32768*Pi^(1/2)*m^9-143/672*m^8+25097/ 49152*Pi^(1/2)*m^7-1859/672*m^6+116065/32768*Pi^(1/2)*m^5-7249/672*m^4+128871/ 16384*Pi^(1/2)*m^3-7689/560*m^2+81/16*Pi^(1/2)*m-9/2 I hope that you enjoyed this article, that took, 62232.295, seconds. to produce. 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