Created: Sept-Dec., 2003. This version: Dec. 1, 2003 This is SMCper, a Maple package to implement Doron Zeilberger's Symbolic Moment Calculus applied to patterns in permutations as it is described in his article Symbolic Moment Calculus: I. Foundations and Permutation-Patterns Written by Doron Zeilberger, zeilberg@math.rutgers.edu `` Please report bugs to zeilberg@math.rutgers.edu `` The most current version of this package and paper are available from http://www.math.rutgers.edu/~zeilberg/ For a list of the MAIN procedures type ezra();, for help with a specific procedure, type ezra(procedure_name); For a list of the supporting procedures type ezra1();, for help with a specific supporting procedure, type ezra1(procedure_name); Warning, the protected name Chi has been redefined and unprotected [[{[2, 5, 4, 1, 6, 3]}, 1493/88519495680000, .1686634101e-10], [{[2, 5, 3, 6, 1 , 4], [2, 6, 4, 1, 5, 3]}, 4619/265558487040000, .1739353184e-10], [{[3, 5, 1, 6, 2, 4]}, 4699/265558487040000, .1769478375e-10], [{[2, 4, 6, 1, 3, 5], [3, 6, 2, 5, 1, 4]}, 101/5419560960000, .1863619595e-10], [{[2, 4, 6, 1, 5, 3], [3, 5, 2, 6, 1, 4]}, 15067/796675461120000, .1891234353e-10], [{[2, 5, 1, 4, 6, 3], [2 , 5, 3, 1, 6, 4]}, 15307/796675461120000, .1921359543e-10], [{[2, 4, 6, 3, 1, 5 ], [2, 6, 3, 5, 1, 4]}, 15637/796675461120000, .1962781680e-10], [{[2, 6, 3, 4, 1, 5], [2, 6, 4, 3, 1, 5]}, 929/44259747840000, .2098972645e-10], [{[2, 4, 5, 1 , 6, 3]}, 16937/796675461120000, .2125959795e-10], [{[2, 5, 1, 3, 6, 4]}, 5759/ 265558487040000, .2168637148e-10], [{[2, 5, 6, 3, 1, 4], [2, 6, 3, 1, 5, 4]}, 17377/796675461120000, .2181189311e-10], [{[2, 5, 1, 6, 3, 4], [3, 1, 5, 6, 2, 4]}, 8831/398337730560000, .2216962975e-10], [{[2, 5, 1, 6, 4, 3], [3, 1, 6, 5, 2, 4]}, 3107/132779243520000, .2339974169e-10], [{[2, 5, 6, 1, 3, 4], [3, 2, 6, 5, 1, 4]}, 1601/66389621760000, .2411521496e-10], [{[2, 5, 6, 1, 4, 3], [3, 2, 5, 6, 1, 4]}, 443/18106260480000, .2446667552e-10], [{[2, 3, 6, 4, 1, 5], [2, 6 , 5, 3, 1, 4]}, 19637/796675461120000, .2464868188e-10], [{[2, 5, 4, 6, 1, 3], [2, 6, 1, 4, 5, 3]}, 19687/796675461120000, .2471144269e-10], [{[2, 4, 1, 6, 3, 5], [3, 1, 5, 2, 6, 4]}, 29/1149603840000, .2522608136e-10], [{[2, 4, 3, 6, 1, 5], [2, 6, 4, 5, 1, 3]}, 20917/796675461120000, .2625535870e-10], [{[2, 3, 6, 5 , 1, 4], [2, 6, 5, 1, 3, 4]}, 10651/398337730560000, .2673861696e-10], [{[2, 3, 5, 6, 1, 4], [2, 6, 5, 1, 4, 3]}, 10891/398337730560000, .2734112077e-10], [{[2 , 4, 1, 6, 5, 3], [3, 1, 6, 2, 5, 4]}, 7289/265558487040000, .2744781416e-10], [{[2, 4, 6, 5, 1, 3], [2, 6, 1, 5, 3, 4]}, 1861/66389621760000, .2803148972e-10 ], [{[2, 5, 6, 4, 1, 3], [2, 6, 1, 3, 5, 4]}, 97/3448811520000, .2812563094e-10 ], [{[2, 3, 6, 1, 5, 4], [3, 5, 6, 2, 1, 4]}, 277/9835499520000, .2816328743e-\ 10], [{[3, 2, 6, 1, 5, 4], [3, 5, 6, 1, 2, 4]}, 22447/796675461120000, .\ 2817583959e-10], [{[2, 3, 5, 1, 6, 4], [2, 4, 1, 5, 6, 3]}, 22457/ 796675461120000, .2818839176e-10], [{[2, 3, 6, 1, 4, 5], [3, 6, 5, 2, 1, 4]}, 7499/265558487040000, .2823860041e-10], [{[2, 4, 5, 6, 1, 3], [2, 6, 1, 5, 4, 3 ]}, 5903/199168865280000, .2963816655e-10], [{[1, 5, 3, 6, 2, 4]}, 23701/ 796675461120000, .2974988079e-10], [{[1, 4, 6, 3, 2, 5], [1, 5, 4, 2, 6, 3]}, 24481/796675461120000, .3072894948e-10], [{[1, 4, 6, 2, 5, 3]}, 8227/ 265558487040000, .3097999274e-10], [{[2, 3, 4, 6, 1, 5], [2, 6, 5, 4, 1, 3]}, 24917/796675461120000, .3127622378e-10], [{[1, 4, 5, 2, 6, 3], [1, 4, 6, 2, 3, 5]}, 3683/113810780160000, .3236073063e-10], [{[1, 4, 3, 6, 2, 5], [1, 5, 3, 2, 6, 4]}, 8747/265558487040000, .3293813012e-10], [{[1, 3, 6, 4, 2, 5], [1, 5, 2, 4, 6, 3]}, 269/8047226880000, .3342766446e-10], [{[1, 4, 6, 3, 5, 2], [1, 6, 4, 2, 5, 3]}, 27211/796675461120000, .3415568990e-10], [{[1, 5, 3, 6, 4, 2], [1, 6 , 3, 5, 2, 4]}, 3119/88519495680000, .3523517589e-10], [{[1, 5, 3, 4, 6, 2], [1 , 6, 3, 4, 2, 5]}, 23/646652160000, .3556780820e-10], [{[1, 3, 5, 6, 2, 4], [1, 5, 2, 6, 3, 4]}, 113/3161410560000, .3574353848e-10], [{[1, 3, 6, 5, 2, 4], [1, 5, 2, 6, 4, 3]}, 7279/199168865280000, .3654687689e-10], [{[1, 5, 4, 3, 6, 2], [1, 6, 4, 3, 2, 5]}, 607/16597405440000, .3657198122e-10], [{[1, 3, 4, 6, 2, 5] , [1, 5, 2, 3, 6, 4]}, 29191/796675461120000, .3664101811e-10], [{[1, 3, 5, 2, 6, 4], [1, 4, 2, 6, 3, 5]}, 30091/796675461120000, .3777071275e-10], [{[1, 4, 5 , 3, 6, 2], [1, 6, 4, 2, 3, 5]}, 30311/796675461120000, .3804686033e-10], [{[1, 6, 4, 3, 5, 2]}, 241/6322821120000, .3811589723e-10], [{[1, 6, 3, 4, 5, 2]}, 15233/398337730560000, .3824141885e-10], [{[1, 4, 3, 6, 5, 2], [1, 6, 3, 2, 5, 4]}, 10207/265558487040000, .3843597738e-10], [{[1, 5, 4, 6, 2, 3], [1, 5, 6, 3 , 2, 4]}, 10247/265558487040000, .3858660333e-10], [{[1, 3, 6, 2, 5, 4], [1, 4, 2, 6, 5, 3]}, 30841/796675461120000, .3871212496e-10], [{[2, 1, 4, 6, 3, 5], [2 , 1, 5, 3, 6, 4]}, 29/739031040000, .3924057100e-10], [{[2, 1, 5, 4, 6, 3], [2, 1, 6, 4, 3, 5]}, 7823/199168865280000, .3927822749e-10], [{[1, 3, 6, 2, 4, 5], [1, 4, 2, 5, 6, 3]}, 31781/796675461120000, .3989202825e-10], [{[1, 3, 6, 4, 5, 2], [1, 6, 2, 4, 5, 3]}, 10687/265558487040000, .4024348880e-10], [{[2, 1, 5, 6 , 3, 4]}, 733/18106260480000, .4048323511e-10], [{[1, 4, 6, 5, 2, 3], [1, 5, 6, 2, 4, 3]}, 491/12070840320000, .4067653842e-10], [{[1, 4, 5, 6, 2, 3], [1, 5, 6 , 2, 3, 4]}, 16283/398337730560000, .4087737302e-10], [{[2, 1, 6, 4, 5, 3]}, 5527/132779243520000, .4162548192e-10], [{[1, 6, 3, 5, 4, 2]}, 433/ 10346434560000, .4185016563e-10], [{[1, 4, 3, 5, 6, 2], [1, 6, 3, 2, 4, 5]}, 689/16258682880000, .4237735646e-10], [{[2, 3, 1, 6, 4, 5], [3, 1, 2, 5, 6, 4]} , 1261/29506498560000, .4273634831e-10], [{[2, 1, 4, 6, 5, 3], [2, 1, 6, 3, 5, 4]}, 1219/28452695040000, .4284304170e-10], [{[1, 3, 5, 4, 6, 2], [1, 6, 2, 4, 3, 5]}, 11437/265558487040000, .4306772541e-10], [{[2, 3, 1, 5, 6, 4]}, 1637/ 37936926720000, .4315056968e-10], [{[1, 5, 4, 6, 3, 2], [1, 6, 5, 3, 2, 4]}, 34471/796675461120000, .4326856001e-10], [{[1, 3, 5, 6, 4, 2], [1, 6, 2, 5, 3, 4]}, 17273/398337730560000, .4336270123e-10], [{[1, 5, 6, 3, 4, 2], [1, 6, 4, 5 , 2, 3]}, 34561/796675461120000, .4338152948e-10], [{[2, 1, 5, 6, 4, 3], [2, 1, 6, 5, 3, 4]}, 311/7113173760000, .4372169309e-10], [{[2, 3, 1, 6, 5, 4], [3, 1, 2, 6, 5, 4]}, 3167/72425041920000, .4372796917e-10], [{[2, 1, 4, 5, 6, 3], [2, 1, 6, 3, 4, 5]}, 17471/398337730560000, .4385976688e-10], [{[1, 3, 4, 6, 5, 2], [1, 6, 2, 3, 5, 4]}, 5053/113810780160000, .4439825465e-10], [{[1, 3, 6, 5, 4, 2], [1, 6, 2, 5, 4, 3]}, 1613/36212520960000, .4454260453e-10], [{[3, 2, 1, 6, 5, 4]}, 11899/265558487040000, .4480745516e-10], [{[1, 5, 6, 4, 2, 3]}, 36181/ 796675461120000, .4541497983e-10], [{[1, 4, 5, 6, 3, 2], [1, 6, 5, 2, 3, 4]}, 9049/199168865280000, .4543380808e-10], [{[1, 4, 6, 5, 3, 2], [1, 6, 5, 2, 4, 3 ]}, 9059/199168865280000, .4548401673e-10], [{[1, 4, 5, 2, 3, 6]}, 1741/ 37936926720000, .4589196201e-10], [{[1, 5, 3, 4, 2, 6]}, 6131/132779243520000, .4617438568e-10], [{[1, 4, 5, 3, 2, 6]}, 12487/265558487040000, .4702165666e-10 ], [{[2, 1, 6, 5, 4, 3]}, 521/11064936960000, .4708567269e-10], [{[1, 5, 4, 3, 2, 6]}, 19193/398337730560000, .4818273171e-10], [{[1, 3, 4, 5, 6, 2], [1, 6, 2 , 3, 4, 5]}, 38561/796675461120000, .4840239455e-10], [{[1, 6, 4, 5, 3, 2], [1, 6, 5, 3, 4, 2]}, 38891/796675461120000, .4881661592e-10], [{[1, 3, 5, 4, 2, 6], [1, 4, 3, 5, 2, 6]}, 3551/72425041920000, .4903000269e-10], [{[1, 4, 3, 2, 6, 5 ]}, 19903/398337730560000, .4996513881e-10], [{[1, 5, 6, 4, 3, 2], [1, 6, 5, 4, 2, 3]}, 1217/24141680640000, .5041074058e-10], [{[1, 2, 5, 4, 6, 3], [1, 2, 6, 4, 3, 5]}, 1121/22129873920000, .5065550776e-10], [{[1, 2, 4, 6, 3, 5], [1, 2, 5, 3, 6, 4]}, 20333/398337730560000, .5104462480e-10], [{[1, 2, 5, 6, 3, 4]}, 1699/33194810880000, .5118269859e-10], [{[1, 3, 5, 2, 4, 6], [1, 4, 2, 5, 3, 6] }, 13637/265558487040000, .5135215279e-10], [{[2, 1, 3, 5, 6, 4], [2, 1, 3, 6, 4, 5]}, 10303/199168865280000, .5172997288e-10], [{[2, 1, 3, 6, 5, 4]}, 6917/ 132779243520000, .5209398560e-10], [{[1, 2, 6, 4, 5, 3]}, 20903/398337730560000 , .5247557135e-10], [{[1, 3, 4, 5, 2, 6]}, 14087/265558487040000, .5304669475e-\ 10], [{[1, 3, 4, 2, 6, 5], [1, 4, 2, 3, 6, 5]}, 10589/199168865280000, .\ 5316594029e-10], [{[2, 1, 4, 3, 6, 5]}, 107/2011806720000, .5318602375e-10], [{ [1, 2, 4, 6, 5, 3], [1, 2, 6, 3, 5, 4]}, 3593/66389621760000, .5411990466e-10], [{[1, 2, 5, 6, 4, 3], [1, 2, 6, 5, 3, 4]}, 2701/49792216320000, .5424542629e-10 ], [{[1, 3, 2, 5, 6, 4], [1, 3, 2, 6, 4, 5]}, 43291/796675461120000, .\ 5433956751e-10], [{[1, 3, 2, 6, 5, 4]}, 14467/265558487040000, .5447764130e-10] , [{[1, 2, 4, 5, 6, 3], [1, 2, 6, 3, 4, 5]}, 22103/398337730560000, .5548809039\ e-10], [{[1, 6, 5, 4, 3, 2]}, 101/1806520320000, .5590858784e-10], [{[1, 2, 6, 5, 4, 3]}, 1271/22129873920000, .5743367561e-10], [{[2, 1, 3, 4, 6, 5]}, 169/ 2766234240000, .6109388625e-10], [{[1, 2, 5, 4, 3, 6]}, 24743/398337730560000, .6211563229e-10], [{[1, 2, 3, 5, 6, 4], [1, 2, 3, 6, 4, 5]}, 4243/ 66389621760000, .6391059156e-10], [{[1, 2, 3, 6, 5, 4]}, 25463/398337730560000, .6392314372e-10], [{[1, 3, 2, 4, 6, 5]}, 8551/132779243520000, .6440012590e-10] , [{[1, 2, 4, 5, 3, 6], [1, 2, 5, 3, 4, 6]}, 1451/22129873920000, .6556747703e-\ 10], [{[1, 2, 4, 3, 6, 5]}, 1097/16597405440000, .6609466787e-10], [{[1, 3, 2, 5, 4, 6]}, 1/14929920000, .6697959534e-10], [{[1, 2, 3, 4, 6, 5]}, 3691/ 49792216320000, .7412805199e-10], [{[1, 2, 3, 5, 4, 6]}, 30743/398337730560000, .7717822752e-10], [{[1, 2, 4, 3, 5, 6]}, 1973/24896108160000, .7924933437e-10], [{[1, 2, 3, 4, 5, 6]}, 829/9484231680000, .8740824012e-10]] It took, 0.197, seconds of CPU time