The characteristic polynomial for the Dimer problem for a 4 by infinity stri\ p is, where z is the activation parameter is the degree 4 polynomial in x 4 2 3 2 2 2 x + 1 - z x - (3 z + 2) x - z x Let's see whether it is the tensor product of two degree-two polynomials true ------------------ The characteristic polynomial for the Dimer problem for a 6 by infinity stri\ p is, where z is the activation parameter is the degree 8 polynomial in x 8 3 7 4 2 6 5 3 5 x + 1 - z x - (6 z + 10 z + 4) x - (5 z + 5 z ) x 6 4 2 4 5 3 3 4 2 2 - (z - 13 z - 20 z - 6) x - (-5 z - 5 z ) x - (6 z + 10 z + 4) x 3 + z x Let's see whether it is the tensor product of three degree-two polynomials true ------------------ The characteristic polynomial for the Dimer problem for a 8 by infinity stri\ p is, where z is the activation parameter is the degree 16 polynomial in x 16 15 4 6 4 2 14 x + 1 - x z - (10 z + 30 z + 28 z + 8) x 8 6 4 13 - (15 z + 35 z + 19 z ) x 10 8 6 4 2 12 - (7 z - 78 z - 300 z - 354 z - 168 z - 28) x 12 10 8 6 4 11 - (z - 75 z - 230 z - 217 z - 63 z ) x 12 10 8 6 4 2 10 - (-15 z + 148 z + 822 z + 1442 z + 1146 z + 420 z + 56) x 12 10 8 6 4 9 - (69 z + 232 z + 303 z + 182 z + 43 z ) x 12 10 8 6 4 2 8 - (-119 z - 642 z - 1673 z - 2304 z - 1644 z - 560 z - 70) x 12 10 8 6 4 7 - (69 z + 232 z + 303 z + 182 z + 43 z ) x 12 10 8 6 4 2 6 - (-15 z + 148 z + 822 z + 1442 z + 1146 z + 420 z + 56) x 12 10 8 6 4 5 - (z - 75 z - 230 z - 217 z - 63 z ) x 10 8 6 4 2 4 - (7 z - 78 z - 300 z - 354 z - 168 z - 28) x 8 6 4 3 6 4 2 2 4 - (15 z + 35 z + 19 z ) x - (10 z + 30 z + 28 z + 8) x - x z Let's see whether it is the tensor product of four degree-two polynomials To speed things up, let's make z=5 true and to be on the safe side, also z=17 true ------------------ The characteristic polynomial for the Dimer problem for a 10 by infinity str\ ip is, where z is the activation parameter is the degree 32 polynomial in x 32 5 31 8 6 4 2 30 1 + x - z x - (15 z + 70 z + 112 z + 72 z + 16) x 11 9 7 5 29 - (35 z + 140 z + 171 z + 65 z ) x - 14 12 10 8 6 4 2 (28 z - 322 z - 2265 z - 5184 z - 5768 z - 3388 z - 1008 z - 120) 28 x 17 15 13 11 9 7 5 27 - (9 z - 566 z - 3215 z - 6692 z - 6587 z - 3087 z - 551 z ) x 20 18 16 14 12 10 - (z - 255 z + 1353 z + 19012 z + 68971 z + 125890 z 8 6 4 2 26 21 + 133221 z + 84938 z + 32032 z + 6552 z + 560) x - (-35 z 19 17 15 13 11 9 + 1984 z + 15158 z + 46708 z + 77312 z + 74348 z + 41517 z 7 5 25 22 20 18 16 + 12474 z + 1561 z ) x - (411 z - 3406 z - 55574 z - 291977 z 14 12 10 8 6 - 829849 z - 1442558 z - 1611098 z - 1174278 z - 552608 z 4 2 24 23 21 19 - 160888 z - 26208 z - 1820) x - (-2164 z - 15597 z - 52968 z 17 15 13 11 9 7 - 105361 z - 129494 z - 99521 z - 47920 z - 14785 z - 3114 z 5 23 24 22 20 18 - 395 z ) x - (5527 z + 61547 z + 386154 z + 1608919 z 16 14 12 10 8 + 4462986 z + 8297046 z + 10472463 z + 9038642 z + 5307687 z 6 4 2 22 25 23 + 2073470 z + 512512 z + 72072 z + 4368) x - (-6907 z - 62987 z 21 19 17 15 13 - 295050 z - 909216 z - 1898966 z - 2657435 z - 2455558 z 11 9 7 5 21 26 - 1463330 z - 535745 z - 108423 z - 9163 z ) x - (4508 z 24 22 20 18 16 - 4591 z - 378657 z - 2676224 z - 9843835 z - 22728088 z 14 12 10 8 6 - 35204576 z - 37654642 z - 28066567 z - 14480232 z - 5043640 z 4 2 20 27 25 23 - 1125124 z - 144144 z - 8008) x - (-1591 z + 41809 z + 525554 z 21 19 17 15 13 + 2582552 z + 7213271 z + 12799308 z + 15047773 z + 11830501 z 11 9 7 5 19 28 + 6121965 z + 1989750 z + 365715 z + 28765 z ) x - (300 z 26 24 22 20 18 - 25078 z - 95157 z + 783883 z + 7101270 z + 25736222 z 16 14 12 10 8 + 55416381 z + 78964798 z + 77734646 z + 53630348 z + 25795557 z 6 4 2 18 29 27 + 8435826 z + 1777776 z + 216216 z + 11440) x - (-28 z + 6237 z 25 23 21 19 17 - 90066 z - 1297784 z - 6358401 z - 17032260 z - 28498360 z 15 13 11 9 7 - 31413624 z - 23177509 z - 11309780 z - 3490046 z - 613764 z 5 17 30 28 26 24 22 - 46563 z ) x - (z - 694 z + 42087 z + 192164 z - 927407 z 20 18 16 14 12 - 9606494 z - 34884094 z - 73719263 z - 102492918 z - 98357116 z 10 8 6 4 2 - 66229900 z - 31153572 z - 9984576 z - 2066064 z - 247104 z - 12870 16 29 27 25 23 21 ) x - (28 z - 6237 z + 90066 z + 1297784 z + 6358401 z 19 17 15 13 11 + 17032260 z + 28498360 z + 31413624 z + 23177509 z + 11309780 z 9 7 5 15 28 26 + 3490046 z + 613764 z + 46563 z ) x - (300 z - 25078 z 24 22 20 18 16 - 95157 z + 783883 z + 7101270 z + 25736222 z + 55416381 z 14 12 10 8 6 + 78964798 z + 77734646 z + 53630348 z + 25795557 z + 8435826 z 4 2 14 27 25 23 + 1777776 z + 216216 z + 11440) x - (1591 z - 41809 z - 525554 z 21 19 17 15 13 - 2582552 z - 7213271 z - 12799308 z - 15047773 z - 11830501 z 11 9 7 5 13 26 - 6121965 z - 1989750 z - 365715 z - 28765 z ) x - (4508 z 24 22 20 18 16 - 4591 z - 378657 z - 2676224 z - 9843835 z - 22728088 z 14 12 10 8 6 - 35204576 z - 37654642 z - 28066567 z - 14480232 z - 5043640 z 4 2 12 25 23 21 - 1125124 z - 144144 z - 8008) x - (6907 z + 62987 z + 295050 z 19 17 15 13 11 + 909216 z + 1898966 z + 2657435 z + 2455558 z + 1463330 z 9 7 5 11 24 22 + 535745 z + 108423 z + 9163 z ) x - (5527 z + 61547 z 20 18 16 14 12 + 386154 z + 1608919 z + 4462986 z + 8297046 z + 10472463 z 10 8 6 4 2 10 + 9038642 z + 5307687 z + 2073470 z + 512512 z + 72072 z + 4368) x 23 21 19 17 15 13 - (2164 z + 15597 z + 52968 z + 105361 z + 129494 z + 99521 z 11 9 7 5 9 22 20 + 47920 z + 14785 z + 3114 z + 395 z ) x - (411 z - 3406 z 18 16 14 12 10 - 55574 z - 291977 z - 829849 z - 1442558 z - 1611098 z 8 6 4 2 8 21 - 1174278 z - 552608 z - 160888 z - 26208 z - 1820) x - (35 z 19 17 15 13 11 9 - 1984 z - 15158 z - 46708 z - 77312 z - 74348 z - 41517 z 7 5 7 20 18 16 14 - 12474 z - 1561 z ) x - (z - 255 z + 1353 z + 19012 z 12 10 8 6 4 2 + 68971 z + 125890 z + 133221 z + 84938 z + 32032 z + 6552 z + 560 6 ) x 17 15 13 11 9 7 5 5 - (-9 z + 566 z + 3215 z + 6692 z + 6587 z + 3087 z + 551 z ) x - 14 12 10 8 6 4 2 (28 z - 322 z - 2265 z - 5184 z - 5768 z - 3388 z - 1008 z - 120) 4 11 9 7 5 3 x - (-35 z - 140 z - 171 z - 65 z ) x 8 6 4 2 2 5 - (15 z + 70 z + 112 z + 72 z + 16) x + z x Let's see whether it is the tensor product of five degree-two polynomials To speed things up, let's make z=5 true and to be on the safe side, also z=17 true ------------------ This took, 16.564, seconds.