***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St000634 ----------------------------------------------------------------------------- Collection: Posets ----------------------------------------------------------------------------- Description: The number of endomorphisms of a poset. ----------------------------------------------------------------------------- References: [1] Prince, R. Whether a total order set of size $n$ has the fewest endomorphisms among posets of size $n$ [[MathOverflow:252899]] ----------------------------------------------------------------------------- Code: def statistic(P): return len(poset_endomorphisms(P)) def poset_endomorphisms(P): P = P.relabel() r = P.cardinality() S = cartesian_product([range(r)]*r) return [pi for pi in S if P.is_poset_morphism(lambda i: pi[i], P)] ----------------------------------------------------------------------------- Statistic values: ([],2) => 4 ([(0,1)],2) => 3 ([],3) => 27 ([(1,2)],3) => 12 ([(0,1),(0,2)],3) => 11 ([(0,2),(2,1)],3) => 10 ([(0,2),(1,2)],3) => 11 ([],4) => 256 ([(2,3)],4) => 80 ([(1,2),(1,3)],4) => 48 ([(0,1),(0,2),(0,3)],4) => 67 ([(0,2),(0,3),(3,1)],4) => 40 ([(0,1),(0,2),(1,3),(2,3)],4) => 36 ([(1,2),(2,3)],4) => 44 ([(0,3),(3,1),(3,2)],4) => 40 ([(1,3),(2,3)],4) => 48 ([(0,3),(1,3),(3,2)],4) => 40 ([(0,3),(1,3),(2,3)],4) => 67 ([(0,3),(1,2)],4) => 36 ([(0,3),(1,2),(1,3)],4) => 31 ([(0,2),(0,3),(1,2),(1,3)],4) => 36 ([(0,3),(2,1),(3,2)],4) => 35 ([(0,3),(1,2),(2,3)],4) => 40 ([],5) => 3125 ([(3,4)],5) => 750 ([(2,3),(2,4)],5) => 325 ([(1,2),(1,3),(1,4)],5) => 340 ([(0,1),(0,2),(0,3),(0,4)],5) => 629 ([(0,2),(0,3),(0,4),(4,1)],5) => 265 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 167 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 178 ([(1,3),(1,4),(4,2)],5) => 205 ([(0,3),(0,4),(4,1),(4,2)],5) => 221 ([(1,2),(1,3),(2,4),(3,4)],5) => 185 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 133 ([(0,3),(0,4),(3,2),(4,1)],5) => 141 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 135 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 133 ([(2,3),(3,4)],5) => 300 ([(1,4),(4,2),(4,3)],5) => 205 ([(0,4),(4,1),(4,2),(4,3)],5) => 262 ([(2,4),(3,4)],5) => 325 ([(1,4),(2,4),(4,3)],5) => 205 ([(0,4),(1,4),(4,2),(4,3)],5) => 145 ([(1,4),(2,4),(3,4)],5) => 340 ([(0,4),(1,4),(2,4),(4,3)],5) => 262 ([(0,4),(1,4),(2,4),(3,4)],5) => 629 ([(0,4),(1,4),(2,3)],5) => 128 ([(0,4),(1,3),(2,3),(2,4)],5) => 99 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 145 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 197 ([(0,4),(1,4),(2,3),(4,2)],5) => 147 ([(0,4),(1,3),(2,3),(3,4)],5) => 221 ([(0,4),(1,4),(2,3),(2,4)],5) => 151 ([(0,4),(1,4),(2,3),(3,4)],5) => 265 ([(1,4),(2,3)],5) => 245 ([(1,4),(2,3),(2,4)],5) => 160 ([(0,4),(1,2),(1,4),(2,3)],5) => 105 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 135 ([(1,3),(1,4),(2,3),(2,4)],5) => 185 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 130 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 133 ([(0,4),(1,2),(1,4),(4,3)],5) => 129 ([(0,4),(1,2),(1,3)],5) => 128 ([(0,4),(1,2),(1,3),(1,4)],5) => 151 ([(0,2),(0,4),(3,1),(4,3)],5) => 155 ([(0,4),(1,2),(1,3),(3,4)],5) => 128 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 136 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 167 ([(0,3),(0,4),(1,2),(1,4)],5) => 99 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 145 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 197 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 109 ([(0,3),(1,2),(1,4),(3,4)],5) => 105 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 130 ([(1,4),(3,2),(4,3)],5) => 180 ([(0,3),(3,4),(4,1),(4,2)],5) => 147 ([(1,4),(2,3),(3,4)],5) => 205 ([(0,4),(1,2),(2,4),(4,3)],5) => 154 ([(0,3),(1,4),(4,2)],5) => 126 ([(0,4),(3,2),(4,1),(4,3)],5) => 154 ([(0,4),(1,2),(2,3),(2,4)],5) => 129 ([(0,4),(2,3),(3,1),(4,2)],5) => 126 ([(0,3),(1,2),(2,4),(3,4)],5) => 141 ([(0,4),(1,2),(2,3),(3,4)],5) => 155 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 133 ([],6) => 46656 ([(4,5)],6) => 9072 ([(3,4),(3,5)],6) => 3024 ([(2,3),(2,4),(2,5)],6) => 2484 ([(1,2),(1,3),(1,4),(1,5)],6) => 3780 ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 7781 ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 2620 ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 1231 ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 1004 ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 1430 ([(1,3),(1,4),(1,5),(5,2)],6) => 1596 ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 1867 ([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 1008 ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 1074 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 693 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) => 579 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) => 490 ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 533 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 586 ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 611 ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 650 ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => 680 ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => 1053 ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 868 ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 783 ([(2,3),(2,4),(4,5)],6) => 1512 ([(1,4),(1,5),(5,2),(5,3)],6) => 1332 ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 1976 ([(2,3),(2,4),(3,5),(4,5)],6) => 1368 ([(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 804 ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 517 ([(1,4),(1,5),(4,3),(5,2)],6) => 852 ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 816 ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 804 ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 509 ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 477 ([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => 533 ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => 801 ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 901 ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => 652 ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 745 ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 824 ([(3,4),(4,5)],6) => 2808 ([(2,3),(3,4),(3,5)],6) => 1512 ([(1,5),(5,2),(5,3),(5,4)],6) => 1578 ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 2558 ([(2,3),(3,5),(5,4)],6) => 1332 ([(1,4),(4,5),(5,2),(5,3)],6) => 888 ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 1005 ([(3,5),(4,5)],6) => 3024 ([(2,5),(3,5),(5,4)],6) => 1512 ([(1,5),(2,5),(5,3),(5,4)],6) => 876 ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 874 ([(2,5),(3,5),(4,5)],6) => 2484 ([(1,5),(2,5),(3,5),(5,4)],6) => 1578 ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 874 ([(1,5),(2,5),(3,5),(4,5)],6) => 3780 ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 2558 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 7781 ([(0,5),(1,5),(2,5),(3,4)],6) => 760 ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 1005 ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 1976 ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 1291 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2620 ([(1,5),(2,5),(3,4)],6) => 918 ([(1,5),(2,4),(3,4),(3,5)],6) => 600 ([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 406 ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 652 ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 876 ([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) => 472 ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 745 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1188 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 704 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 824 ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 650 ([(1,5),(2,5),(3,4),(5,3)],6) => 888 ([(1,5),(2,4),(3,4),(4,5)],6) => 1332 ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 918 ([(0,5),(1,5),(2,3),(5,4)],6) => 552 ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 555 ([(0,5),(1,5),(2,4),(5,3),(5,4)],6) => 629 ([(1,5),(2,5),(3,4),(3,5)],6) => 912 ([(0,5),(1,5),(2,3),(2,5),(5,4)],6) => 763 ([(0,5),(1,5),(2,3),(2,5),(3,4)],6) => 406 ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 901 ([(0,5),(1,5),(2,3),(2,4)],6) => 400 ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 573 ([(0,4),(1,4),(2,3),(2,5),(4,5)],6) => 561 ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 650 ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 560 ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => 603 ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => 704 ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 493 ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 709 ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 717 ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 650 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1231 ([(1,5),(2,5),(3,4),(4,5)],6) => 1596 ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 1122 ([(0,5),(1,5),(2,3),(3,4)],6) => 425 ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 546 ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 801 ([(0,5),(1,4),(3,5),(4,2),(4,3)],6) => 581 ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 700 ([(0,5),(1,5),(2,3),(3,4),(3,5)],6) => 640 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1045 ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 680 ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 693 ([(0,5),(1,5),(2,4),(3,4)],6) => 484 ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 509 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 970 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 692 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1167 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1782 ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 832 ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 517 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1867 ([(2,5),(3,4)],6) => 2304 ([(2,5),(3,4),(3,5)],6) => 1188 ([(1,5),(2,3),(2,5),(3,4)],6) => 636 ([(0,5),(1,4),(1,5),(4,2),(4,3)],6) => 561 ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 401 ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 427 ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 816 ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 556 ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 378 ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) => 426 ([(2,4),(2,5),(3,4),(3,5)],6) => 1368 ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 786 ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 650 ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 804 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) => 418 ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 427 ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 446 ([(0,4),(0,5),(1,4),(1,5),(2,3)],6) => 473 ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => 538 ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 529 ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 496 ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 562 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 783 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 396 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 524 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 626 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 552 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 471 ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 737 ([(1,5),(2,3),(2,5),(5,4)],6) => 780 ([(0,5),(1,2),(1,5),(5,3),(5,4)],6) => 629 ([(1,5),(2,3),(2,4)],6) => 918 ([(1,5),(2,3),(2,4),(2,5)],6) => 912 ([(0,5),(1,3),(1,4),(1,5),(4,2)],6) => 612 ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 510 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 435 ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 611 ([(0,5),(1,2),(1,3),(1,5),(5,4)],6) => 640 ([(0,5),(1,2),(1,3),(1,4)],6) => 760 ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 1291 ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => 1045 ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 709 ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) => 717 ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 662 ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 774 ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 1004 ([(0,4),(1,2),(1,3),(1,5),(4,5)],6) => 406 ([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) => 472 ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 704 ([(1,3),(1,5),(4,2),(5,4)],6) => 936 ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => 832 ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => 521 ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => 515 ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 500 ([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => 475 ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 481 ([(1,5),(2,3),(2,4),(4,5)],6) => 774 ([(0,5),(1,2),(1,3),(3,5),(5,4)],6) => 581 ([(1,3),(1,4),(2,5),(3,5),(4,2)],6) => 822 ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 519 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1008 ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 700 ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => 418 ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 433 ([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 523 ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 605 ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 605 ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) => 510 ([(0,4),(1,3),(1,5),(5,2)],6) => 517 ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => 963 ([(0,5),(1,3),(1,4),(4,2),(4,5)],6) => 619 ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => 418 ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 550 ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => 504 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 579 ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 496 ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 704 ([(1,4),(1,5),(2,3),(2,5)],6) => 600 ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 876 ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 610 ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) => 523 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1188 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 737 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 502 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 586 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) => 471 ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 421 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 533 ([(0,4),(0,5),(1,3),(1,5),(5,2)],6) => 499 ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 660 ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) => 362 ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) => 470 ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 481 ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => 333 ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => 433 ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) => 466 ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 373 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) => 342 ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) => 490 ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) => 416 ([(0,4),(0,5),(1,2),(1,3)],6) => 484 ([(0,4),(0,5),(1,2),(1,3),(1,5)],6) => 509 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 970 ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 513 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 416 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) => 692 ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 1167 ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 1782 ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 552 ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) => 418 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 524 ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => 388 ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 562 ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 496 ([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => 528 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) => 435 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => 342 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 421 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 502 ([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) => 302 ([(1,4),(2,3),(2,5),(4,5)],6) => 636 ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 500 ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 786 ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 490 ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 509 ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 290 ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 515 ([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) => 362 ([(0,5),(1,3),(1,4),(5,2)],6) => 425 ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => 641 ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 918 ([(0,4),(1,3),(1,5),(4,2),(4,5)],6) => 406 ([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) => 650 ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) => 470 ([(2,5),(3,4),(4,5)],6) => 1512 ([(1,5),(2,3),(3,5),(5,4)],6) => 930 ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 555 ([(1,3),(2,4),(4,5)],6) => 900 ([(1,5),(4,3),(5,2),(5,4)],6) => 930 ([(1,5),(2,3),(3,4),(3,5)],6) => 780 ([(0,5),(1,4),(4,2),(4,5),(5,3)],6) => 523 ([(0,4),(1,5),(5,2),(5,3)],6) => 552 ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 1122 ([(0,5),(1,4),(4,2),(4,3),(4,5)],6) => 763 ([(1,5),(3,4),(4,2),(5,3)],6) => 762 ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 546 ([(1,4),(2,3),(3,5),(4,5)],6) => 852 ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 593 ([(0,5),(1,4),(4,2),(5,3)],6) => 400 ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => 606 ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 378 ([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) => 418 ([(1,5),(2,3),(3,4),(4,5)],6) => 936 ([(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 804 ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 494 ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 606 ([(0,5),(1,4),(2,3)],6) => 729 ([(0,5),(1,3),(2,4),(2,5)],6) => 390 ([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => 410 ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => 440 ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 475 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 388 ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 528 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 868 ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 571 ([(0,5),(1,4),(2,3),(2,4),(4,5)],6) => 619 ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 275 ([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 396 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 626 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) => 234 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) => 417 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 646 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 951 ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 466 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 488 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 513 ([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => 410 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 418 ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 333 ([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 610 ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 440 ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) => 538 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 529 ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 556 ([(0,5),(1,4),(2,3),(2,5),(4,5)],6) => 612 ([(0,5),(1,3),(4,2),(5,4)],6) => 520 ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => 593 ([(0,5),(1,4),(3,2),(4,3),(4,5)],6) => 500 ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) => 533 ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 586 ([(0,5),(1,3),(3,4),(4,2),(4,5)],6) => 571 ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 462 ([(0,5),(1,3),(2,4),(4,5)],6) => 517 ([(0,5),(1,4),(2,3),(3,4),(3,5)],6) => 499 ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 586 ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 963 ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 641 ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 496 ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 521 ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 519 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1053 ----------------------------------------------------------------------------- Created: Oct 24, 2016 at 12:49 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 13, 2022 at 11:36 by Martin Rubey