***************************************************************************** * 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: St000958 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of Bruhat factorizations of a permutation. This is the number of factorizations $\pi = t_1 \cdots t_\ell$ for transpositions $\{ t_i \mid 1 \leq i \leq \ell\}$ such that the number of inversions of $t_1 \cdots t_i$ equals $i$ for all $1 \leq i \leq \ell$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: @cached_function def bruhat_poset(n): return Permutations(n).bruhat_poset(facade=True) def statistic(pi): P = bruhat_poset(len(pi)) I = P.subposet(P.principal_order_ideal(pi)) return len(I.maximal_chains()) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 1 [2,1] => 1 [1,2,3] => 1 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 2 [3,1,2] => 2 [3,2,1] => 4 [1,2,3,4] => 1 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 4 [2,1,3,4] => 1 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 6 [2,4,1,3] => 6 [2,4,3,1] => 16 [3,1,2,4] => 2 [3,1,4,2] => 6 [3,2,1,4] => 4 [3,2,4,1] => 16 [3,4,1,2] => 20 [3,4,2,1] => 52 [4,1,2,3] => 6 [4,1,3,2] => 16 [4,2,1,3] => 16 [4,2,3,1] => 64 [4,3,1,2] => 52 [4,3,2,1] => 168 [1,2,3,4,5] => 1 [1,2,3,5,4] => 1 [1,2,4,3,5] => 1 [1,2,4,5,3] => 2 [1,2,5,3,4] => 2 [1,2,5,4,3] => 4 [1,3,2,4,5] => 1 [1,3,2,5,4] => 2 [1,3,4,2,5] => 2 [1,3,4,5,2] => 6 [1,3,5,2,4] => 6 [1,3,5,4,2] => 16 [1,4,2,3,5] => 2 [1,4,2,5,3] => 6 [1,4,3,2,5] => 4 [1,4,3,5,2] => 16 [1,4,5,2,3] => 20 [1,4,5,3,2] => 52 [1,5,2,3,4] => 6 [1,5,2,4,3] => 16 [1,5,3,2,4] => 16 [1,5,3,4,2] => 64 [1,5,4,2,3] => 52 [1,5,4,3,2] => 168 [2,1,3,4,5] => 1 [2,1,3,5,4] => 2 [2,1,4,3,5] => 2 [2,1,4,5,3] => 6 [2,1,5,3,4] => 6 [2,1,5,4,3] => 16 [2,3,1,4,5] => 2 [2,3,1,5,4] => 6 [2,3,4,1,5] => 6 [2,3,4,5,1] => 24 [2,3,5,1,4] => 24 [2,3,5,4,1] => 80 [2,4,1,3,5] => 6 [2,4,1,5,3] => 24 [2,4,3,1,5] => 16 [2,4,3,5,1] => 80 [2,4,5,1,3] => 100 [2,4,5,3,1] => 312 [2,5,1,3,4] => 24 [2,5,1,4,3] => 80 [2,5,3,1,4] => 80 [2,5,3,4,1] => 384 [2,5,4,1,3] => 312 [2,5,4,3,1] => 1176 [3,1,2,4,5] => 2 [3,1,2,5,4] => 6 [3,1,4,2,5] => 6 [3,1,4,5,2] => 24 [3,1,5,2,4] => 24 [3,1,5,4,2] => 80 [3,2,1,4,5] => 4 [3,2,1,5,4] => 16 [3,2,4,1,5] => 16 [3,2,4,5,1] => 80 [3,2,5,1,4] => 80 [3,2,5,4,1] => 320 [3,4,1,2,5] => 20 [3,4,1,5,2] => 100 [3,4,2,1,5] => 52 [3,4,2,5,1] => 312 [3,4,5,1,2] => 464 [3,4,5,2,1] => 1408 [3,5,1,2,4] => 100 [3,5,1,4,2] => 424 [3,5,2,1,4] => 312 [3,5,2,4,1] => 1752 [3,5,4,1,2] => 1680 [3,5,4,2,1] => 6016 [4,1,2,3,5] => 6 [4,1,2,5,3] => 24 [4,1,3,2,5] => 16 [4,1,3,5,2] => 80 [4,1,5,2,3] => 100 [4,1,5,3,2] => 312 [4,2,1,3,5] => 16 [4,2,1,5,3] => 80 [4,2,3,1,5] => 64 [4,2,3,5,1] => 384 [4,2,5,1,3] => 424 [4,2,5,3,1] => 1752 [4,3,1,2,5] => 52 [4,3,1,5,2] => 312 [4,3,2,1,5] => 168 [4,3,2,5,1] => 1176 [4,3,5,1,2] => 1680 [4,3,5,2,1] => 6016 [4,5,1,2,3] => 464 [4,5,1,3,2] => 1680 [4,5,2,1,3] => 1680 [4,5,2,3,1] => 9216 [4,5,3,1,2] => 6720 [4,5,3,2,1] => 27968 [5,1,2,3,4] => 24 [5,1,2,4,3] => 80 [5,1,3,2,4] => 80 [5,1,3,4,2] => 384 [5,1,4,2,3] => 312 [5,1,4,3,2] => 1176 [5,2,1,3,4] => 80 [5,2,1,4,3] => 320 [5,2,3,1,4] => 384 [5,2,3,4,1] => 2176 [5,2,4,1,3] => 1752 [5,2,4,3,1] => 8032 [5,3,1,2,4] => 312 [5,3,1,4,2] => 1752 [5,3,2,1,4] => 1176 [5,3,2,4,1] => 8032 [5,3,4,1,2] => 9216 [5,3,4,2,1] => 37312 [5,4,1,2,3] => 1408 [5,4,1,3,2] => 6016 [5,4,2,1,3] => 6016 [5,4,2,3,1] => 37312 [5,4,3,1,2] => 27968 [5,4,3,2,1] => 130560 [1,2,3,4,5,6] => 1 [1,2,3,4,6,5] => 1 [1,2,3,5,4,6] => 1 [1,2,3,5,6,4] => 2 [1,2,3,6,4,5] => 2 [1,2,3,6,5,4] => 4 [1,2,4,3,5,6] => 1 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 2 [1,2,4,5,6,3] => 6 [1,2,4,6,3,5] => 6 [1,2,4,6,5,3] => 16 [1,2,5,3,4,6] => 2 [1,2,5,3,6,4] => 6 [1,2,5,4,3,6] => 4 [1,2,5,4,6,3] => 16 [1,2,5,6,3,4] => 20 [1,2,5,6,4,3] => 52 [1,2,6,3,4,5] => 6 [1,2,6,3,5,4] => 16 [1,2,6,4,3,5] => 16 [1,2,6,4,5,3] => 64 [1,2,6,5,3,4] => 52 [1,2,6,5,4,3] => 168 [1,3,2,4,5,6] => 1 [1,3,2,4,6,5] => 2 [1,3,2,5,4,6] => 2 [1,3,2,5,6,4] => 6 [1,3,2,6,4,5] => 6 [1,3,2,6,5,4] => 16 [1,3,4,2,5,6] => 2 [1,3,4,2,6,5] => 6 [1,3,4,5,2,6] => 6 [1,3,4,5,6,2] => 24 [1,3,4,6,2,5] => 24 [1,3,4,6,5,2] => 80 [1,3,5,2,4,6] => 6 [1,3,5,2,6,4] => 24 [1,3,5,4,2,6] => 16 [1,3,5,4,6,2] => 80 [1,3,5,6,2,4] => 100 [1,3,5,6,4,2] => 312 [1,3,6,2,4,5] => 24 [1,3,6,2,5,4] => 80 [1,3,6,4,2,5] => 80 [1,3,6,4,5,2] => 384 [1,3,6,5,2,4] => 312 [1,3,6,5,4,2] => 1176 [1,4,2,3,5,6] => 2 [1,4,2,3,6,5] => 6 [1,4,2,5,3,6] => 6 [1,4,2,5,6,3] => 24 [1,4,2,6,3,5] => 24 [1,4,2,6,5,3] => 80 [1,4,3,2,5,6] => 4 [1,4,3,2,6,5] => 16 [1,4,3,5,2,6] => 16 [1,4,3,5,6,2] => 80 [1,4,3,6,2,5] => 80 [1,4,3,6,5,2] => 320 [1,4,5,2,3,6] => 20 [1,4,5,2,6,3] => 100 [1,4,5,3,2,6] => 52 [1,4,5,3,6,2] => 312 [1,4,5,6,2,3] => 464 [1,4,5,6,3,2] => 1408 [1,4,6,2,3,5] => 100 [1,4,6,2,5,3] => 424 [1,4,6,3,2,5] => 312 [1,4,6,3,5,2] => 1752 [1,4,6,5,2,3] => 1680 [1,4,6,5,3,2] => 6016 [1,5,2,3,4,6] => 6 [1,5,2,3,6,4] => 24 [1,5,2,4,3,6] => 16 [1,5,2,4,6,3] => 80 [1,5,2,6,3,4] => 100 [1,5,2,6,4,3] => 312 [1,5,3,2,4,6] => 16 [1,5,3,2,6,4] => 80 [1,5,3,4,2,6] => 64 [1,5,3,4,6,2] => 384 [1,5,3,6,2,4] => 424 [1,5,3,6,4,2] => 1752 [1,5,4,2,3,6] => 52 [1,5,4,2,6,3] => 312 [1,5,4,3,2,6] => 168 [1,5,4,3,6,2] => 1176 [1,5,4,6,2,3] => 1680 [1,5,4,6,3,2] => 6016 [1,5,6,2,3,4] => 464 [1,5,6,2,4,3] => 1680 [1,5,6,3,2,4] => 1680 [1,5,6,3,4,2] => 9216 [1,5,6,4,2,3] => 6720 [1,5,6,4,3,2] => 27968 [1,6,2,3,4,5] => 24 [1,6,2,3,5,4] => 80 [1,6,2,4,3,5] => 80 [1,6,2,4,5,3] => 384 [1,6,2,5,3,4] => 312 [1,6,2,5,4,3] => 1176 [1,6,3,2,4,5] => 80 [1,6,3,2,5,4] => 320 [1,6,3,4,2,5] => 384 [1,6,3,4,5,2] => 2176 [1,6,3,5,2,4] => 1752 [1,6,3,5,4,2] => 8032 [1,6,4,2,3,5] => 312 [1,6,4,2,5,3] => 1752 [1,6,4,3,2,5] => 1176 [1,6,4,3,5,2] => 8032 [1,6,4,5,2,3] => 9216 [1,6,4,5,3,2] => 37312 [1,6,5,2,3,4] => 1408 [1,6,5,2,4,3] => 6016 [1,6,5,3,2,4] => 6016 [1,6,5,3,4,2] => 37312 [1,6,5,4,2,3] => 27968 [1,6,5,4,3,2] => 130560 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 2 [2,1,3,5,4,6] => 2 [2,1,3,5,6,4] => 6 [2,1,3,6,4,5] => 6 [2,1,3,6,5,4] => 16 [2,1,4,3,5,6] => 2 [2,1,4,3,6,5] => 6 [2,1,4,5,3,6] => 6 [2,1,4,5,6,3] => 24 [2,1,4,6,3,5] => 24 [2,1,4,6,5,3] => 80 [2,1,5,3,4,6] => 6 [2,1,5,3,6,4] => 24 [2,1,5,4,3,6] => 16 [2,1,5,4,6,3] => 80 [2,1,5,6,3,4] => 100 [2,1,5,6,4,3] => 312 [2,1,6,3,4,5] => 24 [2,1,6,3,5,4] => 80 [2,1,6,4,3,5] => 80 [2,1,6,4,5,3] => 384 [2,1,6,5,3,4] => 312 [2,1,6,5,4,3] => 1176 [2,3,1,4,5,6] => 2 [2,3,1,4,6,5] => 6 [2,3,1,5,4,6] => 6 [2,3,1,5,6,4] => 24 [2,3,1,6,4,5] => 24 [2,3,1,6,5,4] => 80 [2,3,4,1,5,6] => 6 [2,3,4,1,6,5] => 24 [2,3,4,5,1,6] => 24 [2,3,4,5,6,1] => 120 [2,3,4,6,1,5] => 120 [2,3,4,6,5,1] => 480 [2,3,5,1,4,6] => 24 [2,3,5,1,6,4] => 120 [2,3,5,4,1,6] => 80 [2,3,5,4,6,1] => 480 [2,3,5,6,1,4] => 600 [2,3,5,6,4,1] => 2184 [2,3,6,1,4,5] => 120 [2,3,6,1,5,4] => 480 [2,3,6,4,1,5] => 480 [2,3,6,4,5,1] => 2688 [2,3,6,5,1,4] => 2184 [2,3,6,5,4,1] => 9408 [2,4,1,3,5,6] => 6 [2,4,1,3,6,5] => 24 [2,4,1,5,3,6] => 24 [2,4,1,5,6,3] => 120 [2,4,1,6,3,5] => 120 [2,4,1,6,5,3] => 480 [2,4,3,1,5,6] => 16 [2,4,3,1,6,5] => 80 [2,4,3,5,1,6] => 80 [2,4,3,5,6,1] => 480 [2,4,3,6,1,5] => 480 [2,4,3,6,5,1] => 2240 [2,4,5,1,3,6] => 100 [2,4,5,1,6,3] => 600 [2,4,5,3,1,6] => 312 [2,4,5,3,6,1] => 2184 [2,4,5,6,1,3] => 3248 [2,4,5,6,3,1] => 11264 [2,4,6,1,3,5] => 600 [2,4,6,1,5,3] => 2968 [2,4,6,3,1,5] => 2184 [2,4,6,3,5,1] => 14016 [2,4,6,5,1,3] => 13440 [2,4,6,5,3,1] => 54144 [2,5,1,3,4,6] => 24 [2,5,1,3,6,4] => 120 [2,5,1,4,3,6] => 80 [2,5,1,4,6,3] => 480 [2,5,1,6,3,4] => 600 [2,5,1,6,4,3] => 2184 [2,5,3,1,4,6] => 80 [2,5,3,1,6,4] => 480 [2,5,3,4,1,6] => 384 [2,5,3,4,6,1] => 2688 [2,5,3,6,1,4] => 2968 [2,5,3,6,4,1] => 14016 [2,5,4,1,3,6] => 312 [2,5,4,1,6,3] => 2184 [2,5,4,3,1,6] => 1176 [2,5,4,3,6,1] => 9408 [2,5,4,6,1,3] => 13440 [2,5,4,6,3,1] => 54144 [2,5,6,1,3,4] => 3248 [2,5,6,1,4,3] => 13440 [2,5,6,3,1,4] => 13440 [2,5,6,3,4,1] => 82944 [2,5,6,4,1,3] => 60480 [2,5,6,4,3,1] => 279680 [2,6,1,3,4,5] => 120 [2,6,1,3,5,4] => 480 [2,6,1,4,3,5] => 480 [2,6,1,4,5,3] => 2688 [2,6,1,5,3,4] => 2184 [2,6,1,5,4,3] => 9408 [2,6,3,1,4,5] => 480 [2,6,3,1,5,4] => 2240 [2,6,3,4,1,5] => 2688 [2,6,3,4,5,1] => 17408 [2,6,3,5,1,4] => 14016 [2,6,3,5,4,1] => 72288 [2,6,4,1,3,5] => 2184 [2,6,4,1,5,3] => 14016 [2,6,4,3,1,5] => 9408 [2,6,4,3,5,1] => 72288 [2,6,4,5,1,3] => 82944 [2,6,4,5,3,1] => 373120 [2,6,5,1,3,4] => 11264 [2,6,5,1,4,3] => 54144 [2,6,5,3,1,4] => 54144 [2,6,5,3,4,1] => 373120 [2,6,5,4,1,3] => 279680 [2,6,5,4,3,1] => 1436160 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 6 [3,1,2,5,4,6] => 6 [3,1,2,5,6,4] => 24 [3,1,2,6,4,5] => 24 [3,1,2,6,5,4] => 80 [3,1,4,2,5,6] => 6 [3,1,4,2,6,5] => 24 [3,1,4,5,2,6] => 24 [3,1,4,5,6,2] => 120 [3,1,4,6,2,5] => 120 [3,1,4,6,5,2] => 480 [3,1,5,2,4,6] => 24 [3,1,5,2,6,4] => 120 [3,1,5,4,2,6] => 80 [3,1,5,4,6,2] => 480 [3,1,5,6,2,4] => 600 [3,1,5,6,4,2] => 2184 [3,1,6,2,4,5] => 120 [3,1,6,2,5,4] => 480 [3,1,6,4,2,5] => 480 [3,1,6,4,5,2] => 2688 [3,1,6,5,2,4] => 2184 [3,1,6,5,4,2] => 9408 [3,2,1,4,5,6] => 4 [3,2,1,4,6,5] => 16 [3,2,1,5,4,6] => 16 [3,2,1,5,6,4] => 80 [3,2,1,6,4,5] => 80 [3,2,1,6,5,4] => 320 [3,2,4,1,5,6] => 16 [3,2,4,1,6,5] => 80 [3,2,4,5,1,6] => 80 [3,2,4,5,6,1] => 480 [3,2,4,6,1,5] => 480 [3,2,4,6,5,1] => 2240 [3,2,5,1,4,6] => 80 [3,2,5,1,6,4] => 480 [3,2,5,4,1,6] => 320 [3,2,5,4,6,1] => 2240 [3,2,5,6,1,4] => 2800 [3,2,5,6,4,1] => 11648 [3,2,6,1,4,5] => 480 [3,2,6,1,5,4] => 2240 [3,2,6,4,1,5] => 2240 [3,2,6,4,5,1] => 14336 [3,2,6,5,1,4] => 11648 [3,2,6,5,4,1] => 56448 [3,4,1,2,5,6] => 20 [3,4,1,2,6,5] => 100 [3,4,1,5,2,6] => 100 [3,4,1,5,6,2] => 600 [3,4,1,6,2,5] => 600 [3,4,1,6,5,2] => 2800 [3,4,2,1,5,6] => 52 [3,4,2,1,6,5] => 312 [3,4,2,5,1,6] => 312 [3,4,2,5,6,1] => 2184 [3,4,2,6,1,5] => 2184 [3,4,2,6,5,1] => 11648 [3,4,5,1,2,6] => 464 [3,4,5,1,6,2] => 3248 [3,4,5,2,1,6] => 1408 [3,4,5,2,6,1] => 11264 [3,4,5,6,1,2] => 19280 [3,4,5,6,2,1] => 65104 [3,4,6,1,2,5] => 3248 [3,4,6,1,5,2] => 18944 [3,4,6,2,1,5] => 11264 [3,4,6,2,5,1] => 81472 [3,4,6,5,1,2] => 90000 [3,4,6,5,2,1] => 347168 [3,5,1,2,4,6] => 100 [3,5,1,2,6,4] => 600 [3,5,1,4,2,6] => 424 [3,5,1,4,6,2] => 2968 [3,5,1,6,2,4] => 3568 [3,5,1,6,4,2] => 15456 [3,5,2,1,4,6] => 312 [3,5,2,1,6,4] => 2184 [3,5,2,4,1,6] => 1752 [3,5,2,4,6,1] => 14016 [3,5,2,6,1,4] => 15456 [3,5,2,6,4,1] => 82240 [3,5,4,1,2,6] => 1680 [3,5,4,1,6,2] => 13440 [3,5,4,2,1,6] => 6016 [3,5,4,2,6,1] => 54144 [3,5,4,6,1,2] => 89104 [3,5,4,6,2,1] => 344736 [3,5,6,1,2,4] => 20032 [3,5,6,1,4,2] => 99936 [3,5,6,2,1,4] => 77856 [3,5,6,2,4,1] => 535040 [3,5,6,4,1,2] => 445344 [3,5,6,4,2,1] => 1951968 [3,6,1,2,4,5] => 600 [3,6,1,2,5,4] => 2800 [3,6,1,4,2,5] => 2968 [3,6,1,4,5,2] => 19088 [3,6,1,5,2,4] => 15456 [3,6,1,5,4,2] => 76848 [3,6,2,1,4,5] => 2184 [3,6,2,1,5,4] => 11648 [3,6,2,4,1,5] => 14016 [3,6,2,4,5,1] => 102160 [3,6,2,5,1,4] => 82240 [3,6,2,5,4,1] => 472224 [3,6,4,1,2,5] => 13440 [3,6,4,1,5,2] => 98608 [3,6,4,2,1,5] => 54144 [3,6,4,2,5,1] => 462816 [3,6,4,5,1,2] => 611200 [3,6,4,5,2,1] => 2611264 [3,6,5,1,2,4] => 77856 [3,6,5,1,4,2] => 444704 [3,6,5,2,1,4] => 346240 [3,6,5,2,4,1] => 2634144 [3,6,5,4,1,2] => 2257728 [3,6,5,4,2,1] => 10891264 [4,1,2,3,5,6] => 6 [4,1,2,3,6,5] => 24 [4,1,2,5,3,6] => 24 [4,1,2,5,6,3] => 120 [4,1,2,6,3,5] => 120 [4,1,2,6,5,3] => 480 [4,1,3,2,5,6] => 16 [4,1,3,2,6,5] => 80 [4,1,3,5,2,6] => 80 [4,1,3,5,6,2] => 480 [4,1,3,6,2,5] => 480 [4,1,3,6,5,2] => 2240 [4,1,5,2,3,6] => 100 [4,1,5,2,6,3] => 600 [4,1,5,3,2,6] => 312 [4,1,5,3,6,2] => 2184 [4,1,5,6,2,3] => 3248 [4,1,5,6,3,2] => 11264 [4,1,6,2,3,5] => 600 [4,1,6,2,5,3] => 2968 [4,1,6,3,2,5] => 2184 [4,1,6,3,5,2] => 14016 [4,1,6,5,2,3] => 13440 [4,1,6,5,3,2] => 54144 [4,2,1,3,5,6] => 16 [4,2,1,3,6,5] => 80 [4,2,1,5,3,6] => 80 [4,2,1,5,6,3] => 480 [4,2,1,6,3,5] => 480 [4,2,1,6,5,3] => 2240 [4,2,3,1,5,6] => 64 [4,2,3,1,6,5] => 384 [4,2,3,5,1,6] => 384 [4,2,3,5,6,1] => 2688 [4,2,3,6,1,5] => 2688 [4,2,3,6,5,1] => 14336 [4,2,5,1,3,6] => 424 [4,2,5,1,6,3] => 2968 [4,2,5,3,1,6] => 1752 [4,2,5,3,6,1] => 14016 [4,2,5,6,1,3] => 18944 [4,2,5,6,3,1] => 81472 [4,2,6,1,3,5] => 2968 [4,2,6,1,5,3] => 16352 [4,2,6,3,1,5] => 14016 [4,2,6,3,5,1] => 101088 [4,2,6,5,1,3] => 87840 [4,2,6,5,3,1] => 435136 [4,3,1,2,5,6] => 52 [4,3,1,2,6,5] => 312 [4,3,1,5,2,6] => 312 [4,3,1,5,6,2] => 2184 [4,3,1,6,2,5] => 2184 [4,3,1,6,5,2] => 11648 [4,3,2,1,5,6] => 168 [4,3,2,1,6,5] => 1176 [4,3,2,5,1,6] => 1176 [4,3,2,5,6,1] => 9408 [4,3,2,6,1,5] => 9408 [4,3,2,6,5,1] => 56448 [4,3,5,1,2,6] => 1680 [4,3,5,1,6,2] => 13440 [4,3,5,2,1,6] => 6016 [4,3,5,2,6,1] => 54144 [4,3,5,6,1,2] => 90000 [4,3,5,6,2,1] => 347168 [4,3,6,1,2,5] => 13440 [4,3,6,1,5,2] => 87840 [4,3,6,2,1,5] => 54144 [4,3,6,2,5,1] => 435136 [4,3,6,5,1,2] => 463968 [4,3,6,5,2,1] => 2028576 [4,5,1,2,3,6] => 464 [4,5,1,2,6,3] => 3248 [4,5,1,3,2,6] => 1680 [4,5,1,3,6,2] => 13440 [4,5,1,6,2,3] => 20032 [4,5,1,6,3,2] => 77856 [4,5,2,1,3,6] => 1680 [4,5,2,1,6,3] => 13440 [4,5,2,3,1,6] => 9216 [4,5,2,3,6,1] => 82944 [4,5,2,6,1,3] => 99936 [4,5,2,6,3,1] => 535040 [4,5,3,1,2,6] => 6720 [4,5,3,1,6,2] => 60480 [4,5,3,2,1,6] => 27968 [4,5,3,2,6,1] => 279680 [4,5,3,6,1,2] => 445344 [4,5,3,6,2,1] => 1951968 [4,5,6,1,2,3] => 123616 [4,5,6,1,3,2] => 531840 [4,5,6,2,1,3] => 531840 [4,5,6,2,3,1] => 3563392 [4,5,6,3,1,2] => 2418336 [4,5,6,3,2,1] => 11914240 [4,6,1,2,3,5] => 3248 [4,6,1,2,5,3] => 18944 [4,6,1,3,2,5] => 13440 [4,6,1,3,5,2] => 98608 [4,6,1,5,2,3] => 99936 [4,6,1,5,3,2] => 444704 [4,6,2,1,3,5] => 13440 [4,6,2,1,5,3] => 87840 [4,6,2,3,1,5] => 82944 [4,6,2,3,5,1] => 684320 [4,6,2,5,1,3] => 623680 [4,6,2,5,3,1] => 3568224 [4,6,3,1,2,5] => 60480 [4,6,3,1,5,2] => 493856 [4,6,3,2,1,5] => 279680 [4,6,3,2,5,1] => 2635488 [4,6,3,5,1,2] => 3362432 [4,6,3,5,2,1] => 16157952 [4,6,5,1,2,3] => 531840 [4,6,5,1,3,2] => 2577504 [4,6,5,2,1,3] => 2592960 [4,6,5,2,3,1] => 19007872 [4,6,5,3,1,2] => 13208960 [4,6,5,3,2,1] => 71180288 [5,1,2,3,4,6] => 24 [5,1,2,3,6,4] => 120 [5,1,2,4,3,6] => 80 [5,1,2,4,6,3] => 480 [5,1,2,6,3,4] => 600 [5,1,2,6,4,3] => 2184 [5,1,3,2,4,6] => 80 [5,1,3,2,6,4] => 480 [5,1,3,4,2,6] => 384 [5,1,3,4,6,2] => 2688 [5,1,3,6,2,4] => 2968 [5,1,3,6,4,2] => 14016 [5,1,4,2,3,6] => 312 [5,1,4,2,6,3] => 2184 [5,1,4,3,2,6] => 1176 [5,1,4,3,6,2] => 9408 [5,1,4,6,2,3] => 13440 [5,1,4,6,3,2] => 54144 [5,1,6,2,3,4] => 3248 [5,1,6,2,4,3] => 13440 [5,1,6,3,2,4] => 13440 [5,1,6,3,4,2] => 82944 [5,1,6,4,2,3] => 60480 [5,1,6,4,3,2] => 279680 [5,2,1,3,4,6] => 80 [5,2,1,3,6,4] => 480 [5,2,1,4,3,6] => 320 [5,2,1,4,6,3] => 2240 [5,2,1,6,3,4] => 2800 [5,2,1,6,4,3] => 11648 [5,2,3,1,4,6] => 384 [5,2,3,1,6,4] => 2688 [5,2,3,4,1,6] => 2176 [5,2,3,4,6,1] => 17408 [5,2,3,6,1,4] => 19088 [5,2,3,6,4,1] => 102160 [5,2,4,1,3,6] => 1752 [5,2,4,1,6,3] => 14016 [5,2,4,3,1,6] => 8032 [5,2,4,3,6,1] => 72288 [5,2,4,6,1,3] => 98608 [5,2,4,6,3,1] => 462816 [5,2,6,1,3,4] => 18944 [5,2,6,1,4,3] => 87840 [5,2,6,3,1,4] => 98608 [5,2,6,3,4,1] => 684320 [5,2,6,4,1,3] => 493856 [5,2,6,4,3,1] => 2635488 [5,3,1,2,4,6] => 312 [5,3,1,2,6,4] => 2184 [5,3,1,4,2,6] => 1752 [5,3,1,4,6,2] => 14016 [5,3,1,6,2,4] => 15456 [5,3,1,6,4,2] => 82240 [5,3,2,1,4,6] => 1176 [5,3,2,1,6,4] => 9408 [5,3,2,4,1,6] => 8032 [5,3,2,4,6,1] => 72288 [5,3,2,6,1,4] => 76848 [5,3,2,6,4,1] => 472224 [5,3,4,1,2,6] => 9216 [5,3,4,1,6,2] => 82944 [5,3,4,2,1,6] => 37312 [5,3,4,2,6,1] => 373120 [5,3,4,6,1,2] => 611200 [5,3,4,6,2,1] => 2611264 [5,3,6,1,2,4] => 99936 [5,3,6,1,4,2] => 623680 [5,3,6,2,1,4] => 444704 [5,3,6,2,4,1] => 3568224 [5,3,6,4,1,2] => 3362432 [5,3,6,4,2,1] => 16157952 [5,4,1,2,3,6] => 1408 [5,4,1,2,6,3] => 11264 [5,4,1,3,2,6] => 6016 [5,4,1,3,6,2] => 54144 [5,4,1,6,2,3] => 77856 [5,4,1,6,3,2] => 346240 [5,4,2,1,3,6] => 6016 [5,4,2,1,6,3] => 54144 [5,4,2,3,1,6] => 37312 [5,4,2,3,6,1] => 373120 [5,4,2,6,1,3] => 444704 [5,4,2,6,3,1] => 2634144 [5,4,3,1,2,6] => 27968 [5,4,3,1,6,2] => 279680 [5,4,3,2,1,6] => 130560 [5,4,3,2,6,1] => 1436160 [5,4,3,6,1,2] => 2257728 [5,4,3,6,2,1] => 10891264 [5,4,6,1,2,3] => 531840 [5,4,6,1,3,2] => 2592960 [5,4,6,2,1,3] => 2577504 [5,4,6,2,3,1] => 19007872 ----------------------------------------------------------------------------- Created: Aug 28, 2017 at 11:08 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Mar 12, 2026 at 17:42 by Nupur Jain