***************************************************************************** * 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: St000255 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of reduced Kogan faces with the permutation as type. This is equivalent to finding the number of ways to represent the permutation $\pi \in S_{n+1}$ as a reduced subword of $s_n (s_{n-1} s_n) (s_{n-2} s_{n-1} s_n) \dotsm (s_1 \dotsm s_n)$. ----------------------------------------------------------------------------- References: [1] Kirichenko, V. A., Smirnov, E. Y., Timorin, V. A. Schubert calculus and Gelfand-Zetlin polytopes [[DOI:10.1070/rm2012v067n04abeh004804]] [[arXiv:1101.0278]] ----------------------------------------------------------------------------- Code: def statistic(pi): n = len(pi) if pi == Permutations(n).one(): return 1 else: S = Word([j for i in range(n, 0, -1) for j in range(i, n+1)]) return sum(Word(w).nb_subword_occurrences_in(S) for w in pi.reduced_words()) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 1 [2,1] => 1 [1,2,3] => 1 [1,3,2] => 2 [2,1,3] => 1 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 1 [1,2,3,4] => 1 [1,2,4,3] => 3 [1,3,2,4] => 2 [1,3,4,2] => 3 [1,4,2,3] => 3 [1,4,3,2] => 5 [2,1,3,4] => 1 [2,1,4,3] => 3 [2,3,1,4] => 1 [2,3,4,1] => 1 [2,4,1,3] => 2 [2,4,3,1] => 2 [3,1,2,4] => 1 [3,1,4,2] => 2 [3,2,1,4] => 1 [3,2,4,1] => 1 [3,4,1,2] => 1 [3,4,2,1] => 1 [4,1,2,3] => 1 [4,1,3,2] => 2 [4,2,1,3] => 1 [4,2,3,1] => 1 [4,3,1,2] => 1 [4,3,2,1] => 1 [1,2,3,4,5] => 1 [1,2,3,5,4] => 4 [1,2,4,3,5] => 3 [1,2,4,5,3] => 6 [1,2,5,3,4] => 6 [1,2,5,4,3] => 14 [1,3,2,4,5] => 2 [1,3,2,5,4] => 8 [1,3,4,2,5] => 3 [1,3,4,5,2] => 4 [1,3,5,2,4] => 8 [1,3,5,4,2] => 11 [1,4,2,3,5] => 3 [1,4,2,5,3] => 8 [1,4,3,2,5] => 5 [1,4,3,5,2] => 7 [1,4,5,2,3] => 6 [1,4,5,3,2] => 9 [1,5,2,3,4] => 4 [1,5,2,4,3] => 11 [1,5,3,2,4] => 7 [1,5,3,4,2] => 10 [1,5,4,2,3] => 9 [1,5,4,3,2] => 14 [2,1,3,4,5] => 1 [2,1,3,5,4] => 4 [2,1,4,3,5] => 3 [2,1,4,5,3] => 6 [2,1,5,3,4] => 6 [2,1,5,4,3] => 14 [2,3,1,4,5] => 1 [2,3,1,5,4] => 4 [2,3,4,1,5] => 1 [2,3,4,5,1] => 1 [2,3,5,1,4] => 3 [2,3,5,4,1] => 3 [2,4,1,3,5] => 2 [2,4,1,5,3] => 5 [2,4,3,1,5] => 2 [2,4,3,5,1] => 2 [2,4,5,1,3] => 3 [2,4,5,3,1] => 3 [2,5,1,3,4] => 3 [2,5,1,4,3] => 8 [2,5,3,1,4] => 3 [2,5,3,4,1] => 3 [2,5,4,1,3] => 5 [2,5,4,3,1] => 5 [3,1,2,4,5] => 1 [3,1,2,5,4] => 4 [3,1,4,2,5] => 2 [3,1,4,5,2] => 3 [3,1,5,2,4] => 5 [3,1,5,4,2] => 8 [3,2,1,4,5] => 1 [3,2,1,5,4] => 4 [3,2,4,1,5] => 1 [3,2,4,5,1] => 1 [3,2,5,1,4] => 3 [3,2,5,4,1] => 3 [3,4,1,2,5] => 1 [3,4,1,5,2] => 2 [3,4,2,1,5] => 1 [3,4,2,5,1] => 1 [3,4,5,1,2] => 1 [3,4,5,2,1] => 1 [3,5,1,2,4] => 2 [3,5,1,4,2] => 4 [3,5,2,1,4] => 2 [3,5,2,4,1] => 2 [3,5,4,1,2] => 2 [3,5,4,2,1] => 2 [4,1,2,3,5] => 1 [4,1,2,5,3] => 3 [4,1,3,2,5] => 2 [4,1,3,5,2] => 3 [4,1,5,2,3] => 3 [4,1,5,3,2] => 5 [4,2,1,3,5] => 1 [4,2,1,5,3] => 3 [4,2,3,1,5] => 1 [4,2,3,5,1] => 1 [4,2,5,1,3] => 2 [4,2,5,3,1] => 2 [4,3,1,2,5] => 1 [4,3,1,5,2] => 2 [4,3,2,1,5] => 1 [4,3,2,5,1] => 1 [4,3,5,1,2] => 1 [4,3,5,2,1] => 1 [4,5,1,2,3] => 1 [4,5,1,3,2] => 2 [4,5,2,1,3] => 1 [4,5,2,3,1] => 1 [4,5,3,1,2] => 1 [4,5,3,2,1] => 1 [5,1,2,3,4] => 1 [5,1,2,4,3] => 3 [5,1,3,2,4] => 2 [5,1,3,4,2] => 3 [5,1,4,2,3] => 3 [5,1,4,3,2] => 5 [5,2,1,3,4] => 1 [5,2,1,4,3] => 3 [5,2,3,1,4] => 1 [5,2,3,4,1] => 1 [5,2,4,1,3] => 2 [5,2,4,3,1] => 2 [5,3,1,2,4] => 1 [5,3,1,4,2] => 2 [5,3,2,1,4] => 1 [5,3,2,4,1] => 1 [5,3,4,1,2] => 1 [5,3,4,2,1] => 1 [5,4,1,2,3] => 1 [5,4,1,3,2] => 2 [5,4,2,1,3] => 1 [5,4,2,3,1] => 1 [5,4,3,1,2] => 1 [5,4,3,2,1] => 1 [1,2,3,4,5,6] => 1 [1,2,3,4,6,5] => 5 [1,2,3,5,4,6] => 4 [1,2,3,5,6,4] => 10 [1,2,3,6,4,5] => 10 [1,2,3,6,5,4] => 30 [1,2,4,3,5,6] => 3 [1,2,4,3,6,5] => 15 [1,2,4,5,3,6] => 6 [1,2,4,5,6,3] => 10 [1,2,4,6,3,5] => 20 [1,2,4,6,5,3] => 35 [1,2,5,3,4,6] => 6 [1,2,5,3,6,4] => 20 [1,2,5,4,3,6] => 14 [1,2,5,4,6,3] => 25 [1,2,5,6,3,4] => 20 [1,2,5,6,4,3] => 40 [1,2,6,3,4,5] => 10 [1,2,6,3,5,4] => 35 [1,2,6,4,3,5] => 25 [1,2,6,4,5,3] => 46 [1,2,6,5,3,4] => 40 [1,2,6,5,4,3] => 84 [1,3,2,4,5,6] => 2 [1,3,2,4,6,5] => 10 [1,3,2,5,4,6] => 8 [1,3,2,5,6,4] => 20 [1,3,2,6,4,5] => 20 [1,3,2,6,5,4] => 60 [1,3,4,2,5,6] => 3 [1,3,4,2,6,5] => 15 [1,3,4,5,2,6] => 4 [1,3,4,5,6,2] => 5 [1,3,4,6,2,5] => 15 [1,3,4,6,5,2] => 19 [1,3,5,2,4,6] => 8 [1,3,5,2,6,4] => 25 [1,3,5,4,2,6] => 11 [1,3,5,4,6,2] => 14 [1,3,5,6,2,4] => 20 [1,3,5,6,4,2] => 26 [1,3,6,2,4,5] => 15 [1,3,6,2,5,4] => 51 [1,3,6,4,2,5] => 21 [1,3,6,4,5,2] => 27 [1,3,6,5,2,4] => 44 [1,3,6,5,4,2] => 58 [1,4,2,3,5,6] => 3 [1,4,2,3,6,5] => 15 [1,4,2,5,3,6] => 8 [1,4,2,5,6,3] => 15 [1,4,2,6,3,5] => 25 [1,4,2,6,5,3] => 51 [1,4,3,2,5,6] => 5 [1,4,3,2,6,5] => 25 [1,4,3,5,2,6] => 7 [1,4,3,5,6,2] => 9 [1,4,3,6,2,5] => 26 [1,4,3,6,5,2] => 34 [1,4,5,2,3,6] => 6 [1,4,5,2,6,3] => 15 [1,4,5,3,2,6] => 9 [1,4,5,3,6,2] => 12 [1,4,5,6,2,3] => 10 [1,4,5,6,3,2] => 14 [1,4,6,2,3,5] => 15 [1,4,6,2,5,3] => 38 [1,4,6,3,2,5] => 23 [1,4,6,3,5,2] => 31 [1,4,6,5,2,3] => 26 [1,4,6,5,3,2] => 37 [1,5,2,3,4,6] => 4 [1,5,2,3,6,4] => 15 [1,5,2,4,3,6] => 11 [1,5,2,4,6,3] => 21 [1,5,2,6,3,4] => 20 [1,5,2,6,4,3] => 44 [1,5,3,2,4,6] => 7 [1,5,3,2,6,4] => 26 [1,5,3,4,2,6] => 10 [1,5,3,4,6,2] => 13 [1,5,3,6,2,4] => 24 [1,5,3,6,4,2] => 32 [1,5,4,2,3,6] => 9 [1,5,4,2,6,3] => 23 [1,5,4,3,2,6] => 14 [1,5,4,3,6,2] => 19 [1,5,4,6,2,3] => 16 [1,5,4,6,3,2] => 23 [1,5,6,2,3,4] => 10 [1,5,6,2,4,3] => 26 [1,5,6,3,2,4] => 16 [1,5,6,3,4,2] => 22 [1,5,6,4,2,3] => 19 [1,5,6,4,3,2] => 28 [1,6,2,3,4,5] => 5 [1,6,2,3,5,4] => 19 [1,6,2,4,3,5] => 14 [1,6,2,4,5,3] => 27 [1,6,2,5,3,4] => 26 [1,6,2,5,4,3] => 58 [1,6,3,2,4,5] => 9 [1,6,3,2,5,4] => 34 [1,6,3,4,2,5] => 13 [1,6,3,4,5,2] => 17 [1,6,3,5,2,4] => 32 [1,6,3,5,4,2] => 43 [1,6,4,2,3,5] => 12 [1,6,4,2,5,3] => 31 [1,6,4,3,2,5] => 19 [1,6,4,3,5,2] => 26 [1,6,4,5,2,3] => 22 [1,6,4,5,3,2] => 32 [1,6,5,2,3,4] => 14 [1,6,5,2,4,3] => 37 [1,6,5,3,2,4] => 23 [1,6,5,3,4,2] => 32 [1,6,5,4,2,3] => 28 [1,6,5,4,3,2] => 42 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 5 [2,1,3,5,4,6] => 4 [2,1,3,5,6,4] => 10 [2,1,3,6,4,5] => 10 [2,1,3,6,5,4] => 30 [2,1,4,3,5,6] => 3 [2,1,4,3,6,5] => 15 [2,1,4,5,3,6] => 6 [2,1,4,5,6,3] => 10 [2,1,4,6,3,5] => 20 [2,1,4,6,5,3] => 35 [2,1,5,3,4,6] => 6 [2,1,5,3,6,4] => 20 [2,1,5,4,3,6] => 14 [2,1,5,4,6,3] => 25 [2,1,5,6,3,4] => 20 [2,1,5,6,4,3] => 40 [2,1,6,3,4,5] => 10 [2,1,6,3,5,4] => 35 [2,1,6,4,3,5] => 25 [2,1,6,4,5,3] => 46 [2,1,6,5,3,4] => 40 [2,1,6,5,4,3] => 84 [2,3,1,4,5,6] => 1 [2,3,1,4,6,5] => 5 [2,3,1,5,4,6] => 4 [2,3,1,5,6,4] => 10 [2,3,1,6,4,5] => 10 [2,3,1,6,5,4] => 30 [2,3,4,1,5,6] => 1 [2,3,4,1,6,5] => 5 [2,3,4,5,1,6] => 1 [2,3,4,5,6,1] => 1 [2,3,4,6,1,5] => 4 [2,3,4,6,5,1] => 4 [2,3,5,1,4,6] => 3 [2,3,5,1,6,4] => 9 [2,3,5,4,1,6] => 3 [2,3,5,4,6,1] => 3 [2,3,5,6,1,4] => 6 [2,3,5,6,4,1] => 6 [2,3,6,1,4,5] => 6 [2,3,6,1,5,4] => 20 [2,3,6,4,1,5] => 6 [2,3,6,4,5,1] => 6 [2,3,6,5,1,4] => 14 [2,3,6,5,4,1] => 14 [2,4,1,3,5,6] => 2 [2,4,1,3,6,5] => 10 [2,4,1,5,3,6] => 5 [2,4,1,5,6,3] => 9 [2,4,1,6,3,5] => 16 [2,4,1,6,5,3] => 31 [2,4,3,1,5,6] => 2 [2,4,3,1,6,5] => 10 [2,4,3,5,1,6] => 2 [2,4,3,5,6,1] => 2 [2,4,3,6,1,5] => 8 [2,4,3,6,5,1] => 8 [2,4,5,1,3,6] => 3 [2,4,5,1,6,3] => 7 [2,4,5,3,1,6] => 3 [2,4,5,3,6,1] => 3 [2,4,5,6,1,3] => 4 [2,4,5,6,3,1] => 4 [2,4,6,1,3,5] => 8 [2,4,6,1,5,3] => 19 [2,4,6,3,1,5] => 8 [2,4,6,3,5,1] => 8 [2,4,6,5,1,3] => 11 [2,4,6,5,3,1] => 11 [2,5,1,3,4,6] => 3 [2,5,1,3,6,4] => 11 [2,5,1,4,3,6] => 8 [2,5,1,4,6,3] => 15 [2,5,1,6,3,4] => 14 [2,5,1,6,4,3] => 30 [2,5,3,1,4,6] => 3 [2,5,3,1,6,4] => 11 [2,5,3,4,1,6] => 3 [2,5,3,4,6,1] => 3 [2,5,3,6,1,4] => 8 [2,5,3,6,4,1] => 8 [2,5,4,1,3,6] => 5 [2,5,4,1,6,3] => 12 [2,5,4,3,1,6] => 5 [2,5,4,3,6,1] => 5 [2,5,4,6,1,3] => 7 [2,5,4,6,3,1] => 7 [2,5,6,1,3,4] => 6 [2,5,6,1,4,3] => 15 [2,5,6,3,1,4] => 6 [2,5,6,3,4,1] => 6 [2,5,6,4,1,3] => 9 [2,5,6,4,3,1] => 9 [2,6,1,3,4,5] => 4 [2,6,1,3,5,4] => 15 [2,6,1,4,3,5] => 11 [2,6,1,4,5,3] => 21 [2,6,1,5,3,4] => 20 [2,6,1,5,4,3] => 44 [2,6,3,1,4,5] => 4 [2,6,3,1,5,4] => 15 [2,6,3,4,1,5] => 4 [2,6,3,4,5,1] => 4 [2,6,3,5,1,4] => 11 [2,6,3,5,4,1] => 11 [2,6,4,1,3,5] => 7 [2,6,4,1,5,3] => 17 [2,6,4,3,1,5] => 7 [2,6,4,3,5,1] => 7 [2,6,4,5,1,3] => 10 [2,6,4,5,3,1] => 10 [2,6,5,1,3,4] => 9 [2,6,5,1,4,3] => 23 [2,6,5,3,1,4] => 9 [2,6,5,3,4,1] => 9 [2,6,5,4,1,3] => 14 [2,6,5,4,3,1] => 14 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => 5 [3,1,2,5,4,6] => 4 [3,1,2,5,6,4] => 10 [3,1,2,6,4,5] => 10 [3,1,2,6,5,4] => 30 [3,1,4,2,5,6] => 2 [3,1,4,2,6,5] => 10 [3,1,4,5,2,6] => 3 [3,1,4,5,6,2] => 4 [3,1,4,6,2,5] => 11 [3,1,4,6,5,2] => 15 [3,1,5,2,4,6] => 5 [3,1,5,2,6,4] => 16 [3,1,5,4,2,6] => 8 [3,1,5,4,6,2] => 11 [3,1,5,6,2,4] => 14 [3,1,5,6,4,2] => 20 [3,1,6,2,4,5] => 9 [3,1,6,2,5,4] => 31 [3,1,6,4,2,5] => 15 [3,1,6,4,5,2] => 21 [3,1,6,5,2,4] => 30 [3,1,6,5,4,2] => 44 [3,2,1,4,5,6] => 1 [3,2,1,4,6,5] => 5 [3,2,1,5,4,6] => 4 [3,2,1,5,6,4] => 10 [3,2,1,6,4,5] => 10 [3,2,1,6,5,4] => 30 [3,2,4,1,5,6] => 1 [3,2,4,1,6,5] => 5 [3,2,4,5,1,6] => 1 [3,2,4,5,6,1] => 1 [3,2,4,6,1,5] => 4 [3,2,4,6,5,1] => 4 [3,2,5,1,4,6] => 3 [3,2,5,1,6,4] => 9 [3,2,5,4,1,6] => 3 [3,2,5,4,6,1] => 3 [3,2,5,6,1,4] => 6 [3,2,5,6,4,1] => 6 [3,2,6,1,4,5] => 6 [3,2,6,1,5,4] => 20 [3,2,6,4,1,5] => 6 [3,2,6,4,5,1] => 6 [3,2,6,5,1,4] => 14 [3,2,6,5,4,1] => 14 [3,4,1,2,5,6] => 1 [3,4,1,2,6,5] => 5 [3,4,1,5,2,6] => 2 [3,4,1,5,6,2] => 3 [3,4,1,6,2,5] => 7 [3,4,1,6,5,2] => 11 [3,4,2,1,5,6] => 1 [3,4,2,1,6,5] => 5 [3,4,2,5,1,6] => 1 [3,4,2,5,6,1] => 1 [3,4,2,6,1,5] => 4 [3,4,2,6,5,1] => 4 [3,4,5,1,2,6] => 1 [3,4,5,1,6,2] => 2 [3,4,5,2,1,6] => 1 [3,4,5,2,6,1] => 1 [3,4,5,6,1,2] => 1 [3,4,5,6,2,1] => 1 [3,4,6,1,2,5] => 3 [3,4,6,1,5,2] => 6 [3,4,6,2,1,5] => 3 [3,4,6,2,5,1] => 3 [3,4,6,5,1,2] => 3 [3,4,6,5,2,1] => 3 [3,5,1,2,4,6] => 2 [3,5,1,2,6,4] => 7 [3,5,1,4,2,6] => 4 [3,5,1,4,6,2] => 6 [3,5,1,6,2,4] => 8 [3,5,1,6,4,2] => 13 [3,5,2,1,4,6] => 2 [3,5,2,1,6,4] => 7 [3,5,2,4,1,6] => 2 [3,5,2,4,6,1] => 2 [3,5,2,6,1,4] => 5 [3,5,2,6,4,1] => 5 [3,5,4,1,2,6] => 2 [3,5,4,1,6,2] => 4 [3,5,4,2,1,6] => 2 [3,5,4,2,6,1] => 2 [3,5,4,6,1,2] => 2 [3,5,4,6,2,1] => 2 [3,5,6,1,2,4] => 3 [3,5,6,1,4,2] => 6 [3,5,6,2,1,4] => 3 [3,5,6,2,4,1] => 3 [3,5,6,4,1,2] => 3 [3,5,6,4,2,1] => 3 [3,6,1,2,4,5] => 3 [3,6,1,2,5,4] => 11 [3,6,1,4,2,5] => 6 [3,6,1,4,5,2] => 9 [3,6,1,5,2,4] => 13 [3,6,1,5,4,2] => 21 [3,6,2,1,4,5] => 3 [3,6,2,1,5,4] => 11 [3,6,2,4,1,5] => 3 [3,6,2,4,5,1] => 3 [3,6,2,5,1,4] => 8 [3,6,2,5,4,1] => 8 [3,6,4,1,2,5] => 3 [3,6,4,1,5,2] => 6 [3,6,4,2,1,5] => 3 [3,6,4,2,5,1] => 3 [3,6,4,5,1,2] => 3 [3,6,4,5,2,1] => 3 [3,6,5,1,2,4] => 5 [3,6,5,1,4,2] => 10 [3,6,5,2,1,4] => 5 [3,6,5,2,4,1] => 5 [3,6,5,4,1,2] => 5 [3,6,5,4,2,1] => 5 [4,1,2,3,5,6] => 1 [4,1,2,3,6,5] => 5 [4,1,2,5,3,6] => 3 [4,1,2,5,6,3] => 6 [4,1,2,6,3,5] => 9 [4,1,2,6,5,3] => 20 [4,1,3,2,5,6] => 2 [4,1,3,2,6,5] => 10 [4,1,3,5,2,6] => 3 [4,1,3,5,6,2] => 4 [4,1,3,6,2,5] => 11 [4,1,3,6,5,2] => 15 [4,1,5,2,3,6] => 3 [4,1,5,2,6,3] => 8 [4,1,5,3,2,6] => 5 [4,1,5,3,6,2] => 7 [4,1,5,6,2,3] => 6 [4,1,5,6,3,2] => 9 [4,1,6,2,3,5] => 7 [4,1,6,2,5,3] => 19 [4,1,6,3,2,5] => 12 [4,1,6,3,5,2] => 17 [4,1,6,5,2,3] => 15 [4,1,6,5,3,2] => 23 [4,2,1,3,5,6] => 1 [4,2,1,3,6,5] => 5 [4,2,1,5,3,6] => 3 [4,2,1,5,6,3] => 6 [4,2,1,6,3,5] => 9 [4,2,1,6,5,3] => 20 [4,2,3,1,5,6] => 1 [4,2,3,1,6,5] => 5 [4,2,3,5,1,6] => 1 [4,2,3,5,6,1] => 1 [4,2,3,6,1,5] => 4 [4,2,3,6,5,1] => 4 [4,2,5,1,3,6] => 2 [4,2,5,1,6,3] => 5 [4,2,5,3,1,6] => 2 [4,2,5,3,6,1] => 2 [4,2,5,6,1,3] => 3 [4,2,5,6,3,1] => 3 [4,2,6,1,3,5] => 5 [4,2,6,1,5,3] => 13 [4,2,6,3,1,5] => 5 [4,2,6,3,5,1] => 5 [4,2,6,5,1,3] => 8 [4,2,6,5,3,1] => 8 [4,3,1,2,5,6] => 1 [4,3,1,2,6,5] => 5 [4,3,1,5,2,6] => 2 [4,3,1,5,6,2] => 3 [4,3,1,6,2,5] => 7 [4,3,1,6,5,2] => 11 [4,3,2,1,5,6] => 1 [4,3,2,1,6,5] => 5 [4,3,2,5,1,6] => 1 [4,3,2,5,6,1] => 1 [4,3,2,6,1,5] => 4 [4,3,2,6,5,1] => 4 [4,3,5,1,2,6] => 1 [4,3,5,1,6,2] => 2 [4,3,5,2,1,6] => 1 [4,3,5,2,6,1] => 1 [4,3,5,6,1,2] => 1 [4,3,5,6,2,1] => 1 [4,3,6,1,2,5] => 3 [4,3,6,1,5,2] => 6 [4,3,6,2,1,5] => 3 [4,3,6,2,5,1] => 3 [4,3,6,5,1,2] => 3 [4,3,6,5,2,1] => 3 [4,5,1,2,3,6] => 1 [4,5,1,2,6,3] => 3 [4,5,1,3,2,6] => 2 [4,5,1,3,6,2] => 3 [4,5,1,6,2,3] => 3 [4,5,1,6,3,2] => 5 [4,5,2,1,3,6] => 1 [4,5,2,1,6,3] => 3 [4,5,2,3,1,6] => 1 [4,5,2,3,6,1] => 1 [4,5,2,6,1,3] => 2 [4,5,2,6,3,1] => 2 [4,5,3,1,2,6] => 1 [4,5,3,1,6,2] => 2 [4,5,3,2,1,6] => 1 [4,5,3,2,6,1] => 1 [4,5,3,6,1,2] => 1 [4,5,3,6,2,1] => 1 [4,5,6,1,2,3] => 1 [4,5,6,1,3,2] => 2 [4,5,6,2,1,3] => 1 [4,5,6,2,3,1] => 1 [4,5,6,3,1,2] => 1 [4,5,6,3,2,1] => 1 [4,6,1,2,3,5] => 2 [4,6,1,2,5,3] => 6 [4,6,1,3,2,5] => 4 [4,6,1,3,5,2] => 6 [4,6,1,5,2,3] => 6 [4,6,1,5,3,2] => 10 [4,6,2,1,3,5] => 2 [4,6,2,1,5,3] => 6 [4,6,2,3,1,5] => 2 [4,6,2,3,5,1] => 2 [4,6,2,5,1,3] => 4 [4,6,2,5,3,1] => 4 [4,6,3,1,2,5] => 2 [4,6,3,1,5,2] => 4 [4,6,3,2,1,5] => 2 [4,6,3,2,5,1] => 2 [4,6,3,5,1,2] => 2 [4,6,3,5,2,1] => 2 [4,6,5,1,2,3] => 2 [4,6,5,1,3,2] => 4 [4,6,5,2,1,3] => 2 [4,6,5,2,3,1] => 2 [4,6,5,3,1,2] => 2 [4,6,5,3,2,1] => 2 [5,1,2,3,4,6] => 1 [5,1,2,3,6,4] => 4 [5,1,2,4,3,6] => 3 [5,1,2,4,6,3] => 6 [5,1,2,6,3,4] => 6 [5,1,2,6,4,3] => 14 [5,1,3,2,4,6] => 2 [5,1,3,2,6,4] => 8 [5,1,3,4,2,6] => 3 [5,1,3,4,6,2] => 4 [5,1,3,6,2,4] => 8 [5,1,3,6,4,2] => 11 [5,1,4,2,3,6] => 3 [5,1,4,2,6,3] => 8 [5,1,4,3,2,6] => 5 [5,1,4,3,6,2] => 7 [5,1,4,6,2,3] => 6 [5,1,4,6,3,2] => 9 [5,1,6,2,3,4] => 4 [5,1,6,2,4,3] => 11 [5,1,6,3,2,4] => 7 [5,1,6,3,4,2] => 10 [5,1,6,4,2,3] => 9 [5,1,6,4,3,2] => 14 [5,2,1,3,4,6] => 1 [5,2,1,3,6,4] => 4 [5,2,1,4,3,6] => 3 [5,2,1,4,6,3] => 6 [5,2,1,6,3,4] => 6 [5,2,1,6,4,3] => 14 [5,2,3,1,4,6] => 1 [5,2,3,1,6,4] => 4 [5,2,3,4,1,6] => 1 [5,2,3,4,6,1] => 1 [5,2,3,6,1,4] => 3 [5,2,3,6,4,1] => 3 [5,2,4,1,3,6] => 2 [5,2,4,1,6,3] => 5 [5,2,4,3,1,6] => 2 [5,2,4,3,6,1] => 2 [5,2,4,6,1,3] => 3 [5,2,4,6,3,1] => 3 [5,2,6,1,3,4] => 3 [5,2,6,1,4,3] => 8 [5,2,6,3,1,4] => 3 [5,2,6,3,4,1] => 3 [5,2,6,4,1,3] => 5 [5,2,6,4,3,1] => 5 [5,3,1,2,4,6] => 1 [5,3,1,2,6,4] => 4 [5,3,1,4,2,6] => 2 [5,3,1,4,6,2] => 3 [5,3,1,6,2,4] => 5 [5,3,1,6,4,2] => 8 [5,3,2,1,4,6] => 1 [5,3,2,1,6,4] => 4 [5,3,2,4,1,6] => 1 [5,3,2,4,6,1] => 1 [5,3,2,6,1,4] => 3 [5,3,2,6,4,1] => 3 [5,3,4,1,2,6] => 1 [5,3,4,1,6,2] => 2 [5,3,4,2,1,6] => 1 [5,3,4,2,6,1] => 1 [5,3,4,6,1,2] => 1 [5,3,4,6,2,1] => 1 [5,3,6,1,2,4] => 2 [5,3,6,1,4,2] => 4 [5,3,6,2,1,4] => 2 [5,3,6,2,4,1] => 2 [5,3,6,4,1,2] => 2 [5,3,6,4,2,1] => 2 [5,4,1,2,3,6] => 1 [5,4,1,2,6,3] => 3 [5,4,1,3,2,6] => 2 [5,4,1,3,6,2] => 3 [5,4,1,6,2,3] => 3 [5,4,1,6,3,2] => 5 [5,4,2,1,3,6] => 1 [5,4,2,1,6,3] => 3 [5,4,2,3,1,6] => 1 [5,4,2,3,6,1] => 1 [5,4,2,6,1,3] => 2 [5,4,2,6,3,1] => 2 [5,4,3,1,2,6] => 1 [5,4,3,1,6,2] => 2 [5,4,3,2,1,6] => 1 [5,4,3,2,6,1] => 1 [5,4,3,6,1,2] => 1 [5,4,3,6,2,1] => 1 [5,4,6,1,2,3] => 1 [5,4,6,1,3,2] => 2 [5,4,6,2,1,3] => 1 [5,4,6,2,3,1] => 1 [5,4,6,3,1,2] => 1 [5,4,6,3,2,1] => 1 [5,6,1,2,3,4] => 1 [5,6,1,2,4,3] => 3 [5,6,1,3,2,4] => 2 [5,6,1,3,4,2] => 3 [5,6,1,4,2,3] => 3 [5,6,1,4,3,2] => 5 [5,6,2,1,3,4] => 1 [5,6,2,1,4,3] => 3 [5,6,2,3,1,4] => 1 [5,6,2,3,4,1] => 1 [5,6,2,4,1,3] => 2 [5,6,2,4,3,1] => 2 [5,6,3,1,2,4] => 1 [5,6,3,1,4,2] => 2 [5,6,3,2,1,4] => 1 [5,6,3,2,4,1] => 1 [5,6,3,4,1,2] => 1 [5,6,3,4,2,1] => 1 [5,6,4,1,2,3] => 1 [5,6,4,1,3,2] => 2 [5,6,4,2,1,3] => 1 [5,6,4,2,3,1] => 1 [5,6,4,3,1,2] => 1 [5,6,4,3,2,1] => 1 [6,1,2,3,4,5] => 1 [6,1,2,3,5,4] => 4 [6,1,2,4,3,5] => 3 [6,1,2,4,5,3] => 6 [6,1,2,5,3,4] => 6 [6,1,2,5,4,3] => 14 [6,1,3,2,4,5] => 2 [6,1,3,2,5,4] => 8 [6,1,3,4,2,5] => 3 [6,1,3,4,5,2] => 4 [6,1,3,5,2,4] => 8 [6,1,3,5,4,2] => 11 [6,1,4,2,3,5] => 3 [6,1,4,2,5,3] => 8 [6,1,4,3,2,5] => 5 [6,1,4,3,5,2] => 7 [6,1,4,5,2,3] => 6 [6,1,4,5,3,2] => 9 [6,1,5,2,3,4] => 4 [6,1,5,2,4,3] => 11 [6,1,5,3,2,4] => 7 [6,1,5,3,4,2] => 10 [6,1,5,4,2,3] => 9 [6,1,5,4,3,2] => 14 [6,2,1,3,4,5] => 1 [6,2,1,3,5,4] => 4 [6,2,1,4,3,5] => 3 [6,2,1,4,5,3] => 6 [6,2,1,5,3,4] => 6 [6,2,1,5,4,3] => 14 [6,2,3,1,4,5] => 1 [6,2,3,1,5,4] => 4 [6,2,3,4,1,5] => 1 [6,2,3,4,5,1] => 1 [6,2,3,5,1,4] => 3 [6,2,3,5,4,1] => 3 [6,2,4,1,3,5] => 2 [6,2,4,1,5,3] => 5 [6,2,4,3,1,5] => 2 [6,2,4,3,5,1] => 2 [6,2,4,5,1,3] => 3 [6,2,4,5,3,1] => 3 [6,2,5,1,3,4] => 3 [6,2,5,1,4,3] => 8 [6,2,5,3,1,4] => 3 [6,2,5,3,4,1] => 3 [6,2,5,4,1,3] => 5 [6,2,5,4,3,1] => 5 [6,3,1,2,4,5] => 1 [6,3,1,2,5,4] => 4 [6,3,1,4,2,5] => 2 [6,3,1,4,5,2] => 3 [6,3,1,5,2,4] => 5 [6,3,1,5,4,2] => 8 [6,3,2,1,4,5] => 1 [6,3,2,1,5,4] => 4 [6,3,2,4,1,5] => 1 [6,3,2,4,5,1] => 1 [6,3,2,5,1,4] => 3 [6,3,2,5,4,1] => 3 [6,3,4,1,2,5] => 1 [6,3,4,1,5,2] => 2 [6,3,4,2,1,5] => 1 [6,3,4,2,5,1] => 1 [6,3,4,5,1,2] => 1 [6,3,4,5,2,1] => 1 [6,3,5,1,2,4] => 2 [6,3,5,1,4,2] => 4 [6,3,5,2,1,4] => 2 [6,3,5,2,4,1] => 2 [6,3,5,4,1,2] => 2 [6,3,5,4,2,1] => 2 [6,4,1,2,3,5] => 1 [6,4,1,2,5,3] => 3 [6,4,1,3,2,5] => 2 [6,4,1,3,5,2] => 3 [6,4,1,5,2,3] => 3 [6,4,1,5,3,2] => 5 [6,4,2,1,3,5] => 1 [6,4,2,1,5,3] => 3 [6,4,2,3,1,5] => 1 [6,4,2,3,5,1] => 1 [6,4,2,5,1,3] => 2 [6,4,2,5,3,1] => 2 [6,4,3,1,2,5] => 1 [6,4,3,1,5,2] => 2 [6,4,3,2,1,5] => 1 [6,4,3,2,5,1] => 1 [6,4,3,5,1,2] => 1 [6,4,3,5,2,1] => 1 [6,4,5,1,2,3] => 1 [6,4,5,1,3,2] => 2 [6,4,5,2,1,3] => 1 [6,4,5,2,3,1] => 1 [6,4,5,3,1,2] => 1 [6,4,5,3,2,1] => 1 [6,5,1,2,3,4] => 1 [6,5,1,2,4,3] => 3 [6,5,1,3,2,4] => 2 [6,5,1,3,4,2] => 3 [6,5,1,4,2,3] => 3 [6,5,1,4,3,2] => 5 [6,5,2,1,3,4] => 1 [6,5,2,1,4,3] => 3 [6,5,2,3,1,4] => 1 [6,5,2,3,4,1] => 1 [6,5,2,4,1,3] => 2 [6,5,2,4,3,1] => 2 [6,5,3,1,2,4] => 1 [6,5,3,1,4,2] => 2 [6,5,3,2,1,4] => 1 [6,5,3,2,4,1] => 1 [6,5,3,4,1,2] => 1 [6,5,3,4,2,1] => 1 [6,5,4,1,2,3] => 1 [6,5,4,1,3,2] => 2 [6,5,4,2,1,3] => 1 [6,5,4,2,3,1] => 1 [6,5,4,3,1,2] => 1 [6,5,4,3,2,1] => 1 ----------------------------------------------------------------------------- Created: Jun 15, 2015 at 18:00 by Per Alexandersson ----------------------------------------------------------------------------- Last Updated: Mar 31, 2019 at 22:17 by Martin Rubey