***************************************************************************** * 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: St000882 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of connected components of short braid edges in the graph of braid moves of a permutation. Given a permutation $\pi$, let $\operatorname{Red}(\pi)$ denote the set of reduced words for $\pi$ in terms of simple transpositions $s_i = (i,i+1)$. We now say that two reduced words are connected by a short braid move if they are obtained from each other by a modification of the form $s_i s_j \leftrightarrow s_j s_i$ for $|i-j| > 1$ as a consecutive subword of a reduced word. For example, the two reduced words $s_1s_3s_2$ and $s_3s_1s_2$ for $$(1243) = (12)(34)(23) = (34)(12)(23)$$ share an edge because they are obtained from each other by interchanging $s_1s_3 \leftrightarrow s_3s_1$. This statistic counts the number connected components of such short braid moves among all reduced words. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def short_braid_move_graph(pi): V = [ tuple(w) for w in pi.reduced_words() ] is_edge = lambda w1,w2: w1 != w2 and any( w1[:i] == w2[:i] and w1[i+2:] == w2[i+2:] for i in range(len(w1)-1) ) return Graph([V,is_edge]) def statistic(pi): return len( short_braid_move_graph(pi).connected_components() ) ----------------------------------------------------------------------------- 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] => 1 [3,1,2] => 1 [3,2,1] => 2 [1,2,3,4] => 1 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 1 [1,4,2,3] => 1 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 1 [2,3,1,4] => 1 [2,3,4,1] => 1 [2,4,1,3] => 1 [2,4,3,1] => 2 [3,1,2,4] => 1 [3,1,4,2] => 1 [3,2,1,4] => 2 [3,2,4,1] => 2 [3,4,1,2] => 1 [3,4,2,1] => 3 [4,1,2,3] => 1 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 3 [4,3,1,2] => 3 [4,3,2,1] => 8 [1,2,3,4,5] => 1 [1,2,3,5,4] => 1 [1,2,4,3,5] => 1 [1,2,4,5,3] => 1 [1,2,5,3,4] => 1 [1,2,5,4,3] => 2 [1,3,2,4,5] => 1 [1,3,2,5,4] => 1 [1,3,4,2,5] => 1 [1,3,4,5,2] => 1 [1,3,5,2,4] => 1 [1,3,5,4,2] => 2 [1,4,2,3,5] => 1 [1,4,2,5,3] => 1 [1,4,3,2,5] => 2 [1,4,3,5,2] => 2 [1,4,5,2,3] => 1 [1,4,5,3,2] => 3 [1,5,2,3,4] => 1 [1,5,2,4,3] => 2 [1,5,3,2,4] => 2 [1,5,3,4,2] => 3 [1,5,4,2,3] => 3 [1,5,4,3,2] => 8 [2,1,3,4,5] => 1 [2,1,3,5,4] => 1 [2,1,4,3,5] => 1 [2,1,4,5,3] => 1 [2,1,5,3,4] => 1 [2,1,5,4,3] => 2 [2,3,1,4,5] => 1 [2,3,1,5,4] => 1 [2,3,4,1,5] => 1 [2,3,4,5,1] => 1 [2,3,5,1,4] => 1 [2,3,5,4,1] => 2 [2,4,1,3,5] => 1 [2,4,1,5,3] => 1 [2,4,3,1,5] => 2 [2,4,3,5,1] => 2 [2,4,5,1,3] => 1 [2,4,5,3,1] => 3 [2,5,1,3,4] => 1 [2,5,1,4,3] => 2 [2,5,3,1,4] => 2 [2,5,3,4,1] => 3 [2,5,4,1,3] => 3 [2,5,4,3,1] => 8 [3,1,2,4,5] => 1 [3,1,2,5,4] => 1 [3,1,4,2,5] => 1 [3,1,4,5,2] => 1 [3,1,5,2,4] => 1 [3,1,5,4,2] => 2 [3,2,1,4,5] => 2 [3,2,1,5,4] => 2 [3,2,4,1,5] => 2 [3,2,4,5,1] => 2 [3,2,5,1,4] => 2 [3,2,5,4,1] => 4 [3,4,1,2,5] => 1 [3,4,1,5,2] => 1 [3,4,2,1,5] => 3 [3,4,2,5,1] => 3 [3,4,5,1,2] => 1 [3,4,5,2,1] => 4 [3,5,1,2,4] => 1 [3,5,1,4,2] => 2 [3,5,2,1,4] => 3 [3,5,2,4,1] => 5 [3,5,4,1,2] => 3 [3,5,4,2,1] => 11 [4,1,2,3,5] => 1 [4,1,2,5,3] => 1 [4,1,3,2,5] => 2 [4,1,3,5,2] => 2 [4,1,5,2,3] => 1 [4,1,5,3,2] => 3 [4,2,1,3,5] => 2 [4,2,1,5,3] => 2 [4,2,3,1,5] => 3 [4,2,3,5,1] => 3 [4,2,5,1,3] => 2 [4,2,5,3,1] => 5 [4,3,1,2,5] => 3 [4,3,1,5,2] => 3 [4,3,2,1,5] => 8 [4,3,2,5,1] => 8 [4,3,5,1,2] => 3 [4,3,5,2,1] => 11 [4,5,1,2,3] => 1 [4,5,1,3,2] => 3 [4,5,2,1,3] => 3 [4,5,2,3,1] => 6 [4,5,3,1,2] => 6 [4,5,3,2,1] => 20 [5,1,2,3,4] => 1 [5,1,2,4,3] => 2 [5,1,3,2,4] => 2 [5,1,3,4,2] => 3 [5,1,4,2,3] => 3 [5,1,4,3,2] => 8 [5,2,1,3,4] => 2 [5,2,1,4,3] => 4 [5,2,3,1,4] => 3 [5,2,3,4,1] => 4 [5,2,4,1,3] => 5 [5,2,4,3,1] => 11 [5,3,1,2,4] => 3 [5,3,1,4,2] => 5 [5,3,2,1,4] => 8 [5,3,2,4,1] => 11 [5,3,4,1,2] => 6 [5,3,4,2,1] => 20 [5,4,1,2,3] => 4 [5,4,1,3,2] => 11 [5,4,2,1,3] => 11 [5,4,2,3,1] => 20 [5,4,3,1,2] => 20 [5,4,3,2,1] => 62 [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] => 1 [1,2,3,6,4,5] => 1 [1,2,3,6,5,4] => 2 [1,2,4,3,5,6] => 1 [1,2,4,3,6,5] => 1 [1,2,4,5,3,6] => 1 [1,2,4,5,6,3] => 1 [1,2,4,6,3,5] => 1 [1,2,4,6,5,3] => 2 [1,2,5,3,4,6] => 1 [1,2,5,3,6,4] => 1 [1,2,5,4,3,6] => 2 [1,2,5,4,6,3] => 2 [1,2,5,6,3,4] => 1 [1,2,5,6,4,3] => 3 [1,2,6,3,4,5] => 1 [1,2,6,3,5,4] => 2 [1,2,6,4,3,5] => 2 [1,2,6,4,5,3] => 3 [1,2,6,5,3,4] => 3 [1,2,6,5,4,3] => 8 [1,3,2,4,5,6] => 1 [1,3,2,4,6,5] => 1 [1,3,2,5,4,6] => 1 [1,3,2,5,6,4] => 1 [1,3,2,6,4,5] => 1 [1,3,2,6,5,4] => 2 [1,3,4,2,5,6] => 1 [1,3,4,2,6,5] => 1 [1,3,4,5,2,6] => 1 [1,3,4,5,6,2] => 1 [1,3,4,6,2,5] => 1 [1,3,4,6,5,2] => 2 [1,3,5,2,4,6] => 1 [1,3,5,2,6,4] => 1 [1,3,5,4,2,6] => 2 [1,3,5,4,6,2] => 2 [1,3,5,6,2,4] => 1 [1,3,5,6,4,2] => 3 [1,3,6,2,4,5] => 1 [1,3,6,2,5,4] => 2 [1,3,6,4,2,5] => 2 [1,3,6,4,5,2] => 3 [1,3,6,5,2,4] => 3 [1,3,6,5,4,2] => 8 [1,4,2,3,5,6] => 1 [1,4,2,3,6,5] => 1 [1,4,2,5,3,6] => 1 [1,4,2,5,6,3] => 1 [1,4,2,6,3,5] => 1 [1,4,2,6,5,3] => 2 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 2 [1,4,3,5,2,6] => 2 [1,4,3,5,6,2] => 2 [1,4,3,6,2,5] => 2 [1,4,3,6,5,2] => 4 [1,4,5,2,3,6] => 1 [1,4,5,2,6,3] => 1 [1,4,5,3,2,6] => 3 [1,4,5,3,6,2] => 3 [1,4,5,6,2,3] => 1 [1,4,5,6,3,2] => 4 [1,4,6,2,3,5] => 1 [1,4,6,2,5,3] => 2 [1,4,6,3,2,5] => 3 [1,4,6,3,5,2] => 5 [1,4,6,5,2,3] => 3 [1,4,6,5,3,2] => 11 [1,5,2,3,4,6] => 1 [1,5,2,3,6,4] => 1 [1,5,2,4,3,6] => 2 [1,5,2,4,6,3] => 2 [1,5,2,6,3,4] => 1 [1,5,2,6,4,3] => 3 [1,5,3,2,4,6] => 2 [1,5,3,2,6,4] => 2 [1,5,3,4,2,6] => 3 [1,5,3,4,6,2] => 3 [1,5,3,6,2,4] => 2 [1,5,3,6,4,2] => 5 [1,5,4,2,3,6] => 3 [1,5,4,2,6,3] => 3 [1,5,4,3,2,6] => 8 [1,5,4,3,6,2] => 8 [1,5,4,6,2,3] => 3 [1,5,4,6,3,2] => 11 [1,5,6,2,3,4] => 1 [1,5,6,2,4,3] => 3 [1,5,6,3,2,4] => 3 [1,5,6,3,4,2] => 6 [1,5,6,4,2,3] => 6 [1,5,6,4,3,2] => 20 [1,6,2,3,4,5] => 1 [1,6,2,3,5,4] => 2 [1,6,2,4,3,5] => 2 [1,6,2,4,5,3] => 3 [1,6,2,5,3,4] => 3 [1,6,2,5,4,3] => 8 [1,6,3,2,4,5] => 2 [1,6,3,2,5,4] => 4 [1,6,3,4,2,5] => 3 [1,6,3,4,5,2] => 4 [1,6,3,5,2,4] => 5 [1,6,3,5,4,2] => 11 [1,6,4,2,3,5] => 3 [1,6,4,2,5,3] => 5 [1,6,4,3,2,5] => 8 [1,6,4,3,5,2] => 11 [1,6,4,5,2,3] => 6 [1,6,4,5,3,2] => 20 [1,6,5,2,3,4] => 4 [1,6,5,2,4,3] => 11 [1,6,5,3,2,4] => 11 [1,6,5,3,4,2] => 20 [1,6,5,4,2,3] => 20 [1,6,5,4,3,2] => 62 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 1 [2,1,3,5,4,6] => 1 [2,1,3,5,6,4] => 1 [2,1,3,6,4,5] => 1 [2,1,3,6,5,4] => 2 [2,1,4,3,5,6] => 1 [2,1,4,3,6,5] => 1 [2,1,4,5,3,6] => 1 [2,1,4,5,6,3] => 1 [2,1,4,6,3,5] => 1 [2,1,4,6,5,3] => 2 [2,1,5,3,4,6] => 1 [2,1,5,3,6,4] => 1 [2,1,5,4,3,6] => 2 [2,1,5,4,6,3] => 2 [2,1,5,6,3,4] => 1 [2,1,5,6,4,3] => 3 [2,1,6,3,4,5] => 1 [2,1,6,3,5,4] => 2 [2,1,6,4,3,5] => 2 [2,1,6,4,5,3] => 3 [2,1,6,5,3,4] => 3 [2,1,6,5,4,3] => 8 [2,3,1,4,5,6] => 1 [2,3,1,4,6,5] => 1 [2,3,1,5,4,6] => 1 [2,3,1,5,6,4] => 1 [2,3,1,6,4,5] => 1 [2,3,1,6,5,4] => 2 [2,3,4,1,5,6] => 1 [2,3,4,1,6,5] => 1 [2,3,4,5,1,6] => 1 [2,3,4,5,6,1] => 1 [2,3,4,6,1,5] => 1 [2,3,4,6,5,1] => 2 [2,3,5,1,4,6] => 1 [2,3,5,1,6,4] => 1 [2,3,5,4,1,6] => 2 [2,3,5,4,6,1] => 2 [2,3,5,6,1,4] => 1 [2,3,5,6,4,1] => 3 [2,3,6,1,4,5] => 1 [2,3,6,1,5,4] => 2 [2,3,6,4,1,5] => 2 [2,3,6,4,5,1] => 3 [2,3,6,5,1,4] => 3 [2,3,6,5,4,1] => 8 [2,4,1,3,5,6] => 1 [2,4,1,3,6,5] => 1 [2,4,1,5,3,6] => 1 [2,4,1,5,6,3] => 1 [2,4,1,6,3,5] => 1 [2,4,1,6,5,3] => 2 [2,4,3,1,5,6] => 2 [2,4,3,1,6,5] => 2 [2,4,3,5,1,6] => 2 [2,4,3,5,6,1] => 2 [2,4,3,6,1,5] => 2 [2,4,3,6,5,1] => 4 [2,4,5,1,3,6] => 1 [2,4,5,1,6,3] => 1 [2,4,5,3,1,6] => 3 [2,4,5,3,6,1] => 3 [2,4,5,6,1,3] => 1 [2,4,5,6,3,1] => 4 [2,4,6,1,3,5] => 1 [2,4,6,1,5,3] => 2 [2,4,6,3,1,5] => 3 [2,4,6,3,5,1] => 5 [2,4,6,5,1,3] => 3 [2,4,6,5,3,1] => 11 [2,5,1,3,4,6] => 1 [2,5,1,3,6,4] => 1 [2,5,1,4,3,6] => 2 [2,5,1,4,6,3] => 2 [2,5,1,6,3,4] => 1 [2,5,1,6,4,3] => 3 [2,5,3,1,4,6] => 2 [2,5,3,1,6,4] => 2 [2,5,3,4,1,6] => 3 [2,5,3,4,6,1] => 3 [2,5,3,6,1,4] => 2 [2,5,3,6,4,1] => 5 [2,5,4,1,3,6] => 3 [2,5,4,1,6,3] => 3 [2,5,4,3,1,6] => 8 [2,5,4,3,6,1] => 8 [2,5,4,6,1,3] => 3 [2,5,4,6,3,1] => 11 [2,5,6,1,3,4] => 1 [2,5,6,1,4,3] => 3 [2,5,6,3,1,4] => 3 [2,5,6,3,4,1] => 6 [2,5,6,4,1,3] => 6 [2,5,6,4,3,1] => 20 [2,6,1,3,4,5] => 1 [2,6,1,3,5,4] => 2 [2,6,1,4,3,5] => 2 [2,6,1,4,5,3] => 3 [2,6,1,5,3,4] => 3 [2,6,1,5,4,3] => 8 [2,6,3,1,4,5] => 2 [2,6,3,1,5,4] => 4 [2,6,3,4,1,5] => 3 [2,6,3,4,5,1] => 4 [2,6,3,5,1,4] => 5 [2,6,3,5,4,1] => 11 [2,6,4,1,3,5] => 3 [2,6,4,1,5,3] => 5 [2,6,4,3,1,5] => 8 [2,6,4,3,5,1] => 11 [2,6,4,5,1,3] => 6 [2,6,4,5,3,1] => 20 [2,6,5,1,3,4] => 4 [2,6,5,1,4,3] => 11 [2,6,5,3,1,4] => 11 [2,6,5,3,4,1] => 20 [2,6,5,4,1,3] => 20 [2,6,5,4,3,1] => 62 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => 1 [3,1,2,5,4,6] => 1 [3,1,2,5,6,4] => 1 [3,1,2,6,4,5] => 1 [3,1,2,6,5,4] => 2 [3,1,4,2,5,6] => 1 [3,1,4,2,6,5] => 1 [3,1,4,5,2,6] => 1 [3,1,4,5,6,2] => 1 [3,1,4,6,2,5] => 1 [3,1,4,6,5,2] => 2 [3,1,5,2,4,6] => 1 [3,1,5,2,6,4] => 1 [3,1,5,4,2,6] => 2 [3,1,5,4,6,2] => 2 [3,1,5,6,2,4] => 1 [3,1,5,6,4,2] => 3 [3,1,6,2,4,5] => 1 [3,1,6,2,5,4] => 2 [3,1,6,4,2,5] => 2 [3,1,6,4,5,2] => 3 [3,1,6,5,2,4] => 3 [3,1,6,5,4,2] => 8 [3,2,1,4,5,6] => 2 [3,2,1,4,6,5] => 2 [3,2,1,5,4,6] => 2 [3,2,1,5,6,4] => 2 [3,2,1,6,4,5] => 2 [3,2,1,6,5,4] => 4 [3,2,4,1,5,6] => 2 [3,2,4,1,6,5] => 2 [3,2,4,5,1,6] => 2 [3,2,4,5,6,1] => 2 [3,2,4,6,1,5] => 2 [3,2,4,6,5,1] => 4 [3,2,5,1,4,6] => 2 [3,2,5,1,6,4] => 2 [3,2,5,4,1,6] => 4 [3,2,5,4,6,1] => 4 [3,2,5,6,1,4] => 2 [3,2,5,6,4,1] => 6 [3,2,6,1,4,5] => 2 [3,2,6,1,5,4] => 4 [3,2,6,4,1,5] => 4 [3,2,6,4,5,1] => 6 [3,2,6,5,1,4] => 6 [3,2,6,5,4,1] => 16 [3,4,1,2,5,6] => 1 [3,4,1,2,6,5] => 1 [3,4,1,5,2,6] => 1 [3,4,1,5,6,2] => 1 [3,4,1,6,2,5] => 1 [3,4,1,6,5,2] => 2 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 3 [3,4,2,5,1,6] => 3 [3,4,2,5,6,1] => 3 [3,4,2,6,1,5] => 3 [3,4,2,6,5,1] => 6 [3,4,5,1,2,6] => 1 [3,4,5,1,6,2] => 1 [3,4,5,2,1,6] => 4 [3,4,5,2,6,1] => 4 [3,4,5,6,1,2] => 1 [3,4,5,6,2,1] => 5 [3,4,6,1,2,5] => 1 [3,4,6,1,5,2] => 2 [3,4,6,2,1,5] => 4 [3,4,6,2,5,1] => 7 [3,4,6,5,1,2] => 3 [3,4,6,5,2,1] => 14 [3,5,1,2,4,6] => 1 [3,5,1,2,6,4] => 1 [3,5,1,4,2,6] => 2 [3,5,1,4,6,2] => 2 [3,5,1,6,2,4] => 1 [3,5,1,6,4,2] => 3 [3,5,2,1,4,6] => 3 [3,5,2,1,6,4] => 3 [3,5,2,4,1,6] => 5 [3,5,2,4,6,1] => 5 [3,5,2,6,1,4] => 3 [3,5,2,6,4,1] => 8 [3,5,4,1,2,6] => 3 [3,5,4,1,6,2] => 3 [3,5,4,2,1,6] => 11 [3,5,4,2,6,1] => 11 [3,5,4,6,1,2] => 3 [3,5,4,6,2,1] => 14 [3,5,6,1,2,4] => 1 [3,5,6,1,4,2] => 3 [3,5,6,2,1,4] => 4 [3,5,6,2,4,1] => 9 [3,5,6,4,1,2] => 6 [3,5,6,4,2,1] => 26 [3,6,1,2,4,5] => 1 [3,6,1,2,5,4] => 2 [3,6,1,4,2,5] => 2 [3,6,1,4,5,2] => 3 [3,6,1,5,2,4] => 3 [3,6,1,5,4,2] => 8 [3,6,2,1,4,5] => 3 [3,6,2,1,5,4] => 6 [3,6,2,4,1,5] => 5 [3,6,2,4,5,1] => 7 [3,6,2,5,1,4] => 8 [3,6,2,5,4,1] => 19 [3,6,4,1,2,5] => 3 [3,6,4,1,5,2] => 5 [3,6,4,2,1,5] => 11 [3,6,4,2,5,1] => 16 [3,6,4,5,1,2] => 6 [3,6,4,5,2,1] => 26 [3,6,5,1,2,4] => 4 [3,6,5,1,4,2] => 11 [3,6,5,2,1,4] => 15 [3,6,5,2,4,1] => 31 [3,6,5,4,1,2] => 20 [3,6,5,4,2,1] => 82 [4,1,2,3,5,6] => 1 [4,1,2,3,6,5] => 1 [4,1,2,5,3,6] => 1 [4,1,2,5,6,3] => 1 [4,1,2,6,3,5] => 1 [4,1,2,6,5,3] => 2 [4,1,3,2,5,6] => 2 [4,1,3,2,6,5] => 2 [4,1,3,5,2,6] => 2 [4,1,3,5,6,2] => 2 [4,1,3,6,2,5] => 2 [4,1,3,6,5,2] => 4 [4,1,5,2,3,6] => 1 [4,1,5,2,6,3] => 1 [4,1,5,3,2,6] => 3 [4,1,5,3,6,2] => 3 [4,1,5,6,2,3] => 1 [4,1,5,6,3,2] => 4 [4,1,6,2,3,5] => 1 [4,1,6,2,5,3] => 2 [4,1,6,3,2,5] => 3 [4,1,6,3,5,2] => 5 [4,1,6,5,2,3] => 3 [4,1,6,5,3,2] => 11 [4,2,1,3,5,6] => 2 [4,2,1,3,6,5] => 2 [4,2,1,5,3,6] => 2 [4,2,1,5,6,3] => 2 [4,2,1,6,3,5] => 2 [4,2,1,6,5,3] => 4 [4,2,3,1,5,6] => 3 [4,2,3,1,6,5] => 3 [4,2,3,5,1,6] => 3 [4,2,3,5,6,1] => 3 [4,2,3,6,1,5] => 3 [4,2,3,6,5,1] => 6 [4,2,5,1,3,6] => 2 [4,2,5,1,6,3] => 2 [4,2,5,3,1,6] => 5 [4,2,5,3,6,1] => 5 [4,2,5,6,1,3] => 2 [4,2,5,6,3,1] => 7 [4,2,6,1,3,5] => 2 [4,2,6,1,5,3] => 4 [4,2,6,3,1,5] => 5 [4,2,6,3,5,1] => 8 [4,2,6,5,1,3] => 6 [4,2,6,5,3,1] => 19 [4,3,1,2,5,6] => 3 [4,3,1,2,6,5] => 3 [4,3,1,5,2,6] => 3 [4,3,1,5,6,2] => 3 [4,3,1,6,2,5] => 3 [4,3,1,6,5,2] => 6 [4,3,2,1,5,6] => 8 [4,3,2,1,6,5] => 8 [4,3,2,5,1,6] => 8 [4,3,2,5,6,1] => 8 [4,3,2,6,1,5] => 8 [4,3,2,6,5,1] => 16 [4,3,5,1,2,6] => 3 [4,3,5,1,6,2] => 3 [4,3,5,2,1,6] => 11 [4,3,5,2,6,1] => 11 [4,3,5,6,1,2] => 3 [4,3,5,6,2,1] => 14 [4,3,6,1,2,5] => 3 [4,3,6,1,5,2] => 6 [4,3,6,2,1,5] => 11 [4,3,6,2,5,1] => 19 [4,3,6,5,1,2] => 9 [4,3,6,5,2,1] => 39 [4,5,1,2,3,6] => 1 [4,5,1,2,6,3] => 1 [4,5,1,3,2,6] => 3 [4,5,1,3,6,2] => 3 [4,5,1,6,2,3] => 1 [4,5,1,6,3,2] => 4 [4,5,2,1,3,6] => 3 [4,5,2,1,6,3] => 3 [4,5,2,3,1,6] => 6 [4,5,2,3,6,1] => 6 [4,5,2,6,1,3] => 3 [4,5,2,6,3,1] => 9 [4,5,3,1,2,6] => 6 [4,5,3,1,6,2] => 6 [4,5,3,2,1,6] => 20 [4,5,3,2,6,1] => 20 [4,5,3,6,1,2] => 6 [4,5,3,6,2,1] => 26 [4,5,6,1,2,3] => 1 [4,5,6,1,3,2] => 4 [4,5,6,2,1,3] => 4 [4,5,6,2,3,1] => 10 [4,5,6,3,1,2] => 10 [4,5,6,3,2,1] => 40 [4,6,1,2,3,5] => 1 [4,6,1,2,5,3] => 2 [4,6,1,3,5,2] => 5 [4,6,1,5,2,3] => 3 [4,6,1,5,3,2] => 11 [4,6,2,1,3,5] => 3 [4,6,2,1,5,3] => 6 [4,6,2,3,1,5] => 6 [4,6,2,3,5,1] => 9 [4,6,2,5,1,3] => 8 [4,6,2,5,3,1] => 22 [4,6,3,1,2,5] => 6 [4,6,3,1,5,2] => 11 [4,6,3,2,1,5] => 20 [4,6,3,2,5,1] => 31 [6,2,1,4,3,5] => 4 [6,4,2,1,3,5] => 11 ----------------------------------------------------------------------------- Created: Jul 03, 2017 at 16:58 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Dec 25, 2017 at 17:32 by Martin Rubey