***************************************************************************** * 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: St001856 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of edges in the reduced word graph of a permutation. The reduced word graph of a permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(pi): return pi.reduced_word_graph().size() ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 0 [1,2,3] => 0 [1,3,2] => 0 [2,1,3] => 0 [2,3,1] => 0 [3,1,2] => 0 [3,2,1] => 1 [1,2,3,4] => 0 [1,2,4,3] => 0 [1,3,2,4] => 0 [1,3,4,2] => 0 [1,4,2,3] => 0 [1,4,3,2] => 1 [2,1,3,4] => 0 [2,1,4,3] => 1 [2,3,1,4] => 0 [2,3,4,1] => 0 [2,4,1,3] => 1 [2,4,3,1] => 2 [3,1,2,4] => 0 [3,1,4,2] => 1 [3,2,1,4] => 1 [3,2,4,1] => 2 [3,4,1,2] => 1 [3,4,2,1] => 4 [4,1,2,3] => 0 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 6 [4,3,1,2] => 4 [4,3,2,1] => 18 [1,2,3,4,5] => 0 [1,2,3,5,4] => 0 [1,2,4,3,5] => 0 [1,2,4,5,3] => 0 [1,2,5,3,4] => 0 [1,2,5,4,3] => 1 [1,3,2,4,5] => 0 [1,3,2,5,4] => 1 [1,3,4,2,5] => 0 [1,3,4,5,2] => 0 [1,3,5,2,4] => 1 [1,3,5,4,2] => 2 [1,4,2,3,5] => 0 [1,4,2,5,3] => 1 [1,4,3,2,5] => 1 [1,4,3,5,2] => 2 [1,4,5,2,3] => 1 [1,4,5,3,2] => 4 [1,5,2,3,4] => 0 [1,5,2,4,3] => 2 [1,5,3,2,4] => 2 [1,5,3,4,2] => 6 [1,5,4,2,3] => 4 [1,5,4,3,2] => 18 [2,1,3,4,5] => 0 [2,1,3,5,4] => 1 [2,1,4,3,5] => 1 [2,1,4,5,3] => 2 [2,1,5,3,4] => 2 [2,1,5,4,3] => 8 [2,3,1,4,5] => 0 [2,3,1,5,4] => 2 [2,3,4,1,5] => 0 [2,3,4,5,1] => 0 [2,3,5,1,4] => 2 [2,3,5,4,1] => 3 [2,4,1,3,5] => 1 [2,4,1,5,3] => 5 [2,4,3,1,5] => 2 [2,4,3,5,1] => 3 [2,4,5,1,3] => 5 [2,4,5,3,1] => 10 [2,5,1,3,4] => 2 [2,5,1,4,3] => 13 [2,5,3,1,4] => 6 [2,5,3,4,1] => 12 [2,5,4,1,3] => 21 [2,5,4,3,1] => 52 [3,1,2,4,5] => 0 [3,1,2,5,4] => 2 [3,1,4,2,5] => 1 [3,1,4,5,2] => 2 [3,1,5,2,4] => 5 [3,1,5,4,2] => 13 [3,2,1,4,5] => 1 [3,2,1,5,4] => 8 [3,2,4,1,5] => 2 [3,2,4,5,1] => 3 [3,2,5,1,4] => 13 [3,2,5,4,1] => 25 [3,4,1,2,5] => 1 [3,4,1,5,2] => 5 [3,4,2,1,5] => 4 [3,4,2,5,1] => 10 [3,4,5,1,2] => 5 [3,4,5,2,1] => 17 [3,5,1,2,4] => 5 [3,5,1,4,2] => 23 [3,5,2,1,4] => 21 [3,5,2,4,1] => 57 [3,5,4,1,2] => 31 [3,5,4,2,1] => 119 [4,1,2,3,5] => 0 [4,1,2,5,3] => 2 [4,1,3,2,5] => 2 [4,1,3,5,2] => 6 [4,1,5,2,3] => 5 [4,1,5,3,2] => 21 [4,2,1,3,5] => 2 [4,2,1,5,3] => 13 [4,2,3,1,5] => 6 [4,2,3,5,1] => 12 [4,2,5,1,3] => 23 [4,2,5,3,1] => 57 [4,3,1,2,5] => 4 [4,3,1,5,2] => 21 [4,3,2,1,5] => 18 [4,3,2,5,1] => 52 [4,3,5,1,2] => 31 [4,3,5,2,1] => 119 [4,5,1,2,3] => 5 [4,5,1,3,2] => 31 [4,5,2,1,3] => 31 [4,5,2,3,1] => 104 [4,5,3,1,2] => 68 [4,5,3,2,1] => 327 [5,1,2,3,4] => 0 [5,1,2,4,3] => 3 [5,1,3,2,4] => 3 [5,1,3,4,2] => 12 [5,1,4,2,3] => 10 [5,1,4,3,2] => 52 [5,2,1,3,4] => 3 [5,2,1,4,3] => 25 [5,2,3,1,4] => 12 [5,2,3,4,1] => 30 [5,2,4,1,3] => 57 [5,2,4,3,1] => 169 [5,3,1,2,4] => 10 [5,3,1,4,2] => 57 [5,3,2,1,4] => 52 [5,3,2,4,1] => 169 [5,3,4,1,2] => 104 [5,3,4,2,1] => 457 [5,4,1,2,3] => 17 [5,4,1,3,2] => 119 [5,4,2,1,3] => 119 [5,4,2,3,1] => 457 [5,4,3,1,2] => 327 [5,4,3,2,1] => 1770 ----------------------------------------------------------------------------- Created: Nov 27, 2022 at 20:18 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 27, 2022 at 20:18 by Martin Rubey