***************************************************************************** * 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: St001857 ----------------------------------------------------------------------------- Collection: Signed permutations ----------------------------------------------------------------------------- Description: The number of edges in the reduced word graph of a signed permutation. The reduced word graph of a signed 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] => 0 [1,2] => 0 [1,-2] => 0 [-1,2] => 0 [-1,-2] => 1 [2,1] => 0 [2,-1] => 0 [-2,1] => 0 [-2,-1] => 0 [1,2,3] => 0 [1,2,-3] => 0 [1,-2,3] => 0 [1,-2,-3] => 1 [-1,2,3] => 0 [-1,2,-3] => 3 [-1,-2,3] => 17 [-1,-2,-3] => 60 [1,3,2] => 0 [1,3,-2] => 0 [1,-3,2] => 0 [1,-3,-2] => 0 [-1,3,2] => 3 [-1,3,-2] => 10 [-1,-3,2] => 10 [-1,-3,-2] => 22 [2,1,3] => 0 [2,1,-3] => 1 [2,-1,3] => 0 [2,-1,-3] => 2 [-2,1,3] => 0 [-2,1,-3] => 2 [-2,-1,3] => 5 [-2,-1,-3] => 13 [2,3,1] => 0 [2,3,-1] => 0 [2,-3,1] => 1 [2,-3,-1] => 1 [-2,3,1] => 2 [-2,3,-1] => 5 [-2,-3,1] => 4 [-2,-3,-1] => 7 [3,1,2] => 0 [3,1,-2] => 1 [3,-1,2] => 2 [3,-1,-2] => 4 [-3,1,2] => 0 [-3,1,-2] => 1 [-3,-1,2] => 5 [-3,-1,-2] => 7 [3,2,1] => 1 [3,2,-1] => 2 [3,-2,1] => 1 [3,-2,-1] => 1 [-3,2,1] => 2 [-3,2,-1] => 5 [-3,-2,1] => 1 [-3,-2,-1] => 1 ----------------------------------------------------------------------------- Created: Nov 27, 2022 at 20:32 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 27, 2022 at 20:32 by Martin Rubey