***************************************************************************** * 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: St001860 ----------------------------------------------------------------------------- Collection: Signed permutations ----------------------------------------------------------------------------- Description: The number of factors of the Stanley symmetric function associated with a signed permutation. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(pi): return sum(m for _, m in pi.stanley_symmetric_function().factor()) ----------------------------------------------------------------------------- Statistic values: [1,2] => 0 [1,-2] => 1 [-1,2] => 1 [-1,-2] => 2 [2,1] => 1 [2,-1] => 2 [-2,1] => 2 [-2,-1] => 1 [1,2,3] => 0 [1,2,-3] => 1 [1,-2,3] => 1 [1,-2,-3] => 2 [-1,2,3] => 1 [-1,2,-3] => 1 [-1,-2,3] => 1 [-1,-2,-3] => 2 [1,3,2] => 1 [1,3,-2] => 2 [1,-3,2] => 2 [1,-3,-2] => 1 [-1,3,2] => 1 [-1,3,-2] => 1 [-1,-3,2] => 1 [-1,-3,-2] => 1 [2,1,3] => 1 [2,1,-3] => 2 [2,-1,3] => 2 [2,-1,-3] => 1 [-2,1,3] => 2 [-2,1,-3] => 1 [-2,-1,3] => 1 [-2,-1,-3] => 1 [2,3,1] => 2 [2,3,-1] => 1 [2,-3,1] => 1 [2,-3,-1] => 2 [-2,3,1] => 1 [-2,3,-1] => 2 [-2,-3,1] => 2 [-2,-3,-1] => 2 [3,1,2] => 2 [3,1,-2] => 1 [3,-1,2] => 1 [3,-1,-2] => 2 [-3,1,2] => 1 [-3,1,-2] => 2 [-3,-1,2] => 2 [-3,-1,-2] => 2 [3,2,1] => 1 [3,2,-1] => 4 [3,-2,1] => 2 [3,-2,-1] => 1 [-3,2,1] => 4 [-3,2,-1] => 3 [-3,-2,1] => 1 [-3,-2,-1] => 1 [1,2,3,4] => 0 [1,2,3,-4] => 1 [1,2,-3,4] => 1 [1,2,-3,-4] => 2 [1,-2,3,4] => 1 [1,-2,3,-4] => 1 [1,-2,-3,4] => 1 [1,-2,-3,-4] => 2 [-1,2,3,4] => 1 [-1,2,3,-4] => 1 [-1,2,-3,4] => 1 [-1,2,-3,-4] => 1 [-1,-2,3,4] => 1 [-1,-2,3,-4] => 1 [-1,-2,-3,4] => 1 [-1,-2,-3,-4] => 2 [1,2,4,3] => 1 [1,2,4,-3] => 2 [1,2,-4,3] => 2 [1,2,-4,-3] => 1 [1,-2,4,3] => 1 [1,-2,4,-3] => 1 [1,-2,-4,3] => 1 [1,-2,-4,-3] => 1 [-1,2,4,3] => 1 [-1,2,4,-3] => 1 [-1,2,-4,3] => 1 [-1,2,-4,-3] => 1 [-1,-2,4,3] => 1 [-1,-2,4,-3] => 1 [-1,-2,-4,3] => 1 [-1,-2,-4,-3] => 1 [1,3,2,4] => 1 [1,3,2,-4] => 2 [1,3,-2,4] => 2 [1,3,-2,-4] => 1 [1,-3,2,4] => 2 [1,-3,2,-4] => 1 [1,-3,-2,4] => 1 [1,-3,-2,-4] => 1 [-1,3,2,4] => 1 [-1,3,2,-4] => 1 [-1,3,-2,4] => 1 [-1,3,-2,-4] => 1 [-1,-3,2,4] => 1 [-1,-3,2,-4] => 1 [-1,-3,-2,4] => 1 [-1,-3,-2,-4] => 1 [1,3,4,2] => 2 [1,3,4,-2] => 1 [1,3,-4,2] => 1 [1,3,-4,-2] => 2 [1,-3,4,2] => 1 [1,-3,4,-2] => 2 [1,-3,-4,2] => 2 [1,-3,-4,-2] => 2 [-1,3,4,2] => 1 [-1,3,4,-2] => 1 [-1,3,-4,2] => 1 [-1,3,-4,-2] => 1 [-1,-3,4,2] => 1 [-1,-3,4,-2] => 1 [-1,-3,-4,2] => 1 [-1,-3,-4,-2] => 1 [1,4,2,3] => 2 [1,4,2,-3] => 1 [1,4,-2,3] => 1 [1,4,-2,-3] => 2 [1,-4,2,3] => 1 [1,-4,2,-3] => 2 [1,-4,-2,3] => 2 [1,-4,-2,-3] => 2 [-1,4,2,3] => 1 [-1,4,2,-3] => 1 [-1,4,-2,3] => 1 [-1,4,-2,-3] => 1 [-1,-4,2,3] => 1 [-1,-4,2,-3] => 1 [-1,-4,-2,3] => 1 [-1,-4,-2,-3] => 1 [1,4,3,2] => 1 [1,4,3,-2] => 4 [1,4,-3,2] => 2 [1,4,-3,-2] => 1 [1,-4,3,2] => 4 [1,-4,3,-2] => 3 [1,-4,-3,2] => 1 [1,-4,-3,-2] => 1 [-1,4,3,2] => 1 [-1,4,3,-2] => 1 [-1,4,-3,2] => 1 [-1,4,-3,-2] => 1 [-1,-4,3,2] => 1 [-1,-4,3,-2] => 1 [-1,-4,-3,2] => 1 [-1,-4,-3,-2] => 1 [2,1,3,4] => 1 [2,1,3,-4] => 2 [2,1,-3,4] => 2 [2,1,-3,-4] => 3 [2,-1,3,4] => 1 [2,-1,3,-4] => 1 [2,-1,-3,4] => 1 [2,-1,-3,-4] => 1 [-2,1,3,4] => 1 [-2,1,3,-4] => 1 [-2,1,-3,4] => 1 [-2,1,-3,-4] => 1 [-2,-1,3,4] => 1 [-2,-1,3,-4] => 1 [-2,-1,-3,4] => 1 [-2,-1,-3,-4] => 1 [2,1,4,3] => 2 [2,1,4,-3] => 3 [2,1,-4,3] => 3 [2,1,-4,-3] => 2 [2,-1,4,3] => 1 [2,-1,4,-3] => 2 [2,-1,-4,3] => 2 [2,-1,-4,-3] => 1 [-2,1,4,3] => 1 [-2,1,4,-3] => 2 [-2,1,-4,3] => 2 [-2,1,-4,-3] => 1 [-2,-1,4,3] => 1 [-2,-1,4,-3] => 1 [-2,-1,-4,3] => 1 [-2,-1,-4,-3] => 1 [2,3,1,4] => 2 [2,3,1,-4] => 3 [2,3,-1,4] => 1 [2,3,-1,-4] => 1 [2,-3,1,4] => 1 [2,-3,1,-4] => 1 [2,-3,-1,4] => 1 [2,-3,-1,-4] => 2 [-2,3,1,4] => 1 [-2,3,1,-4] => 2 [-2,3,-1,4] => 1 [-2,3,-1,-4] => 1 [-2,-3,1,4] => 1 [-2,-3,1,-4] => 1 [-2,-3,-1,4] => 1 [-2,-3,-1,-4] => 1 [2,3,4,1] => 1 [2,3,4,-1] => 2 [2,3,-4,1] => 4 [2,3,-4,-1] => 1 [2,-3,4,1] => 2 [2,-3,4,-1] => 2 [2,-3,-4,1] => 3 [2,-3,-4,-1] => 3 [-2,3,4,1] => 2 [-2,3,4,-1] => 1 [-2,3,-4,1] => 1 [-2,3,-4,-1] => 1 [-2,-3,4,1] => 1 [-2,-3,4,-1] => 2 [-2,-3,-4,1] => 2 [-2,-3,-4,-1] => 2 [2,4,1,3] => 1 [2,4,1,-3] => 2 [2,4,-1,3] => 1 [2,4,-1,-3] => 1 [2,-4,1,3] => 4 [2,-4,1,-3] => 1 [2,-4,-1,3] => 1 [2,-4,-1,-3] => 1 [-2,4,1,3] => 2 [-2,4,1,-3] => 1 [-2,4,-1,3] => 1 [-2,4,-1,-3] => 2 [-2,-4,1,3] => 1 [-2,-4,1,-3] => 1 [-2,-4,-1,3] => 2 [-2,-4,-1,-3] => 2 [2,4,3,1] => 4 [2,4,3,-1] => 1 [2,4,-3,1] => 3 [2,4,-3,-1] => 2 [2,-4,3,1] => 1 [2,-4,3,-1] => 2 [2,-4,-3,1] => 1 [2,-4,-3,-1] => 2 [-2,4,3,1] => 1 [-2,4,3,-1] => 1 [-2,4,-3,1] => 1 [-2,4,-3,-1] => 1 [-2,-4,3,1] => 1 [-2,-4,3,-1] => 1 [-2,-4,-3,1] => 1 [-2,-4,-3,-1] => 1 [3,1,2,4] => 2 [3,1,2,-4] => 3 [3,1,-2,4] => 1 [3,1,-2,-4] => 1 [3,-1,2,4] => 1 [3,-1,2,-4] => 2 [3,-1,-2,4] => 1 [3,-1,-2,-4] => 1 [-3,1,2,4] => 1 [-3,1,2,-4] => 1 [-3,1,-2,4] => 1 [-3,1,-2,-4] => 2 [-3,-1,2,4] => 1 [-3,-1,2,-4] => 1 [-3,-1,-2,4] => 1 [-3,-1,-2,-4] => 1 [3,1,4,2] => 1 [3,1,4,-2] => 4 [3,1,-4,2] => 2 [3,1,-4,-2] => 1 [3,-1,4,2] => 2 [3,-1,4,-2] => 1 [3,-1,-4,2] => 1 [3,-1,-4,-2] => 1 [-3,1,4,2] => 1 [-3,1,4,-2] => 1 [-3,1,-4,2] => 1 [-3,1,-4,-2] => 1 [-3,-1,4,2] => 1 [-3,-1,4,-2] => 2 [-3,-1,-4,2] => 2 [-3,-1,-4,-2] => 2 [3,2,1,4] => 1 [3,2,1,-4] => 2 [3,2,-1,4] => 1 [3,2,-1,-4] => 1 [3,-2,1,4] => 1 [3,-2,1,-4] => 1 [3,-2,-1,4] => 1 [3,-2,-1,-4] => 1 [-3,2,1,4] => 1 [-3,2,1,-4] => 1 [-3,2,-1,4] => 1 [-3,2,-1,-4] => 1 [-3,-2,1,4] => 1 [-3,-2,1,-4] => 1 [-3,-2,-1,4] => 1 [-3,-2,-1,-4] => 1 [3,2,4,1] => 4 [3,2,4,-1] => 1 [3,2,-4,1] => 1 [3,2,-4,-1] => 1 [3,-2,4,1] => 1 [3,-2,4,-1] => 1 [3,-2,-4,1] => 1 [3,-2,-4,-1] => 2 [-3,2,4,1] => 2 [-3,2,4,-1] => 1 [-3,2,-4,1] => 1 [-3,2,-4,-1] => 2 [-3,-2,4,1] => 1 [-3,-2,4,-1] => 1 [-3,-2,-4,1] => 1 [-3,-2,-4,-1] => 1 [3,4,1,2] => 2 [3,4,1,-2] => 3 [3,4,-1,2] => 1 [3,4,-1,-2] => 1 [3,-4,1,2] => 3 [3,-4,1,-2] => 2 [3,-4,-1,2] => 1 [3,-4,-1,-2] => 2 [-3,4,1,2] => 1 [-3,4,1,-2] => 1 [-3,4,-1,2] => 1 [-3,4,-1,-2] => 2 [-3,-4,1,2] => 1 [-3,-4,1,-2] => 2 [-3,-4,-1,2] => 2 [-3,-4,-1,-2] => 3 [3,4,2,1] => 3 [3,4,2,-1] => 2 [3,4,-2,1] => 2 [3,4,-2,-1] => 1 [3,-4,2,1] => 1 [3,-4,2,-1] => 1 [3,-4,-2,1] => 1 [3,-4,-2,-1] => 1 [-3,4,2,1] => 1 [-3,4,2,-1] => 1 [-3,4,-2,1] => 2 [-3,4,-2,-1] => 1 [-3,-4,2,1] => 1 [-3,-4,2,-1] => 3 [-3,-4,-2,1] => 1 [-3,-4,-2,-1] => 2 [4,1,2,3] => 1 [4,1,2,-3] => 4 [4,1,-2,3] => 2 [4,1,-2,-3] => 3 [4,-1,2,3] => 2 [4,-1,2,-3] => 1 [4,-1,-2,3] => 1 [4,-1,-2,-3] => 2 [-4,1,2,3] => 2 [-4,1,2,-3] => 1 [-4,1,-2,3] => 2 [-4,1,-2,-3] => 3 [-4,-1,2,3] => 1 [-4,-1,2,-3] => 1 [-4,-1,-2,3] => 2 [-4,-1,-2,-3] => 2 [4,1,3,2] => 4 [4,1,3,-2] => 1 [4,1,-3,2] => 3 [4,1,-3,-2] => 1 [4,-1,3,2] => 1 [4,-1,3,-2] => 1 [4,-1,-3,2] => 1 [4,-1,-3,-2] => 1 [-4,1,3,2] => 1 [-4,1,3,-2] => 2 [-4,1,-3,2] => 2 [-4,1,-3,-2] => 2 [-4,-1,3,2] => 1 [-4,-1,3,-2] => 1 [-4,-1,-3,2] => 1 [-4,-1,-3,-2] => 1 [4,2,1,3] => 4 [4,2,1,-3] => 1 [4,2,-1,3] => 2 [4,2,-1,-3] => 1 [4,-2,1,3] => 1 [4,-2,1,-3] => 1 [4,-2,-1,3] => 1 [4,-2,-1,-3] => 1 [-4,2,1,3] => 1 [-4,2,1,-3] => 1 [-4,2,-1,3] => 1 [-4,2,-1,-3] => 2 [-4,-2,1,3] => 1 [-4,-2,1,-3] => 2 [-4,-2,-1,3] => 1 [-4,-2,-1,-3] => 1 [4,2,3,1] => 1 [4,2,3,-1] => 2 [4,2,-3,1] => 1 [4,2,-3,-1] => 3 [4,-2,3,1] => 1 [4,-2,3,-1] => 1 [4,-2,-3,1] => 2 [4,-2,-3,-1] => 1 [-4,2,3,1] => 2 [-4,2,3,-1] => 1 [-4,2,-3,1] => 3 [-4,2,-3,-1] => 3 [-4,-2,3,1] => 1 [-4,-2,3,-1] => 1 [-4,-2,-3,1] => 1 [-4,-2,-3,-1] => 2 [4,3,1,2] => 3 [4,3,1,-2] => 1 [4,3,-1,2] => 1 [4,3,-1,-2] => 1 [4,-3,1,2] => 2 [4,-3,1,-2] => 1 [4,-3,-1,2] => 2 [4,-3,-1,-2] => 1 [-4,3,1,2] => 2 [-4,3,1,-2] => 1 [-4,3,-1,2] => 1 [-4,3,-1,-2] => 3 [-4,-3,1,2] => 1 [-4,-3,1,-2] => 1 [-4,-3,-1,2] => 1 [-4,-3,-1,-2] => 2 [4,3,2,1] => 1 [4,3,2,-1] => 3 [4,3,-2,1] => 3 [4,3,-2,-1] => 1 [4,-3,2,1] => 3 [4,-3,2,-1] => 1 [4,-3,-2,1] => 1 [4,-3,-2,-1] => 1 [-4,3,2,1] => 3 [-4,3,2,-1] => 2 [-4,3,-2,1] => 1 [-4,3,-2,-1] => 2 [-4,-3,2,1] => 1 [-4,-3,2,-1] => 2 [-4,-3,-2,1] => 1 [-4,-3,-2,-1] => 1 ----------------------------------------------------------------------------- Created: Nov 29, 2022 at 13:58 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 29, 2022 at 13:58 by Martin Rubey