***************************************************************************** * 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: St001543 ----------------------------------------------------------------------------- Collection: Decorated permutations ----------------------------------------------------------------------------- Description: The largest step for the associated bounded affine permutation. The largest step is the largest distance between any two consecutive terms. ----------------------------------------------------------------------------- References: [1] Lam, T. Totally nonnegative Grassmannian and Grassmann polytopes [[MathSciNet:3468251]] [[arXiv:1506.00603]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [+,+] => 1 [-,+] => 3 [+,-] => 1 [-,-] => 1 [2,1] => 1 [+,+,+] => 1 [-,+,+] => 4 [+,-,+] => 4 [+,+,-] => 2 [-,-,+] => 4 [-,+,-] => 4 [+,-,-] => 2 [-,-,-] => 1 [+,3,2] => 2 [-,3,2] => 2 [2,1,+] => 2 [2,1,-] => 2 [2,3,1] => 1 [3,1,2] => 1 [3,+,1] => 2 [3,-,1] => 2 [+,+,+,+] => 1 [-,+,+,+] => 5 [+,-,+,+] => 5 [+,+,-,+] => 5 [+,+,+,-] => 3 [-,-,+,+] => 5 [-,+,-,+] => 5 [-,+,+,-] => 5 [+,-,-,+] => 5 [+,-,+,-] => 5 [+,+,-,-] => 3 [-,-,-,+] => 5 [-,-,+,-] => 5 [-,+,-,-] => 5 [+,-,-,-] => 3 [-,-,-,-] => 1 [+,+,4,3] => 3 [-,+,4,3] => 5 [+,-,4,3] => 3 [-,-,4,3] => 3 [+,3,2,+] => 3 [-,3,2,+] => 3 [+,3,2,-] => 3 [-,3,2,-] => 3 [+,3,4,2] => 2 [-,3,4,2] => 2 [+,4,2,3] => 2 [-,4,2,3] => 3 [+,4,+,2] => 3 [-,4,+,2] => 3 [+,4,-,2] => 3 [-,4,-,2] => 3 [2,1,+,+] => 3 [2,1,-,+] => 5 [2,1,+,-] => 3 [2,1,-,-] => 3 [2,1,4,3] => 3 [2,3,1,+] => 3 [2,3,1,-] => 2 [2,3,4,1] => 1 [2,4,1,3] => 2 [2,4,+,1] => 3 [2,4,-,1] => 2 [3,1,2,+] => 2 [3,1,2,-] => 2 [3,1,4,2] => 2 [3,+,1,+] => 3 [3,-,1,+] => 3 [3,+,1,-] => 3 [3,-,1,-] => 3 [3,+,4,1] => 3 [3,-,4,1] => 2 [3,4,1,2] => 1 [3,4,2,1] => 2 [4,1,2,3] => 1 [4,1,+,2] => 2 [4,1,-,2] => 3 [4,+,1,3] => 2 [4,-,1,3] => 3 [4,+,+,1] => 2 [4,-,+,1] => 5 [4,+,-,1] => 3 [4,-,-,1] => 2 [4,3,1,2] => 2 [4,3,2,1] => 3 [+,+,+,+,+] => 1 [-,+,+,+,+] => 6 [+,-,+,+,+] => 6 [+,+,-,+,+] => 6 [+,+,+,-,+] => 6 [+,+,+,+,-] => 4 [-,-,+,+,+] => 6 [-,+,-,+,+] => 6 [-,+,+,-,+] => 6 [-,+,+,+,-] => 6 [+,-,-,+,+] => 6 [+,-,+,-,+] => 6 [+,-,+,+,-] => 6 [+,+,-,-,+] => 6 [+,+,-,+,-] => 6 [+,+,+,-,-] => 4 [-,-,-,+,+] => 6 [-,-,+,-,+] => 6 [-,-,+,+,-] => 6 [-,+,-,-,+] => 6 [-,+,-,+,-] => 6 [-,+,+,-,-] => 6 [+,-,-,-,+] => 6 [+,-,-,+,-] => 6 [+,-,+,-,-] => 6 [+,+,-,-,-] => 4 [-,-,-,-,+] => 6 [-,-,-,+,-] => 6 [-,-,+,-,-] => 6 [-,+,-,-,-] => 6 [+,-,-,-,-] => 4 [-,-,-,-,-] => 1 [+,+,+,5,4] => 4 [-,+,+,5,4] => 6 [+,-,+,5,4] => 6 [+,+,-,5,4] => 4 [-,-,+,5,4] => 6 [-,+,-,5,4] => 6 [+,-,-,5,4] => 4 [-,-,-,5,4] => 4 [+,+,4,3,+] => 4 [-,+,4,3,+] => 6 [+,-,4,3,+] => 4 [+,+,4,3,-] => 4 [-,-,4,3,+] => 4 [-,+,4,3,-] => 6 [+,-,4,3,-] => 4 [-,-,4,3,-] => 4 [+,+,4,5,3] => 3 [-,+,4,5,3] => 6 [+,-,4,5,3] => 4 [-,-,4,5,3] => 3 [+,+,5,3,4] => 3 [-,+,5,3,4] => 6 [+,-,5,3,4] => 4 [-,-,5,3,4] => 3 [+,+,5,+,3] => 4 [-,+,5,+,3] => 6 [+,-,5,+,3] => 4 [+,+,5,-,3] => 4 [-,-,5,+,3] => 4 [-,+,5,-,3] => 6 [+,-,5,-,3] => 4 [-,-,5,-,3] => 4 [+,3,2,+,+] => 4 [-,3,2,+,+] => 4 [+,3,2,-,+] => 6 [+,3,2,+,-] => 4 [-,3,2,-,+] => 6 [-,3,2,+,-] => 4 [+,3,2,-,-] => 4 [-,3,2,-,-] => 4 [+,3,2,5,4] => 4 [-,3,2,5,4] => 4 [+,3,4,2,+] => 3 [-,3,4,2,+] => 3 [+,3,4,2,-] => 3 [-,3,4,2,-] => 3 [+,3,4,5,2] => 3 [-,3,4,5,2] => 2 [+,3,5,2,4] => 3 [-,3,5,2,4] => 2 [+,3,5,+,2] => 4 [-,3,5,+,2] => 4 [+,3,5,-,2] => 3 [-,3,5,-,2] => 3 [+,4,2,3,+] => 3 [-,4,2,3,+] => 3 [+,4,2,3,-] => 3 [-,4,2,3,-] => 3 [+,4,2,5,3] => 3 [-,4,2,5,3] => 3 [+,4,+,2,+] => 4 [-,4,+,2,+] => 4 [+,4,-,2,+] => 4 [+,4,+,2,-] => 4 [-,4,-,2,+] => 4 [-,4,+,2,-] => 4 [+,4,-,2,-] => 4 [-,4,-,2,-] => 4 [+,4,+,5,2] => 4 [-,4,+,5,2] => 4 [+,4,-,5,2] => 2 [-,4,-,5,2] => 3 [+,4,5,2,3] => 2 [-,4,5,2,3] => 3 [+,4,5,3,2] => 3 [-,4,5,3,2] => 3 [+,5,2,3,4] => 2 [-,5,2,3,4] => 4 [+,5,2,+,3] => 2 [-,5,2,+,3] => 4 [+,5,2,-,3] => 4 [-,5,2,-,3] => 4 [+,5,+,2,4] => 3 [-,5,+,2,4] => 4 [+,5,-,2,4] => 4 [-,5,-,2,4] => 4 [+,5,+,+,2] => 3 [-,5,+,+,2] => 4 [+,5,-,+,2] => 6 [+,5,+,-,2] => 4 [-,5,-,+,2] => 6 [-,5,+,-,2] => 4 [+,5,-,-,2] => 3 [-,5,-,-,2] => 4 [+,5,4,2,3] => 3 [-,5,4,2,3] => 4 [+,5,4,3,2] => 4 [-,5,4,3,2] => 4 [2,1,+,+,+] => 4 [2,1,-,+,+] => 6 [2,1,+,-,+] => 6 [2,1,+,+,-] => 4 [2,1,-,-,+] => 6 [2,1,-,+,-] => 6 [2,1,+,-,-] => 4 [2,1,-,-,-] => 4 [2,1,+,5,4] => 4 [2,1,-,5,4] => 4 [2,1,4,3,+] => 4 [2,1,4,3,-] => 4 [2,1,4,5,3] => 4 [2,1,5,3,4] => 4 [2,1,5,+,3] => 4 [2,1,5,-,3] => 4 [2,3,1,+,+] => 3 [2,3,1,-,+] => 6 [2,3,1,+,-] => 4 [2,3,1,-,-] => 3 [2,3,1,5,4] => 4 [2,3,4,1,+] => 4 [2,3,4,1,-] => 2 [2,3,4,5,1] => 1 [2,3,5,1,4] => 3 [2,3,5,+,1] => 4 [2,3,5,-,1] => 2 [2,4,1,3,+] => 2 [2,4,1,3,-] => 3 [2,4,1,5,3] => 3 [2,4,+,1,+] => 4 [2,4,-,1,+] => 4 [2,4,+,1,-] => 4 [2,4,-,1,-] => 3 [2,4,+,5,1] => 4 [2,4,-,5,1] => 2 [2,4,5,1,3] => 2 [2,4,5,3,1] => 3 [2,5,1,3,4] => 3 [2,5,1,+,3] => 3 [2,5,1,-,3] => 4 [2,5,+,1,4] => 3 [2,5,-,1,4] => 3 [2,5,+,+,1] => 3 [2,5,-,+,1] => 6 [2,5,+,-,1] => 4 [2,5,-,-,1] => 3 [2,5,4,1,3] => 3 [2,5,4,3,1] => 4 [3,1,2,+,+] => 3 [3,1,2,-,+] => 6 [3,1,2,+,-] => 4 [3,1,2,-,-] => 3 [3,1,2,5,4] => 4 [3,1,4,2,+] => 3 [3,1,4,2,-] => 3 [3,1,4,5,2] => 3 [3,1,5,2,4] => 3 [3,1,5,+,2] => 4 [3,1,5,-,2] => 3 [3,+,1,+,+] => 4 [3,-,1,+,+] => 4 [3,+,1,-,+] => 6 [3,+,1,+,-] => 4 [3,-,1,-,+] => 6 [3,-,1,+,-] => 4 [3,+,1,-,-] => 4 [3,-,1,-,-] => 4 [3,+,1,5,4] => 4 [3,-,1,5,4] => 4 [3,+,4,1,+] => 4 [3,-,4,1,+] => 4 [3,+,4,1,-] => 4 [3,-,4,1,-] => 2 [3,+,4,5,1] => 4 [3,-,4,5,1] => 2 [3,+,5,1,4] => 4 [3,-,5,1,4] => 3 [3,+,5,+,1] => 4 [3,-,5,+,1] => 4 [3,+,5,-,1] => 4 [3,-,5,-,1] => 3 [3,4,1,2,+] => 3 [3,4,1,2,-] => 2 [3,4,1,5,2] => 2 [3,4,2,1,+] => 4 [3,4,2,1,-] => 3 [3,4,2,5,1] => 3 [3,4,5,1,2] => 1 [3,4,5,2,1] => 2 [3,5,1,2,4] => 2 [3,5,1,+,2] => 3 [3,5,1,-,2] => 3 [3,5,2,1,4] => 3 [3,5,2,+,1] => 3 [3,5,2,-,1] => 3 [3,5,4,1,2] => 2 [3,5,4,2,1] => 3 [4,1,2,3,+] => 2 [4,1,2,3,-] => 3 [4,1,2,5,3] => 3 [4,1,+,2,+] => 3 [4,1,-,2,+] => 4 [4,1,+,2,-] => 2 [4,1,-,2,-] => 4 [4,1,+,5,2] => 3 [4,1,-,5,2] => 3 [4,1,5,2,3] => 2 [4,1,5,3,2] => 3 [4,+,1,3,+] => 3 [4,-,1,3,+] => 4 [4,+,1,3,-] => 3 [4,-,1,3,-] => 4 [4,+,1,5,3] => 3 [4,-,1,5,3] => 4 [4,+,+,1,+] => 4 [4,-,+,1,+] => 6 [4,+,-,1,+] => 4 [4,+,+,1,-] => 3 [4,-,-,1,+] => 4 [4,-,+,1,-] => 6 [4,+,-,1,-] => 4 [4,-,-,1,-] => 3 [4,+,+,5,1] => 3 [4,-,+,5,1] => 6 [4,+,-,5,1] => 4 [4,-,-,5,1] => 2 [4,+,5,1,3] => 3 [4,-,5,1,3] => 3 [4,+,5,3,1] => 3 [4,-,5,3,1] => 3 [4,3,1,2,+] => 3 [4,3,1,2,-] => 3 [4,3,1,5,2] => 3 [4,3,2,1,+] => 4 [4,3,2,1,-] => 4 [4,3,2,5,1] => 4 [4,3,5,1,2] => 2 [4,3,5,2,1] => 2 [4,5,1,2,3] => 1 [4,5,1,3,2] => 2 [4,5,2,1,3] => 2 [4,5,2,3,1] => 2 [4,5,+,1,2] => 3 [4,5,-,1,2] => 3 [4,5,+,2,1] => 3 [4,5,-,2,1] => 4 [5,1,2,3,4] => 1 [5,1,2,+,3] => 2 [5,1,2,-,3] => 4 [5,1,+,2,4] => 2 [5,1,-,2,4] => 4 [5,1,+,+,2] => 2 [5,1,-,+,2] => 6 [5,1,+,-,2] => 4 [5,1,-,-,2] => 3 [5,1,4,2,3] => 3 [5,1,4,3,2] => 4 [5,+,1,3,4] => 2 [5,-,1,3,4] => 4 [5,+,1,+,3] => 3 [5,-,1,+,3] => 4 [5,+,1,-,3] => 4 [5,-,1,-,3] => 4 [5,+,+,1,4] => 3 [5,-,+,1,4] => 6 [5,+,-,1,4] => 4 [5,-,-,1,4] => 3 [5,+,+,+,1] => 3 [5,-,+,+,1] => 6 [5,+,-,+,1] => 6 [5,+,+,-,1] => 4 [5,-,-,+,1] => 6 [5,-,+,-,1] => 6 [5,+,-,-,1] => 4 [5,-,-,-,1] => 3 [5,+,4,1,3] => 3 [5,-,4,1,3] => 3 [5,+,4,3,1] => 4 [5,-,4,3,1] => 4 [5,3,1,2,4] => 3 [5,3,1,+,2] => 3 [5,3,1,-,2] => 3 [5,3,2,1,4] => 4 [5,3,2,+,1] => 4 [5,3,2,-,1] => 4 [5,3,4,1,2] => 2 [5,3,4,2,1] => 3 [5,4,1,2,3] => 2 [5,4,1,3,2] => 2 [5,4,2,1,3] => 3 [5,4,2,3,1] => 3 [5,4,+,1,2] => 4 [5,4,-,1,2] => 3 [5,4,+,2,1] => 4 [5,4,-,2,1] => 4 ----------------------------------------------------------------------------- Created: May 12, 2020 at 22:50 by Danny Luecke ----------------------------------------------------------------------------- Last Updated: May 12, 2020 at 22:50 by Danny Luecke