***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew <info@findstat.org> * * * * 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: St001583 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,2] => 1 [2,1] => 0 [1,2,3] => 3 [1,3,2] => 2 [2,1,3] => 2 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 0 [1,2,3,4] => 6 [1,2,4,3] => 5 [1,3,2,4] => 5 [1,3,4,2] => 4 [1,4,2,3] => 4 [1,4,3,2] => 3 [2,1,3,4] => 5 [2,1,4,3] => 4 [2,3,1,4] => 4 [2,3,4,1] => 3 [2,4,1,3] => 3 [2,4,3,1] => 2 [3,1,2,4] => 4 [3,1,4,2] => 3 [3,2,1,4] => 3 [3,2,4,1] => 2 [3,4,1,2] => 2 [3,4,2,1] => 1 [4,1,2,3] => 3 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 1 [4,3,1,2] => 1 [4,3,2,1] => 0 ----------------------------------------------------------------------------- Created: Aug 10, 2020 at 10:02 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Aug 10, 2020 at 10:02 by Rene Marczinzik