***************************************************************************** * 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: St001207 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The Lowey length of the algebra \$A/T\$ when \$T\$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of \$K[x]/(x^n)\$. ----------------------------------------------------------------------------- References: [1] Iyama, O., Zhang, X. Classifying τ-tilting modules over the Auslander algebra of \$K[x]/(x^n)\$ [[arXiv:1602.05037]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 2 [3,1,2] => 2 [3,2,1] => 2 [1,2,3,4] => 0 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 1 [2,3,1,4] => 2 [2,3,4,1] => 3 [2,4,1,3] => 2 [2,4,3,1] => 3 [3,1,2,4] => 2 [3,1,4,2] => 2 [3,2,1,4] => 2 [3,2,4,1] => 3 [3,4,1,2] => 3 [3,4,2,1] => 3 [4,1,2,3] => 3 [4,1,3,2] => 3 [4,2,1,3] => 3 [4,2,3,1] => 3 [4,3,1,2] => 3 [4,3,2,1] => 3 ----------------------------------------------------------------------------- Created: May 24, 2018 at 13:02 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: May 24, 2018 at 13:02 by Rene Marczinzik