***************************************************************************** * 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: St001171 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The vector space dimension of \$Ext_A^1(I_o,A)\$ when \$I_o\$ is the tilting module corresponding to the permutation \$o\$ in the Auslander algebra \$A\$ 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] => 0 [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 3 [3,1,2] => 3 [3,2,1] => 4 [1,2,3,4] => 0 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 3 [1,4,2,3] => 3 [1,4,3,2] => 4 [2,1,3,4] => 1 [2,1,4,3] => 2 [2,3,1,4] => 3 [2,3,4,1] => 6 [2,4,1,3] => 5 [2,4,3,1] => 7 [3,1,2,4] => 3 [3,1,4,2] => 5 [3,2,1,4] => 4 [3,2,4,1] => 7 [3,4,1,2] => 8 [3,4,2,1] => 9 [4,1,2,3] => 6 [4,1,3,2] => 7 [4,2,1,3] => 7 [4,2,3,1] => 9 [4,3,1,2] => 9 [4,3,2,1] => 10 ----------------------------------------------------------------------------- Created: Apr 30, 2018 at 17:08 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: May 02, 2018 at 11:21 by Rene Marczinzik