***************************************************************************** * 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: St001168 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The vector space dimension of the 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] => 5 [2,1] => 4 [1,2,3] => 14 [1,3,2] => 13 [2,1,3] => 13 [2,3,1] => 11 [3,1,2] => 11 [3,2,1] => 10 [1,2,4,3] => 29 [1,3,2,4] => 29 [1,3,4,2] => 27 [1,4,2,3] => 27 [1,4,3,2] => 26 [2,1,3,4] => 29 [2,1,4,3] => 28 [2,3,1,4] => 27 [2,3,4,1] => 24 [2,4,1,3] => 25 [2,4,3,1] => 23 [3,1,2,4] => 27 [3,1,4,2] => 25 [3,2,1,4] => 26 [3,2,4,1] => 23 [3,4,1,2] => 22 [3,4,2,1] => 21 [4,1,2,3] => 24 [4,1,3,2] => 23 [4,2,1,3] => 23 [4,2,3,1] => 21 [4,3,1,2] => 21 [4,3,2,1] => 20 ----------------------------------------------------------------------------- Created: Apr 30, 2018 at 23:58 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Apr 30, 2018 at 23:58 by Rene Marczinzik