***************************************************************************** * 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: St001231 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. Actually the same statistics results for algebras with at most 7 simple modules when dropping the assumption that the module has projective dimension one. The author is not sure whether this holds in general. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 0 [1,0,1,0] => 0 [1,1,0,0] => 0 [1,0,1,0,1,0] => 0 [1,0,1,1,0,0] => 0 [1,1,0,0,1,0] => 0 [1,1,0,1,0,0] => 0 [1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,1,0,0] => 0 [1,0,1,1,0,0,1,0] => 0 [1,0,1,1,0,1,0,0] => 0 [1,0,1,1,1,0,0,0] => 0 [1,1,0,0,1,0,1,0] => 0 [1,1,0,0,1,1,0,0] => 0 [1,1,0,1,0,0,1,0] => 0 [1,1,0,1,0,1,0,0] => 0 [1,1,0,1,1,0,0,0] => 0 [1,1,1,0,0,0,1,0] => 1 [1,1,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,0,0] => 1 [1,1,1,1,0,0,0,0] => 2 [1,0,1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,0,1,1,0,0] => 0 [1,0,1,0,1,1,0,0,1,0] => 0 [1,0,1,0,1,1,0,1,0,0] => 0 [1,0,1,0,1,1,1,0,0,0] => 0 [1,0,1,1,0,0,1,0,1,0] => 0 [1,0,1,1,0,0,1,1,0,0] => 0 [1,0,1,1,0,1,0,0,1,0] => 0 [1,0,1,1,0,1,0,1,0,0] => 0 [1,0,1,1,0,1,1,0,0,0] => 0 [1,0,1,1,1,0,0,0,1,0] => 0 [1,0,1,1,1,0,0,1,0,0] => 0 [1,0,1,1,1,0,1,0,0,0] => 0 [1,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,0] => 0 [1,1,0,0,1,0,1,1,0,0] => 0 [1,1,0,0,1,1,0,0,1,0] => 0 [1,1,0,0,1,1,0,1,0,0] => 0 [1,1,0,0,1,1,1,0,0,0] => 0 [1,1,0,1,0,0,1,0,1,0] => 0 [1,1,0,1,0,0,1,1,0,0] => 0 [1,1,0,1,0,1,0,0,1,0] => 0 [1,1,0,1,0,1,0,1,0,0] => 0 [1,1,0,1,0,1,1,0,0,0] => 0 [1,1,0,1,1,0,0,0,1,0] => 0 [1,1,0,1,1,0,0,1,0,0] => 0 [1,1,0,1,1,0,1,0,0,0] => 0 [1,1,0,1,1,1,0,0,0,0] => 0 [1,1,1,0,0,0,1,0,1,0] => 1 [1,1,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,0,1,0,0,1,0] => 1 [1,1,1,0,0,1,0,1,0,0] => 1 [1,1,1,0,0,1,1,0,0,0] => 1 [1,1,1,0,1,0,0,0,1,0] => 1 [1,1,1,0,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,1,0,0,0] => 1 [1,1,1,0,1,1,0,0,0,0] => 1 [1,1,1,1,0,0,0,0,1,0] => 2 [1,1,1,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0] => 3 [1,0,1,0,1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,0,1,0,1,1,0,0] => 0 [1,0,1,0,1,0,1,1,0,0,1,0] => 0 [1,0,1,0,1,0,1,1,0,1,0,0] => 0 [1,0,1,0,1,0,1,1,1,0,0,0] => 0 [1,0,1,0,1,1,0,0,1,0,1,0] => 0 [1,0,1,0,1,1,0,0,1,1,0,0] => 0 [1,0,1,0,1,1,0,1,0,0,1,0] => 0 [1,0,1,0,1,1,0,1,0,1,0,0] => 0 [1,0,1,0,1,1,0,1,1,0,0,0] => 0 [1,0,1,0,1,1,1,0,0,0,1,0] => 0 [1,0,1,0,1,1,1,0,0,1,0,0] => 0 [1,0,1,0,1,1,1,0,1,0,0,0] => 0 [1,0,1,0,1,1,1,1,0,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,0,1,0] => 0 [1,0,1,1,0,0,1,0,1,1,0,0] => 0 [1,0,1,1,0,0,1,1,0,0,1,0] => 0 [1,0,1,1,0,0,1,1,0,1,0,0] => 0 [1,0,1,1,0,0,1,1,1,0,0,0] => 0 [1,0,1,1,0,1,0,0,1,0,1,0] => 0 [1,0,1,1,0,1,0,0,1,1,0,0] => 0 [1,0,1,1,0,1,0,1,0,0,1,0] => 0 [1,0,1,1,0,1,0,1,0,1,0,0] => 0 [1,0,1,1,0,1,0,1,1,0,0,0] => 0 [1,0,1,1,0,1,1,0,0,0,1,0] => 0 [1,0,1,1,0,1,1,0,0,1,0,0] => 0 [1,0,1,1,0,1,1,0,1,0,0,0] => 0 [1,0,1,1,0,1,1,1,0,0,0,0] => 0 [1,0,1,1,1,0,0,0,1,0,1,0] => 0 [1,0,1,1,1,0,0,0,1,1,0,0] => 0 [1,0,1,1,1,0,0,1,0,0,1,0] => 0 [1,0,1,1,1,0,0,1,0,1,0,0] => 0 [1,0,1,1,1,0,0,1,1,0,0,0] => 0 [1,0,1,1,1,0,1,0,0,0,1,0] => 0 [1,0,1,1,1,0,1,0,0,1,0,0] => 0 [1,0,1,1,1,0,1,0,1,0,0,0] => 0 [1,0,1,1,1,0,1,1,0,0,0,0] => 0 [1,0,1,1,1,1,0,0,0,0,1,0] => 1 [1,0,1,1,1,1,0,0,0,1,0,0] => 1 [1,0,1,1,1,1,0,0,1,0,0,0] => 1 [1,0,1,1,1,1,0,1,0,0,0,0] => 1 [1,0,1,1,1,1,1,0,0,0,0,0] => 2 [1,1,0,0,1,0,1,0,1,0,1,0] => 0 [1,1,0,0,1,0,1,0,1,1,0,0] => 0 [1,1,0,0,1,0,1,1,0,0,1,0] => 0 [1,1,0,0,1,0,1,1,0,1,0,0] => 0 [1,1,0,0,1,0,1,1,1,0,0,0] => 0 [1,1,0,0,1,1,0,0,1,0,1,0] => 0 [1,1,0,0,1,1,0,0,1,1,0,0] => 0 [1,1,0,0,1,1,0,1,0,0,1,0] => 0 [1,1,0,0,1,1,0,1,0,1,0,0] => 0 [1,1,0,0,1,1,0,1,1,0,0,0] => 0 [1,1,0,0,1,1,1,0,0,0,1,0] => 0 [1,1,0,0,1,1,1,0,0,1,0,0] => 0 [1,1,0,0,1,1,1,0,1,0,0,0] => 0 [1,1,0,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,0,1,0] => 0 [1,1,0,1,0,0,1,0,1,1,0,0] => 0 [1,1,0,1,0,0,1,1,0,0,1,0] => 0 [1,1,0,1,0,0,1,1,0,1,0,0] => 0 [1,1,0,1,0,0,1,1,1,0,0,0] => 0 [1,1,0,1,0,1,0,0,1,0,1,0] => 0 [1,1,0,1,0,1,0,0,1,1,0,0] => 0 [1,1,0,1,0,1,0,1,0,0,1,0] => 0 [1,1,0,1,0,1,0,1,0,1,0,0] => 0 [1,1,0,1,0,1,0,1,1,0,0,0] => 0 [1,1,0,1,0,1,1,0,0,0,1,0] => 0 [1,1,0,1,0,1,1,0,0,1,0,0] => 0 [1,1,0,1,0,1,1,0,1,0,0,0] => 0 [1,1,0,1,0,1,1,1,0,0,0,0] => 0 [1,1,0,1,1,0,0,0,1,0,1,0] => 0 [1,1,0,1,1,0,0,0,1,1,0,0] => 0 [1,1,0,1,1,0,0,1,0,0,1,0] => 0 [1,1,0,1,1,0,0,1,0,1,0,0] => 0 [1,1,0,1,1,0,0,1,1,0,0,0] => 0 [1,1,0,1,1,0,1,0,0,0,1,0] => 0 [1,1,0,1,1,0,1,0,0,1,0,0] => 0 [1,1,0,1,1,0,1,0,1,0,0,0] => 0 [1,1,0,1,1,0,1,1,0,0,0,0] => 0 [1,1,0,1,1,1,0,0,0,0,1,0] => 0 [1,1,0,1,1,1,0,0,0,1,0,0] => 0 [1,1,0,1,1,1,0,0,1,0,0,0] => 0 [1,1,0,1,1,1,0,1,0,0,0,0] => 0 [1,1,0,1,1,1,1,0,0,0,0,0] => 1 [1,1,1,0,0,0,1,0,1,0,1,0] => 1 [1,1,1,0,0,0,1,0,1,1,0,0] => 1 [1,1,1,0,0,0,1,1,0,0,1,0] => 1 [1,1,1,0,0,0,1,1,0,1,0,0] => 1 [1,1,1,0,0,0,1,1,1,0,0,0] => 1 [1,1,1,0,0,1,0,0,1,0,1,0] => 1 [1,1,1,0,0,1,0,0,1,1,0,0] => 1 [1,1,1,0,0,1,0,1,0,0,1,0] => 1 [1,1,1,0,0,1,0,1,0,1,0,0] => 1 [1,1,1,0,0,1,0,1,1,0,0,0] => 1 [1,1,1,0,0,1,1,0,0,0,1,0] => 1 [1,1,1,0,0,1,1,0,0,1,0,0] => 1 [1,1,1,0,0,1,1,0,1,0,0,0] => 1 [1,1,1,0,0,1,1,1,0,0,0,0] => 1 [1,1,1,0,1,0,0,0,1,0,1,0] => 1 [1,1,1,0,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,1,0,0,1,0,0,1,0] => 1 [1,1,1,0,1,0,0,1,0,1,0,0] => 1 [1,1,1,0,1,0,0,1,1,0,0,0] => 1 [1,1,1,0,1,0,1,0,0,0,1,0] => 1 [1,1,1,0,1,0,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,1,0,1,0,0,0] => 1 [1,1,1,0,1,0,1,1,0,0,0,0] => 1 [1,1,1,0,1,1,0,0,0,0,1,0] => 1 [1,1,1,0,1,1,0,0,0,1,0,0] => 1 [1,1,1,0,1,1,0,0,1,0,0,0] => 1 [1,1,1,0,1,1,0,1,0,0,0,0] => 1 [1,1,1,0,1,1,1,0,0,0,0,0] => 1 [1,1,1,1,0,0,0,0,1,0,1,0] => 2 [1,1,1,1,0,0,0,0,1,1,0,0] => 2 [1,1,1,1,0,0,0,1,0,0,1,0] => 2 [1,1,1,1,0,0,0,1,0,1,0,0] => 2 [1,1,1,1,0,0,0,1,1,0,0,0] => 2 [1,1,1,1,0,0,1,0,0,0,1,0] => 2 [1,1,1,1,0,0,1,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0,1,0] => 2 [1,1,1,1,0,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,1,0,0,0,0] => 2 [1,1,1,1,0,1,1,0,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0,1,0] => 3 [1,1,1,1,1,0,0,0,0,1,0,0] => 3 [1,1,1,1,1,0,0,0,1,0,0,0] => 3 [1,1,1,1,1,0,0,1,0,0,0,0] => 3 [1,1,1,1,1,0,1,0,0,0,0,0] => 3 [1,1,1,1,1,1,0,0,0,0,0,0] => 4 ----------------------------------------------------------------------------- Created: Aug 08, 2018 at 13:01 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Aug 08, 2018 at 13:01 by Rene Marczinzik