***************************************************************************** * 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: St001224 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. Then the statistic gives the vector space dimension of the first Ext-group between X and the regular module. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 1 [1,1,0,0] => 2 [1,0,1,0,1,0] => 1 [1,0,1,1,0,0] => 2 [1,1,0,0,1,0] => 2 [1,1,0,1,0,0] => 2 [1,1,1,0,0,0] => 3 [1,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,0] => 2 [1,0,1,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,0] => 2 [1,0,1,1,1,0,0,0] => 3 [1,1,0,0,1,0,1,0] => 2 [1,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,0] => 2 [1,1,0,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,0] => 3 [1,1,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,0,0] => 3 [1,1,1,1,0,0,0,0] => 4 [1,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,0] => 2 [1,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,1,0,0] => 2 [1,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0] => 2 [1,0,1,1,0,0,1,1,0,0] => 3 [1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,1,0,0] => 2 [1,0,1,1,0,1,1,0,0,0] => 3 [1,0,1,1,1,0,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,0,0] => 3 [1,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,0,0,0] => 4 [1,1,0,0,1,0,1,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,0] => 4 [1,1,0,1,0,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,1,0,0] => 2 [1,1,0,1,0,1,1,0,0,0] => 3 [1,1,0,1,1,0,0,0,1,0] => 3 [1,1,0,1,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,0,0,0] => 4 [1,1,1,0,0,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,0] => 4 [1,1,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,0,0] => 4 [1,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,0,0,0] => 4 [1,1,1,1,0,0,0,0,1,0] => 4 [1,1,1,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,0,0,0] => 4 [1,1,1,1,1,0,0,0,0,0] => 5 [1,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,0,1,1,0,0] => 2 [1,0,1,0,1,0,1,1,0,0,1,0] => 2 [1,0,1,0,1,0,1,1,0,1,0,0] => 2 [1,0,1,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,0,1,1,0,0,1,0,1,0] => 2 [1,0,1,0,1,1,0,0,1,1,0,0] => 3 [1,0,1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,1,0,1,0,0] => 2 [1,0,1,0,1,1,0,1,1,0,0,0] => 3 [1,0,1,0,1,1,1,0,0,0,1,0] => 3 [1,0,1,0,1,1,1,0,0,1,0,0] => 3 [1,0,1,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,0,1,1,1,1,0,0,0,0] => 4 [1,0,1,1,0,0,1,0,1,0,1,0] => 2 [1,0,1,1,0,0,1,0,1,1,0,0] => 3 [1,0,1,1,0,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,0,1,1,0,1,0,0] => 3 [1,0,1,1,0,0,1,1,1,0,0,0] => 4 [1,0,1,1,0,1,0,0,1,0,1,0] => 2 [1,0,1,1,0,1,0,0,1,1,0,0] => 3 [1,0,1,1,0,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,1,0,1,0,0] => 2 [1,0,1,1,0,1,0,1,1,0,0,0] => 3 [1,0,1,1,0,1,1,0,0,0,1,0] => 3 [1,0,1,1,0,1,1,0,0,1,0,0] => 3 [1,0,1,1,0,1,1,0,1,0,0,0] => 3 [1,0,1,1,0,1,1,1,0,0,0,0] => 4 [1,0,1,1,1,0,0,0,1,0,1,0] => 3 [1,0,1,1,1,0,0,0,1,1,0,0] => 4 [1,0,1,1,1,0,0,1,0,0,1,0] => 3 [1,0,1,1,1,0,0,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,1,1,0,0,0] => 4 [1,0,1,1,1,0,1,0,0,0,1,0] => 3 [1,0,1,1,1,0,1,0,0,1,0,0] => 3 [1,0,1,1,1,0,1,0,1,0,0,0] => 3 [1,0,1,1,1,0,1,1,0,0,0,0] => 4 [1,0,1,1,1,1,0,0,0,0,1,0] => 4 [1,0,1,1,1,1,0,0,0,1,0,0] => 4 [1,0,1,1,1,1,0,0,1,0,0,0] => 4 [1,0,1,1,1,1,0,1,0,0,0,0] => 4 [1,0,1,1,1,1,1,0,0,0,0,0] => 5 [1,1,0,0,1,0,1,0,1,0,1,0] => 2 [1,1,0,0,1,0,1,0,1,1,0,0] => 3 [1,1,0,0,1,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,0,1,1,1,0,0,0] => 4 [1,1,0,0,1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,0,1,1,0,0] => 4 [1,1,0,0,1,1,0,1,0,0,1,0] => 3 [1,1,0,0,1,1,0,1,0,1,0,0] => 3 [1,1,0,0,1,1,0,1,1,0,0,0] => 4 [1,1,0,0,1,1,1,0,0,0,1,0] => 4 [1,1,0,0,1,1,1,0,0,1,0,0] => 4 [1,1,0,0,1,1,1,0,1,0,0,0] => 4 [1,1,0,0,1,1,1,1,0,0,0,0] => 5 [1,1,0,1,0,0,1,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,0,1,1,0,0] => 3 [1,1,0,1,0,0,1,1,0,0,1,0] => 3 [1,1,0,1,0,0,1,1,0,1,0,0] => 3 [1,1,0,1,0,0,1,1,1,0,0,0] => 4 [1,1,0,1,0,1,0,0,1,0,1,0] => 2 [1,1,0,1,0,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,1,0,1,0,0] => 2 [1,1,0,1,0,1,0,1,1,0,0,0] => 3 [1,1,0,1,0,1,1,0,0,0,1,0] => 3 [1,1,0,1,0,1,1,0,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,0,1,1,1,0,0,0,0] => 4 [1,1,0,1,1,0,0,0,1,0,1,0] => 3 [1,1,0,1,1,0,0,0,1,1,0,0] => 4 [1,1,0,1,1,0,0,1,0,0,1,0] => 3 [1,1,0,1,1,0,0,1,0,1,0,0] => 3 [1,1,0,1,1,0,0,1,1,0,0,0] => 4 [1,1,0,1,1,0,1,0,0,0,1,0] => 3 [1,1,0,1,1,0,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,1,0,0,0] => 3 [1,1,0,1,1,0,1,1,0,0,0,0] => 4 [1,1,0,1,1,1,0,0,0,0,1,0] => 4 [1,1,0,1,1,1,0,0,0,1,0,0] => 4 [1,1,0,1,1,1,0,0,1,0,0,0] => 4 [1,1,0,1,1,1,0,1,0,0,0,0] => 4 [1,1,0,1,1,1,1,0,0,0,0,0] => 5 [1,1,1,0,0,0,1,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,0,1,1,0,0] => 4 [1,1,1,0,0,0,1,1,0,0,1,0] => 4 [1,1,1,0,0,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,0,1,1,1,0,0,0] => 5 [1,1,1,0,0,1,0,0,1,0,1,0] => 3 [1,1,1,0,0,1,0,0,1,1,0,0] => 4 [1,1,1,0,0,1,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,0,1,1,0,0,0] => 4 [1,1,1,0,0,1,1,0,0,0,1,0] => 4 [1,1,1,0,0,1,1,0,0,1,0,0] => 4 [1,1,1,0,0,1,1,0,1,0,0,0] => 4 [1,1,1,0,0,1,1,1,0,0,0,0] => 5 [1,1,1,0,1,0,0,0,1,0,1,0] => 3 [1,1,1,0,1,0,0,0,1,1,0,0] => 4 [1,1,1,0,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,1,0,0,1,1,0,0,0] => 4 [1,1,1,0,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,0,1,1,0,0,0,0] => 4 [1,1,1,0,1,1,0,0,0,0,1,0] => 4 [1,1,1,0,1,1,0,0,0,1,0,0] => 4 [1,1,1,0,1,1,0,0,1,0,0,0] => 4 [1,1,1,0,1,1,0,1,0,0,0,0] => 4 [1,1,1,0,1,1,1,0,0,0,0,0] => 5 [1,1,1,1,0,0,0,0,1,0,1,0] => 4 [1,1,1,1,0,0,0,0,1,1,0,0] => 5 [1,1,1,1,0,0,0,1,0,0,1,0] => 4 [1,1,1,1,0,0,0,1,0,1,0,0] => 4 [1,1,1,1,0,0,0,1,1,0,0,0] => 5 [1,1,1,1,0,0,1,0,0,0,1,0] => 4 [1,1,1,1,0,0,1,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,0,1,0,0,0] => 4 [1,1,1,1,0,0,1,1,0,0,0,0] => 5 [1,1,1,1,0,1,0,0,0,0,1,0] => 4 [1,1,1,1,0,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,1,0,0,0,0] => 4 [1,1,1,1,0,1,1,0,0,0,0,0] => 5 [1,1,1,1,1,0,0,0,0,0,1,0] => 5 [1,1,1,1,1,0,0,0,0,1,0,0] => 5 [1,1,1,1,1,0,0,0,1,0,0,0] => 5 [1,1,1,1,1,0,0,1,0,0,0,0] => 5 [1,1,1,1,1,0,1,0,0,0,0,0] => 5 [1,1,1,1,1,1,0,0,0,0,0,0] => 6 ----------------------------------------------------------------------------- Created: Jun 20, 2018 at 22:27 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Jun 20, 2018 at 22:27 by Rene Marczinzik