***************************************************************************** * 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: St001212 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 0 [1,0,1,0] => 1 [1,1,0,0] => 0 [1,0,1,0,1,0] => 1 [1,0,1,1,0,0] => 1 [1,1,0,0,1,0] => 1 [1,1,0,1,0,0] => 1 [1,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,0] => 1 [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] => 1 [1,1,0,0,1,0,1,0] => 1 [1,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,0] => 1 [1,1,0,1,1,0,0,0] => 1 [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] => 0 [1,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,0] => 1 [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] => 1 [1,0,1,1,0,0,1,0,1,0] => 2 [1,0,1,1,0,0,1,1,0,0] => 2 [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] => 2 [1,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,0] => 1 [1,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,0] => 1 [1,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,1,1,0,0,1,0,0] => 2 [1,1,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,1,1,0,0,0,0] => 1 [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] => 1 [1,1,1,1,0,0,0,1,0,0] => 1 [1,1,1,1,0,0,1,0,0,0] => 1 [1,1,1,1,0,1,0,0,0,0] => 1 [1,1,1,1,1,0,0,0,0,0] => 0 [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] => 1 [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] => 1 [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] => 2 [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] => 2 [1,0,1,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,0,1,1,1,0,0,1,0,0] => 2 [1,0,1,0,1,1,1,0,1,0,0,0] => 2 [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] => 2 [1,0,1,1,0,0,1,0,1,1,0,0] => 2 [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] => 2 [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] => 2 [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] => 2 [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] => 2 [1,0,1,1,1,0,0,0,1,0,1,0] => 2 [1,0,1,1,1,0,0,0,1,1,0,0] => 2 [1,0,1,1,1,0,0,1,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,1,0,0] => 2 [1,0,1,1,1,0,0,1,1,0,0,0] => 2 [1,0,1,1,1,0,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,1,0,0,1,0,0] => 2 [1,0,1,1,1,0,1,0,1,0,0,0] => 2 [1,0,1,1,1,0,1,1,0,0,0,0] => 2 [1,0,1,1,1,1,0,0,0,0,1,0] => 2 [1,0,1,1,1,1,0,0,0,1,0,0] => 2 [1,0,1,1,1,1,0,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,1,0,0,0,0] => 2 [1,0,1,1,1,1,1,0,0,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,0,1,1,1,0,0,0] => 1 [1,1,0,0,1,1,0,0,1,0,1,0] => 2 [1,1,0,0,1,1,0,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,1,0,0] => 2 [1,1,0,0,1,1,0,1,1,0,0,0] => 2 [1,1,0,0,1,1,1,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,0,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,1,0,0,0] => 2 [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] => 1 [1,1,0,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,1,0,0,1,1,0,1,0,0] => 2 [1,1,0,1,0,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,1,0,0,1,0,1,0] => 1 [1,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,0] => 1 [1,1,0,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,1,0,1,1,0,0,1,0,0] => 2 [1,1,0,1,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,0,1,1,1,0,0,0,0] => 1 [1,1,0,1,1,0,0,0,1,0,1,0] => 2 [1,1,0,1,1,0,0,0,1,1,0,0] => 2 [1,1,0,1,1,0,0,1,0,0,1,0] => 2 [1,1,0,1,1,0,0,1,0,1,0,0] => 2 [1,1,0,1,1,0,0,1,1,0,0,0] => 2 [1,1,0,1,1,0,1,0,0,0,1,0] => 2 [1,1,0,1,1,0,1,0,0,1,0,0] => 2 [1,1,0,1,1,0,1,0,1,0,0,0] => 2 [1,1,0,1,1,0,1,1,0,0,0,0] => 2 [1,1,0,1,1,1,0,0,0,0,1,0] => 2 [1,1,0,1,1,1,0,0,0,1,0,0] => 2 [1,1,0,1,1,1,0,0,1,0,0,0] => 2 [1,1,0,1,1,1,0,1,0,0,0,0] => 2 [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] => 2 [1,1,1,0,0,0,1,1,0,1,0,0] => 2 [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] => 2 [1,1,1,0,0,1,1,0,0,1,0,0] => 2 [1,1,1,0,0,1,1,0,1,0,0,0] => 2 [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] => 2 [1,1,1,0,1,1,0,0,0,1,0,0] => 2 [1,1,1,0,1,1,0,0,1,0,0,0] => 2 [1,1,1,0,1,1,0,1,0,0,0,0] => 2 [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] => 1 [1,1,1,1,0,0,0,0,1,1,0,0] => 1 [1,1,1,1,0,0,0,1,0,0,1,0] => 1 [1,1,1,1,0,0,0,1,0,1,0,0] => 1 [1,1,1,1,0,0,0,1,1,0,0,0] => 1 [1,1,1,1,0,0,1,0,0,0,1,0] => 1 [1,1,1,1,0,0,1,0,0,1,0,0] => 1 [1,1,1,1,0,0,1,0,1,0,0,0] => 1 [1,1,1,1,0,0,1,1,0,0,0,0] => 1 [1,1,1,1,0,1,0,0,0,0,1,0] => 1 [1,1,1,1,0,1,0,0,0,1,0,0] => 1 [1,1,1,1,0,1,0,0,1,0,0,0] => 1 [1,1,1,1,0,1,0,1,0,0,0,0] => 1 [1,1,1,1,0,1,1,0,0,0,0,0] => 1 [1,1,1,1,1,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,0,0,0,0,1,0,0] => 1 [1,1,1,1,1,0,0,0,1,0,0,0] => 1 [1,1,1,1,1,0,0,1,0,0,0,0] => 1 [1,1,1,1,1,0,1,0,0,0,0,0] => 1 [1,1,1,1,1,1,0,0,0,0,0,0] => 0 ----------------------------------------------------------------------------- Created: Jun 20, 2018 at 15:47 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Jun 20, 2018 at 15:47 by Rene Marczinzik