***************************************************************************** * 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: St001159 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: Number of simple modules with dominant dimension equal to the global dimension in the corresponding Nakayama algebra. ----------------------------------------------------------------------------- References: [1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. [[zbMATH:06820683]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 1 [1,1,0,0] => 1 [1,0,1,0,1,0] => 1 [1,0,1,1,0,0] => 1 [1,1,0,0,1,0] => 0 [1,1,0,1,0,0] => 1 [1,1,1,0,0,0] => 1 [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] => 1 [1,0,1,1,0,1,0,0] => 1 [1,0,1,1,1,0,0,0] => 1 [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] => 1 [1,1,0,1,0,1,0,0] => 0 [1,1,0,1,1,0,0,0] => 1 [1,1,1,0,0,0,1,0] => 0 [1,1,1,0,0,1,0,0] => 0 [1,1,1,0,1,0,0,0] => 1 [1,1,1,1,0,0,0,0] => 1 [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] => 1 [1,0,1,0,1,1,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,0] => 0 [1,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,0] => 0 [1,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,0] => 1 [1,0,1,1,1,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,0,0] => 1 [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] => 1 [1,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,0,1,0] => 0 [1,1,0,1,0,1,0,1,0,0] => 1 [1,1,0,1,0,1,1,0,0,0] => 0 [1,1,0,1,1,0,0,0,1,0] => 1 [1,1,0,1,1,0,0,1,0,0] => 1 [1,1,0,1,1,0,1,0,0,0] => 0 [1,1,0,1,1,1,0,0,0,0] => 1 [1,1,1,0,0,0,1,0,1,0] => 0 [1,1,1,0,0,0,1,1,0,0] => 0 [1,1,1,0,0,1,0,0,1,0] => 0 [1,1,1,0,0,1,0,1,0,0] => 0 [1,1,1,0,0,1,1,0,0,0] => 0 [1,1,1,0,1,0,0,0,1,0] => 1 [1,1,1,0,1,0,0,1,0,0] => 0 [1,1,1,0,1,0,1,0,0,0] => 0 [1,1,1,0,1,1,0,0,0,0] => 1 [1,1,1,1,0,0,0,0,1,0] => 0 [1,1,1,1,0,0,0,1,0,0] => 0 [1,1,1,1,0,0,1,0,0,0] => 0 [1,1,1,1,0,1,0,0,0,0] => 1 [1,1,1,1,1,0,0,0,0,0] => 1 [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] => 1 [1,0,1,0,1,0,1,1,0,1,0,0] => 1 [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] => 1 [1,0,1,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,1,0,0,1,0] => 1 [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] => 1 [1,0,1,0,1,1,1,0,0,0,1,0] => 1 [1,0,1,0,1,1,1,0,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,1,0,0,0] => 1 [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] => 1 [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] => 1 [1,0,1,1,0,1,0,0,1,0,1,0] => 1 [1,0,1,1,0,1,0,0,1,1,0,0] => 1 [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] => 1 [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] => 1 [1,0,1,1,0,1,1,0,0,1,0,0] => 1 [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] => 1 [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] => 1 [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] => 1 [1,0,1,1,1,0,1,0,0,0,1,0] => 1 [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] => 1 [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] => 1 [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] => 0 [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] => 1 [1,1,0,1,0,0,1,1,0,1,0,0] => 1 [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] => 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] => 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] => 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] => 1 [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] => 1 [1,1,0,1,1,0,0,1,0,0,1,0] => 1 [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] => 1 [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] => 1 [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] => 1 [1,1,0,1,1,1,0,0,0,1,0,0] => 1 [1,1,0,1,1,1,0,0,1,0,0,0] => 1 [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] => 0 [1,1,1,0,0,0,1,0,1,1,0,0] => 0 [1,1,1,0,0,0,1,1,0,0,1,0] => 0 [1,1,1,0,0,0,1,1,0,1,0,0] => 0 [1,1,1,0,0,0,1,1,1,0,0,0] => 0 [1,1,1,0,0,1,0,0,1,0,1,0] => 0 [1,1,1,0,0,1,0,0,1,1,0,0] => 0 [1,1,1,0,0,1,0,1,0,0,1,0] => 0 [1,1,1,0,0,1,0,1,0,1,0,0] => 0 [1,1,1,0,0,1,0,1,1,0,0,0] => 0 [1,1,1,0,0,1,1,0,0,0,1,0] => 0 [1,1,1,0,0,1,1,0,0,1,0,0] => 0 [1,1,1,0,0,1,1,0,1,0,0,0] => 0 [1,1,1,0,0,1,1,1,0,0,0,0] => 0 [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] => 0 [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] => 0 [1,1,1,0,1,0,1,0,0,0,1,0] => 0 [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] => 0 [1,1,1,0,1,0,1,1,0,0,0,0] => 0 [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] => 0 [1,1,1,0,1,1,0,1,0,0,0,0] => 0 [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] => 0 [1,1,1,1,0,0,0,0,1,1,0,0] => 0 [1,1,1,1,0,0,0,1,0,0,1,0] => 0 [1,1,1,1,0,0,0,1,0,1,0,0] => 0 [1,1,1,1,0,0,0,1,1,0,0,0] => 0 [1,1,1,1,0,0,1,0,0,0,1,0] => 0 [1,1,1,1,0,0,1,0,0,1,0,0] => 0 [1,1,1,1,0,0,1,0,1,0,0,0] => 0 [1,1,1,1,0,0,1,1,0,0,0,0] => 0 [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] => 0 [1,1,1,1,0,1,0,0,1,0,0,0] => 0 [1,1,1,1,0,1,0,1,0,0,0,0] => 0 [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] => 0 [1,1,1,1,1,0,0,0,0,1,0,0] => 0 [1,1,1,1,1,0,0,0,1,0,0,0] => 0 [1,1,1,1,1,0,0,1,0,0,0,0] => 0 [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] => 1 ----------------------------------------------------------------------------- Created: Apr 23, 2018 at 14:08 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Apr 23, 2018 at 14:08 by Rene Marczinzik