***************************************************************************** * 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: St001170 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes 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] => 2 [1,1,0,0] => 1 [1,0,1,0,1,0] => 3 [1,0,1,1,0,0] => 3 [1,1,0,0,1,0] => 3 [1,1,0,1,0,0] => 3 [1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,0] => 4 [1,0,1,0,1,1,0,0] => 4 [1,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,1,0,0] => 4 [1,0,1,1,1,0,0,0] => 4 [1,1,0,0,1,0,1,0] => 4 [1,1,0,0,1,1,0,0] => 4 [1,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,0,0] => 4 [1,1,0,1,1,0,0,0] => 4 [1,1,1,0,0,0,1,0] => 4 [1,1,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,0,0] => 4 [1,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0] => 5 [1,0,1,0,1,0,1,1,0,0] => 5 [1,0,1,0,1,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,0] => 5 [1,0,1,0,1,1,1,0,0,0] => 5 [1,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,0,1,1,0,0] => 4 [1,0,1,1,0,1,0,0,1,0] => 5 [1,0,1,1,0,1,0,1,0,0] => 5 [1,0,1,1,0,1,1,0,0,0] => 5 [1,0,1,1,1,0,0,0,1,0] => 4 [1,0,1,1,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,0,0,0] => 5 [1,0,1,1,1,1,0,0,0,0] => 5 [1,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,0] => 5 [1,1,0,0,1,1,0,0,1,0] => 4 [1,1,0,0,1,1,0,1,0,0] => 5 [1,1,0,0,1,1,1,0,0,0] => 5 [1,1,0,1,0,0,1,0,1,0] => 5 [1,1,0,1,0,0,1,1,0,0] => 5 [1,1,0,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,1,1,0,0,0] => 5 [1,1,0,1,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,0,0] => 5 [1,1,0,1,1,0,1,0,0,0] => 5 [1,1,0,1,1,1,0,0,0,0] => 5 [1,1,1,0,0,0,1,0,1,0] => 5 [1,1,1,0,0,0,1,1,0,0] => 5 [1,1,1,0,0,1,0,0,1,0] => 5 [1,1,1,0,0,1,0,1,0,0] => 5 [1,1,1,0,0,1,1,0,0,0] => 5 [1,1,1,0,1,0,0,0,1,0] => 5 [1,1,1,0,1,0,0,1,0,0] => 5 [1,1,1,0,1,0,1,0,0,0] => 5 [1,1,1,0,1,1,0,0,0,0] => 5 [1,1,1,1,0,0,0,0,1,0] => 5 [1,1,1,1,0,0,0,1,0,0] => 5 [1,1,1,1,0,0,1,0,0,0] => 5 [1,1,1,1,0,1,0,0,0,0] => 5 [1,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,0,1,0,1,1,0,0] => 6 [1,0,1,0,1,0,1,1,0,0,1,0] => 6 [1,0,1,0,1,0,1,1,0,1,0,0] => 6 [1,0,1,0,1,0,1,1,1,0,0,0] => 6 [1,0,1,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,0,1,1,0,0,1,1,0,0] => 6 [1,0,1,0,1,1,0,1,0,0,1,0] => 6 [1,0,1,0,1,1,0,1,0,1,0,0] => 6 [1,0,1,0,1,1,0,1,1,0,0,0] => 6 [1,0,1,0,1,1,1,0,0,0,1,0] => 6 [1,0,1,0,1,1,1,0,0,1,0,0] => 6 [1,0,1,0,1,1,1,0,1,0,0,0] => 6 [1,0,1,0,1,1,1,1,0,0,0,0] => 6 [1,0,1,1,0,0,1,0,1,0,1,0] => 6 [1,0,1,1,0,0,1,0,1,1,0,0] => 6 [1,0,1,1,0,0,1,1,0,0,1,0] => 4 [1,0,1,1,0,0,1,1,0,1,0,0] => 6 [1,0,1,1,0,0,1,1,1,0,0,0] => 5 [1,0,1,1,0,1,0,0,1,0,1,0] => 6 [1,0,1,1,0,1,0,0,1,1,0,0] => 6 [1,0,1,1,0,1,0,1,0,0,1,0] => 6 [1,0,1,1,0,1,0,1,0,1,0,0] => 6 [1,0,1,1,0,1,0,1,1,0,0,0] => 6 [1,0,1,1,0,1,1,0,0,0,1,0] => 6 [1,0,1,1,0,1,1,0,0,1,0,0] => 6 [1,0,1,1,0,1,1,0,1,0,0,0] => 6 [1,0,1,1,0,1,1,1,0,0,0,0] => 6 [1,0,1,1,1,0,0,0,1,0,1,0] => 6 [1,0,1,1,1,0,0,0,1,1,0,0] => 5 [1,0,1,1,1,0,0,1,0,0,1,0] => 6 [1,0,1,1,1,0,0,1,0,1,0,0] => 6 [1,0,1,1,1,0,0,1,1,0,0,0] => 5 [1,0,1,1,1,0,1,0,0,0,1,0] => 6 [1,0,1,1,1,0,1,0,0,1,0,0] => 6 [1,0,1,1,1,0,1,0,1,0,0,0] => 6 [1,0,1,1,1,0,1,1,0,0,0,0] => 6 [1,0,1,1,1,1,0,0,0,0,1,0] => 5 [1,0,1,1,1,1,0,0,0,1,0,0] => 5 [1,0,1,1,1,1,0,0,1,0,0,0] => 5 [1,0,1,1,1,1,0,1,0,0,0,0] => 6 [1,0,1,1,1,1,1,0,0,0,0,0] => 6 [1,1,0,0,1,0,1,0,1,0,1,0] => 6 [1,1,0,0,1,0,1,0,1,1,0,0] => 6 [1,1,0,0,1,0,1,1,0,0,1,0] => 6 [1,1,0,0,1,0,1,1,0,1,0,0] => 6 [1,1,0,0,1,0,1,1,1,0,0,0] => 6 [1,1,0,0,1,1,0,0,1,0,1,0] => 6 [1,1,0,0,1,1,0,0,1,1,0,0] => 5 [1,1,0,0,1,1,0,1,0,0,1,0] => 6 [1,1,0,0,1,1,0,1,0,1,0,0] => 6 [1,1,0,0,1,1,0,1,1,0,0,0] => 6 [1,1,0,0,1,1,1,0,0,0,1,0] => 5 [1,1,0,0,1,1,1,0,0,1,0,0] => 5 [1,1,0,0,1,1,1,0,1,0,0,0] => 6 [1,1,0,0,1,1,1,1,0,0,0,0] => 6 [1,1,0,1,0,0,1,0,1,0,1,0] => 6 [1,1,0,1,0,0,1,0,1,1,0,0] => 6 [1,1,0,1,0,0,1,1,0,0,1,0] => 6 [1,1,0,1,0,0,1,1,0,1,0,0] => 6 [1,1,0,1,0,0,1,1,1,0,0,0] => 6 [1,1,0,1,0,1,0,0,1,0,1,0] => 6 [1,1,0,1,0,1,0,0,1,1,0,0] => 6 [1,1,0,1,0,1,0,1,0,0,1,0] => 6 [1,1,0,1,0,1,0,1,0,1,0,0] => 6 [1,1,0,1,0,1,0,1,1,0,0,0] => 5 [1,1,0,1,0,1,1,0,0,0,1,0] => 6 [1,1,0,1,0,1,1,0,0,1,0,0] => 6 [1,1,0,1,0,1,1,0,1,0,0,0] => 5 [1,1,0,1,0,1,1,1,0,0,0,0] => 6 [1,1,0,1,1,0,0,0,1,0,1,0] => 6 [1,1,0,1,1,0,0,0,1,1,0,0] => 5 [1,1,0,1,1,0,0,1,0,0,1,0] => 6 [1,1,0,1,1,0,0,1,0,1,0,0] => 6 [1,1,0,1,1,0,0,1,1,0,0,0] => 6 [1,1,0,1,1,0,1,0,0,0,1,0] => 6 [1,1,0,1,1,0,1,0,0,1,0,0] => 6 [1,1,0,1,1,0,1,0,1,0,0,0] => 5 [1,1,0,1,1,0,1,1,0,0,0,0] => 6 [1,1,0,1,1,1,0,0,0,0,1,0] => 5 [1,1,0,1,1,1,0,0,0,1,0,0] => 5 [1,1,0,1,1,1,0,0,1,0,0,0] => 6 [1,1,0,1,1,1,0,1,0,0,0,0] => 6 [1,1,0,1,1,1,1,0,0,0,0,0] => 6 [1,1,1,0,0,0,1,0,1,0,1,0] => 6 [1,1,1,0,0,0,1,0,1,1,0,0] => 6 [1,1,1,0,0,0,1,1,0,0,1,0] => 5 [1,1,1,0,0,0,1,1,0,1,0,0] => 6 [1,1,1,0,0,0,1,1,1,0,0,0] => 6 [1,1,1,0,0,1,0,0,1,0,1,0] => 6 [1,1,1,0,0,1,0,0,1,1,0,0] => 6 [1,1,1,0,0,1,0,1,0,0,1,0] => 6 [1,1,1,0,0,1,0,1,0,1,0,0] => 5 [1,1,1,0,0,1,0,1,1,0,0,0] => 6 [1,1,1,0,0,1,1,0,0,0,1,0] => 5 [1,1,1,0,0,1,1,0,0,1,0,0] => 6 [1,1,1,0,0,1,1,0,1,0,0,0] => 6 [1,1,1,0,0,1,1,1,0,0,0,0] => 6 [1,1,1,0,1,0,0,0,1,0,1,0] => 6 [1,1,1,0,1,0,0,0,1,1,0,0] => 6 [1,1,1,0,1,0,0,1,0,0,1,0] => 6 [1,1,1,0,1,0,0,1,0,1,0,0] => 5 [1,1,1,0,1,0,0,1,1,0,0,0] => 6 [1,1,1,0,1,0,1,0,0,0,1,0] => 6 [1,1,1,0,1,0,1,0,0,1,0,0] => 5 [1,1,1,0,1,0,1,0,1,0,0,0] => 5 [1,1,1,0,1,0,1,1,0,0,0,0] => 6 [1,1,1,0,1,1,0,0,0,0,1,0] => 5 [1,1,1,0,1,1,0,0,0,1,0,0] => 6 [1,1,1,0,1,1,0,0,1,0,0,0] => 6 [1,1,1,0,1,1,0,1,0,0,0,0] => 6 [1,1,1,0,1,1,1,0,0,0,0,0] => 6 [1,1,1,1,0,0,0,0,1,0,1,0] => 6 [1,1,1,1,0,0,0,0,1,1,0,0] => 6 [1,1,1,1,0,0,0,1,0,0,1,0] => 6 [1,1,1,1,0,0,0,1,0,1,0,0] => 6 [1,1,1,1,0,0,0,1,1,0,0,0] => 6 [1,1,1,1,0,0,1,0,0,0,1,0] => 6 [1,1,1,1,0,0,1,0,0,1,0,0] => 6 [1,1,1,1,0,0,1,0,1,0,0,0] => 6 [1,1,1,1,0,0,1,1,0,0,0,0] => 6 [1,1,1,1,0,1,0,0,0,0,1,0] => 6 [1,1,1,1,0,1,0,0,0,1,0,0] => 6 [1,1,1,1,0,1,0,0,1,0,0,0] => 6 [1,1,1,1,0,1,0,1,0,0,0,0] => 6 [1,1,1,1,0,1,1,0,0,0,0,0] => 6 [1,1,1,1,1,0,0,0,0,0,1,0] => 6 [1,1,1,1,1,0,0,0,0,1,0,0] => 6 [1,1,1,1,1,0,0,0,1,0,0,0] => 6 [1,1,1,1,1,0,0,1,0,0,0,0] => 6 [1,1,1,1,1,0,1,0,0,0,0,0] => 6 [1,1,1,1,1,1,0,0,0,0,0,0] => 1 ----------------------------------------------------------------------------- Created: Apr 29, 2018 at 14:14 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: May 02, 2018 at 11:34 by Rene Marczinzik