***************************************************************************** * 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: St001138 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The number of indecomposable modules with projective dimension or injective dimension at most one 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] => 3 [1,0,1,0] => 5 [1,1,0,0] => 6 [1,0,1,0,1,0] => 7 [1,0,1,1,0,0] => 8 [1,1,0,0,1,0] => 8 [1,1,0,1,0,0] => 9 [1,1,1,0,0,0] => 10 [1,0,1,0,1,0,1,0] => 8 [1,0,1,0,1,1,0,0] => 10 [1,0,1,1,0,0,1,0] => 9 [1,0,1,1,0,1,0,0] => 11 [1,0,1,1,1,0,0,0] => 12 [1,1,0,0,1,0,1,0] => 10 [1,1,0,0,1,1,0,0] => 11 [1,1,0,1,0,0,1,0] => 11 [1,1,0,1,0,1,0,0] => 12 [1,1,0,1,1,0,0,0] => 13 [1,1,1,0,0,0,1,0] => 12 [1,1,1,0,0,1,0,0] => 13 [1,1,1,0,1,0,0,0] => 14 [1,1,1,1,0,0,0,0] => 15 [1,0,1,0,1,0,1,0,1,0] => 9 [1,0,1,0,1,0,1,1,0,0] => 11 [1,0,1,0,1,1,0,0,1,0] => 11 [1,0,1,0,1,1,0,1,0,0] => 12 [1,0,1,0,1,1,1,0,0,0] => 14 [1,0,1,1,0,0,1,0,1,0] => 11 [1,0,1,1,0,0,1,1,0,0] => 12 [1,0,1,1,0,1,0,0,1,0] => 12 [1,0,1,1,0,1,0,1,0,0] => 12 [1,0,1,1,0,1,1,0,0,0] => 15 [1,0,1,1,1,0,0,0,1,0] => 13 [1,0,1,1,1,0,0,1,0,0] => 13 [1,0,1,1,1,0,1,0,0,0] => 16 [1,0,1,1,1,1,0,0,0,0] => 17 [1,1,0,0,1,0,1,0,1,0] => 11 [1,1,0,0,1,0,1,1,0,0] => 13 [1,1,0,0,1,1,0,0,1,0] => 12 [1,1,0,0,1,1,0,1,0,0] => 14 [1,1,0,0,1,1,1,0,0,0] => 15 [1,1,0,1,0,0,1,0,1,0] => 12 [1,1,0,1,0,0,1,1,0,0] => 14 [1,1,0,1,0,1,0,0,1,0] => 12 [1,1,0,1,0,1,0,1,0,0] => 14 [1,1,0,1,0,1,1,0,0,0] => 16 [1,1,0,1,1,0,0,0,1,0] => 13 [1,1,0,1,1,0,0,1,0,0] => 15 [1,1,0,1,1,0,1,0,0,0] => 17 [1,1,0,1,1,1,0,0,0,0] => 18 [1,1,1,0,0,0,1,0,1,0] => 14 [1,1,1,0,0,0,1,1,0,0] => 15 [1,1,1,0,0,1,0,0,1,0] => 15 [1,1,1,0,0,1,0,1,0,0] => 16 [1,1,1,0,0,1,1,0,0,0] => 17 [1,1,1,0,1,0,0,0,1,0] => 16 [1,1,1,0,1,0,0,1,0,0] => 17 [1,1,1,0,1,0,1,0,0,0] => 18 [1,1,1,0,1,1,0,0,0,0] => 19 [1,1,1,1,0,0,0,0,1,0] => 17 [1,1,1,1,0,0,0,1,0,0] => 18 [1,1,1,1,0,0,1,0,0,0] => 19 [1,1,1,1,0,1,0,0,0,0] => 20 [1,1,1,1,1,0,0,0,0,0] => 21 [1,0,1,0,1,0,1,0,1,0,1,0] => 10 [1,0,1,0,1,0,1,0,1,1,0,0] => 12 [1,0,1,0,1,0,1,1,0,0,1,0] => 12 [1,0,1,0,1,0,1,1,0,1,0,0] => 13 [1,0,1,0,1,0,1,1,1,0,0,0] => 15 [1,0,1,0,1,1,0,0,1,0,1,0] => 13 [1,0,1,0,1,1,0,0,1,1,0,0] => 14 [1,0,1,0,1,1,0,1,0,0,1,0] => 13 [1,0,1,0,1,1,0,1,0,1,0,0] => 13 [1,0,1,0,1,1,0,1,1,0,0,0] => 16 [1,0,1,0,1,1,1,0,0,0,1,0] => 15 [1,0,1,0,1,1,1,0,0,1,0,0] => 15 [1,0,1,0,1,1,1,0,1,0,0,0] => 17 [1,0,1,0,1,1,1,1,0,0,0,0] => 19 [1,0,1,1,0,0,1,0,1,0,1,0] => 12 [1,0,1,1,0,0,1,0,1,1,0,0] => 14 [1,0,1,1,0,0,1,1,0,0,1,0] => 13 [1,0,1,1,0,0,1,1,0,1,0,0] => 15 [1,0,1,1,0,0,1,1,1,0,0,0] => 16 [1,0,1,1,0,1,0,0,1,0,1,0] => 13 [1,0,1,1,0,1,0,0,1,1,0,0] => 15 [1,0,1,1,0,1,0,1,0,0,1,0] => 12 [1,0,1,1,0,1,0,1,0,1,0,0] => 14 [1,0,1,1,0,1,0,1,1,0,0,0] => 16 [1,0,1,1,0,1,1,0,0,0,1,0] => 15 [1,0,1,1,0,1,1,0,0,1,0,0] => 16 [1,0,1,1,0,1,1,0,1,0,0,0] => 17 [1,0,1,1,0,1,1,1,0,0,0,0] => 20 [1,0,1,1,1,0,0,0,1,0,1,0] => 15 [1,0,1,1,1,0,0,0,1,1,0,0] => 16 [1,0,1,1,1,0,0,1,0,0,1,0] => 15 [1,0,1,1,1,0,0,1,0,1,0,0] => 16 [1,0,1,1,1,0,0,1,1,0,0,0] => 17 [1,0,1,1,1,0,1,0,0,0,1,0] => 17 [1,0,1,1,1,0,1,0,0,1,0,0] => 17 [1,0,1,1,1,0,1,0,1,0,0,0] => 17 [1,0,1,1,1,0,1,1,0,0,0,0] => 21 [1,0,1,1,1,1,0,0,0,0,1,0] => 18 [1,0,1,1,1,1,0,0,0,1,0,0] => 18 [1,0,1,1,1,1,0,0,1,0,0,0] => 18 [1,0,1,1,1,1,0,1,0,0,0,0] => 22 [1,0,1,1,1,1,1,0,0,0,0,0] => 23 [1,1,0,0,1,0,1,0,1,0,1,0] => 12 [1,1,0,0,1,0,1,0,1,1,0,0] => 14 [1,1,0,0,1,0,1,1,0,0,1,0] => 14 [1,1,0,0,1,0,1,1,0,1,0,0] => 15 [1,1,0,0,1,0,1,1,1,0,0,0] => 17 [1,1,0,0,1,1,0,0,1,0,1,0] => 14 [1,1,0,0,1,1,0,0,1,1,0,0] => 15 [1,1,0,0,1,1,0,1,0,0,1,0] => 15 [1,1,0,0,1,1,0,1,0,1,0,0] => 15 [1,1,0,0,1,1,0,1,1,0,0,0] => 18 [1,1,0,0,1,1,1,0,0,0,1,0] => 16 [1,1,0,0,1,1,1,0,0,1,0,0] => 16 [1,1,0,0,1,1,1,0,1,0,0,0] => 19 [1,1,0,0,1,1,1,1,0,0,0,0] => 20 [1,1,0,1,0,0,1,0,1,0,1,0] => 13 [1,1,0,1,0,0,1,0,1,1,0,0] => 15 [1,1,0,1,0,0,1,1,0,0,1,0] => 15 [1,1,0,1,0,0,1,1,0,1,0,0] => 16 [1,1,0,1,0,0,1,1,1,0,0,0] => 18 [1,1,0,1,0,1,0,0,1,0,1,0] => 13 [1,1,0,1,0,1,0,0,1,1,0,0] => 15 [1,1,0,1,0,1,0,1,0,0,1,0] => 14 [1,1,0,1,0,1,0,1,0,1,0,0] => 15 [1,1,0,1,0,1,0,1,1,0,0,0] => 18 [1,1,0,1,0,1,1,0,0,0,1,0] => 16 [1,1,0,1,0,1,1,0,0,1,0,0] => 16 [1,1,0,1,0,1,1,0,1,0,0,0] => 19 [1,1,0,1,0,1,1,1,0,0,0,0] => 21 [1,1,0,1,1,0,0,0,1,0,1,0] => 15 [1,1,0,1,1,0,0,0,1,1,0,0] => 16 [1,1,0,1,1,0,0,1,0,0,1,0] => 16 [1,1,0,1,1,0,0,1,0,1,0,0] => 16 [1,1,0,1,1,0,0,1,1,0,0,0] => 19 [1,1,0,1,1,0,1,0,0,0,1,0] => 17 [1,1,0,1,1,0,1,0,0,1,0,0] => 16 [1,1,0,1,1,0,1,0,1,0,0,0] => 19 [1,1,0,1,1,0,1,1,0,0,0,0] => 22 [1,1,0,1,1,1,0,0,0,0,1,0] => 18 [1,1,0,1,1,1,0,0,0,1,0,0] => 17 [1,1,0,1,1,1,0,0,1,0,0,0] => 20 [1,1,0,1,1,1,0,1,0,0,0,0] => 23 [1,1,0,1,1,1,1,0,0,0,0,0] => 24 [1,1,1,0,0,0,1,0,1,0,1,0] => 15 [1,1,1,0,0,0,1,0,1,1,0,0] => 17 [1,1,1,0,0,0,1,1,0,0,1,0] => 16 [1,1,1,0,0,0,1,1,0,1,0,0] => 18 [1,1,1,0,0,0,1,1,1,0,0,0] => 19 [1,1,1,0,0,1,0,0,1,0,1,0] => 16 [1,1,1,0,0,1,0,0,1,1,0,0] => 18 [1,1,1,0,0,1,0,1,0,0,1,0] => 16 [1,1,1,0,0,1,0,1,0,1,0,0] => 18 [1,1,1,0,0,1,0,1,1,0,0,0] => 20 [1,1,1,0,0,1,1,0,0,0,1,0] => 17 [1,1,1,0,0,1,1,0,0,1,0,0] => 19 [1,1,1,0,0,1,1,0,1,0,0,0] => 21 [1,1,1,0,0,1,1,1,0,0,0,0] => 22 [1,1,1,0,1,0,0,0,1,0,1,0] => 17 [1,1,1,0,1,0,0,0,1,1,0,0] => 19 [1,1,1,0,1,0,0,1,0,0,1,0] => 17 [1,1,1,0,1,0,0,1,0,1,0,0] => 19 [1,1,1,0,1,0,0,1,1,0,0,0] => 21 [1,1,1,0,1,0,1,0,0,0,1,0] => 17 [1,1,1,0,1,0,1,0,0,1,0,0] => 19 [1,1,1,0,1,0,1,0,1,0,0,0] => 21 [1,1,1,0,1,0,1,1,0,0,0,0] => 23 [1,1,1,0,1,1,0,0,0,0,1,0] => 18 [1,1,1,0,1,1,0,0,0,1,0,0] => 20 [1,1,1,0,1,1,0,0,1,0,0,0] => 22 [1,1,1,0,1,1,0,1,0,0,0,0] => 24 [1,1,1,0,1,1,1,0,0,0,0,0] => 25 [1,1,1,1,0,0,0,0,1,0,1,0] => 19 [1,1,1,1,0,0,0,0,1,1,0,0] => 20 [1,1,1,1,0,0,0,1,0,0,1,0] => 20 [1,1,1,1,0,0,0,1,0,1,0,0] => 21 [1,1,1,1,0,0,0,1,1,0,0,0] => 22 [1,1,1,1,0,0,1,0,0,0,1,0] => 21 [1,1,1,1,0,0,1,0,0,1,0,0] => 22 [1,1,1,1,0,0,1,0,1,0,0,0] => 23 [1,1,1,1,0,0,1,1,0,0,0,0] => 24 [1,1,1,1,0,1,0,0,0,0,1,0] => 22 [1,1,1,1,0,1,0,0,0,1,0,0] => 23 [1,1,1,1,0,1,0,0,1,0,0,0] => 24 [1,1,1,1,0,1,0,1,0,0,0,0] => 25 [1,1,1,1,0,1,1,0,0,0,0,0] => 26 [1,1,1,1,1,0,0,0,0,0,1,0] => 23 [1,1,1,1,1,0,0,0,0,1,0,0] => 24 [1,1,1,1,1,0,0,0,1,0,0,0] => 25 [1,1,1,1,1,0,0,1,0,0,0,0] => 26 [1,1,1,1,1,0,1,0,0,0,0,0] => 27 [1,1,1,1,1,1,0,0,0,0,0,0] => 28 ----------------------------------------------------------------------------- Created: Apr 09, 2018 at 14:03 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: May 02, 2018 at 12:35 by Rene Marczinzik