***************************************************************************** * 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: St001213 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 2 [1,0,1,0] => 4 [1,1,0,0] => 3 [1,0,1,0,1,0] => 6 [1,0,1,1,0,0] => 5 [1,1,0,0,1,0] => 5 [1,1,0,1,0,0] => 6 [1,1,1,0,0,0] => 4 [1,0,1,0,1,0,1,0] => 8 [1,0,1,0,1,1,0,0] => 7 [1,0,1,1,0,0,1,0] => 7 [1,0,1,1,0,1,0,0] => 8 [1,0,1,1,1,0,0,0] => 6 [1,1,0,0,1,0,1,0] => 7 [1,1,0,0,1,1,0,0] => 6 [1,1,0,1,0,0,1,0] => 8 [1,1,0,1,0,1,0,0] => 9 [1,1,0,1,1,0,0,0] => 7 [1,1,1,0,0,0,1,0] => 6 [1,1,1,0,0,1,0,0] => 7 [1,1,1,0,1,0,0,0] => 8 [1,1,1,1,0,0,0,0] => 5 [1,0,1,0,1,0,1,0,1,0] => 10 [1,0,1,0,1,0,1,1,0,0] => 9 [1,0,1,0,1,1,0,0,1,0] => 9 [1,0,1,0,1,1,0,1,0,0] => 10 [1,0,1,0,1,1,1,0,0,0] => 8 [1,0,1,1,0,0,1,0,1,0] => 9 [1,0,1,1,0,0,1,1,0,0] => 8 [1,0,1,1,0,1,0,0,1,0] => 10 [1,0,1,1,0,1,0,1,0,0] => 11 [1,0,1,1,0,1,1,0,0,0] => 9 [1,0,1,1,1,0,0,0,1,0] => 8 [1,0,1,1,1,0,0,1,0,0] => 9 [1,0,1,1,1,0,1,0,0,0] => 10 [1,0,1,1,1,1,0,0,0,0] => 7 [1,1,0,0,1,0,1,0,1,0] => 9 [1,1,0,0,1,0,1,1,0,0] => 8 [1,1,0,0,1,1,0,0,1,0] => 8 [1,1,0,0,1,1,0,1,0,0] => 9 [1,1,0,0,1,1,1,0,0,0] => 7 [1,1,0,1,0,0,1,0,1,0] => 10 [1,1,0,1,0,0,1,1,0,0] => 9 [1,1,0,1,0,1,0,0,1,0] => 11 [1,1,0,1,0,1,0,1,0,0] => 12 [1,1,0,1,0,1,1,0,0,0] => 10 [1,1,0,1,1,0,0,0,1,0] => 9 [1,1,0,1,1,0,0,1,0,0] => 10 [1,1,0,1,1,0,1,0,0,0] => 11 [1,1,0,1,1,1,0,0,0,0] => 8 [1,1,1,0,0,0,1,0,1,0] => 8 [1,1,1,0,0,0,1,1,0,0] => 7 [1,1,1,0,0,1,0,0,1,0] => 9 [1,1,1,0,0,1,0,1,0,0] => 10 [1,1,1,0,0,1,1,0,0,0] => 8 [1,1,1,0,1,0,0,0,1,0] => 10 [1,1,1,0,1,0,0,1,0,0] => 11 [1,1,1,0,1,0,1,0,0,0] => 12 [1,1,1,0,1,1,0,0,0,0] => 9 [1,1,1,1,0,0,0,0,1,0] => 7 [1,1,1,1,0,0,0,1,0,0] => 8 [1,1,1,1,0,0,1,0,0,0] => 9 [1,1,1,1,0,1,0,0,0,0] => 10 [1,1,1,1,1,0,0,0,0,0] => 6 [1,0,1,0,1,0,1,0,1,0,1,0] => 12 [1,0,1,0,1,0,1,0,1,1,0,0] => 11 [1,0,1,0,1,0,1,1,0,0,1,0] => 11 [1,0,1,0,1,0,1,1,0,1,0,0] => 12 [1,0,1,0,1,0,1,1,1,0,0,0] => 10 [1,0,1,0,1,1,0,0,1,0,1,0] => 11 [1,0,1,0,1,1,0,0,1,1,0,0] => 10 [1,0,1,0,1,1,0,1,0,0,1,0] => 12 [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] => 11 [1,0,1,0,1,1,1,0,0,0,1,0] => 10 [1,0,1,0,1,1,1,0,0,1,0,0] => 11 [1,0,1,0,1,1,1,0,1,0,0,0] => 12 [1,0,1,0,1,1,1,1,0,0,0,0] => 9 [1,0,1,1,0,0,1,0,1,0,1,0] => 11 [1,0,1,1,0,0,1,0,1,1,0,0] => 10 [1,0,1,1,0,0,1,1,0,0,1,0] => 10 [1,0,1,1,0,0,1,1,0,1,0,0] => 11 [1,0,1,1,0,0,1,1,1,0,0,0] => 9 [1,0,1,1,0,1,0,0,1,0,1,0] => 12 [1,0,1,1,0,1,0,0,1,1,0,0] => 11 [1,0,1,1,0,1,0,1,0,0,1,0] => 13 [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] => 12 [1,0,1,1,0,1,1,0,0,0,1,0] => 11 [1,0,1,1,0,1,1,0,0,1,0,0] => 12 [1,0,1,1,0,1,1,0,1,0,0,0] => 13 [1,0,1,1,0,1,1,1,0,0,0,0] => 10 [1,0,1,1,1,0,0,0,1,0,1,0] => 10 [1,0,1,1,1,0,0,0,1,1,0,0] => 9 [1,0,1,1,1,0,0,1,0,0,1,0] => 11 [1,0,1,1,1,0,0,1,0,1,0,0] => 12 [1,0,1,1,1,0,0,1,1,0,0,0] => 10 [1,0,1,1,1,0,1,0,0,0,1,0] => 12 [1,0,1,1,1,0,1,0,0,1,0,0] => 13 [1,0,1,1,1,0,1,0,1,0,0,0] => 14 [1,0,1,1,1,0,1,1,0,0,0,0] => 11 [1,0,1,1,1,1,0,0,0,0,1,0] => 9 [1,0,1,1,1,1,0,0,0,1,0,0] => 10 [1,0,1,1,1,1,0,0,1,0,0,0] => 11 [1,0,1,1,1,1,0,1,0,0,0,0] => 12 [1,0,1,1,1,1,1,0,0,0,0,0] => 8 [1,1,0,0,1,0,1,0,1,0,1,0] => 11 [1,1,0,0,1,0,1,0,1,1,0,0] => 10 [1,1,0,0,1,0,1,1,0,0,1,0] => 10 [1,1,0,0,1,0,1,1,0,1,0,0] => 11 [1,1,0,0,1,0,1,1,1,0,0,0] => 9 [1,1,0,0,1,1,0,0,1,0,1,0] => 10 [1,1,0,0,1,1,0,0,1,1,0,0] => 9 [1,1,0,0,1,1,0,1,0,0,1,0] => 11 [1,1,0,0,1,1,0,1,0,1,0,0] => 12 [1,1,0,0,1,1,0,1,1,0,0,0] => 10 [1,1,0,0,1,1,1,0,0,0,1,0] => 9 [1,1,0,0,1,1,1,0,0,1,0,0] => 10 [1,1,0,0,1,1,1,0,1,0,0,0] => 11 [1,1,0,0,1,1,1,1,0,0,0,0] => 8 [1,1,0,1,0,0,1,0,1,0,1,0] => 12 [1,1,0,1,0,0,1,0,1,1,0,0] => 11 [1,1,0,1,0,0,1,1,0,0,1,0] => 11 [1,1,0,1,0,0,1,1,0,1,0,0] => 12 [1,1,0,1,0,0,1,1,1,0,0,0] => 10 [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] => 12 [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] => 13 [1,1,0,1,0,1,1,0,0,0,1,0] => 12 [1,1,0,1,0,1,1,0,0,1,0,0] => 13 [1,1,0,1,0,1,1,0,1,0,0,0] => 14 [1,1,0,1,0,1,1,1,0,0,0,0] => 11 [1,1,0,1,1,0,0,0,1,0,1,0] => 11 [1,1,0,1,1,0,0,0,1,1,0,0] => 10 [1,1,0,1,1,0,0,1,0,0,1,0] => 12 [1,1,0,1,1,0,0,1,0,1,0,0] => 13 [1,1,0,1,1,0,0,1,1,0,0,0] => 11 [1,1,0,1,1,0,1,0,0,0,1,0] => 13 [1,1,0,1,1,0,1,0,0,1,0,0] => 14 [1,1,0,1,1,0,1,0,1,0,0,0] => 15 [1,1,0,1,1,0,1,1,0,0,0,0] => 12 [1,1,0,1,1,1,0,0,0,0,1,0] => 10 [1,1,0,1,1,1,0,0,0,1,0,0] => 11 [1,1,0,1,1,1,0,0,1,0,0,0] => 12 [1,1,0,1,1,1,0,1,0,0,0,0] => 13 [1,1,0,1,1,1,1,0,0,0,0,0] => 9 [1,1,1,0,0,0,1,0,1,0,1,0] => 10 [1,1,1,0,0,0,1,0,1,1,0,0] => 9 [1,1,1,0,0,0,1,1,0,0,1,0] => 9 [1,1,1,0,0,0,1,1,0,1,0,0] => 10 [1,1,1,0,0,0,1,1,1,0,0,0] => 8 [1,1,1,0,0,1,0,0,1,0,1,0] => 11 [1,1,1,0,0,1,0,0,1,1,0,0] => 10 [1,1,1,0,0,1,0,1,0,0,1,0] => 12 [1,1,1,0,0,1,0,1,0,1,0,0] => 13 [1,1,1,0,0,1,0,1,1,0,0,0] => 11 [1,1,1,0,0,1,1,0,0,0,1,0] => 10 [1,1,1,0,0,1,1,0,0,1,0,0] => 11 [1,1,1,0,0,1,1,0,1,0,0,0] => 12 [1,1,1,0,0,1,1,1,0,0,0,0] => 9 [1,1,1,0,1,0,0,0,1,0,1,0] => 12 [1,1,1,0,1,0,0,0,1,1,0,0] => 11 [1,1,1,0,1,0,0,1,0,0,1,0] => 13 [1,1,1,0,1,0,0,1,0,1,0,0] => 14 [1,1,1,0,1,0,0,1,1,0,0,0] => 12 [1,1,1,0,1,0,1,0,0,0,1,0] => 14 [1,1,1,0,1,0,1,0,0,1,0,0] => 15 [1,1,1,0,1,0,1,0,1,0,0,0] => 16 [1,1,1,0,1,0,1,1,0,0,0,0] => 13 [1,1,1,0,1,1,0,0,0,0,1,0] => 11 [1,1,1,0,1,1,0,0,0,1,0,0] => 12 [1,1,1,0,1,1,0,0,1,0,0,0] => 13 [1,1,1,0,1,1,0,1,0,0,0,0] => 14 [1,1,1,0,1,1,1,0,0,0,0,0] => 10 [1,1,1,1,0,0,0,0,1,0,1,0] => 9 [1,1,1,1,0,0,0,0,1,1,0,0] => 8 [1,1,1,1,0,0,0,1,0,0,1,0] => 10 [1,1,1,1,0,0,0,1,0,1,0,0] => 11 [1,1,1,1,0,0,0,1,1,0,0,0] => 9 [1,1,1,1,0,0,1,0,0,0,1,0] => 11 [1,1,1,1,0,0,1,0,0,1,0,0] => 12 [1,1,1,1,0,0,1,0,1,0,0,0] => 13 [1,1,1,1,0,0,1,1,0,0,0,0] => 10 [1,1,1,1,0,1,0,0,0,0,1,0] => 12 [1,1,1,1,0,1,0,0,0,1,0,0] => 13 [1,1,1,1,0,1,0,0,1,0,0,0] => 14 [1,1,1,1,0,1,0,1,0,0,0,0] => 15 [1,1,1,1,0,1,1,0,0,0,0,0] => 11 [1,1,1,1,1,0,0,0,0,0,1,0] => 8 [1,1,1,1,1,0,0,0,0,1,0,0] => 9 [1,1,1,1,1,0,0,0,1,0,0,0] => 10 [1,1,1,1,1,0,0,1,0,0,0,0] => 11 [1,1,1,1,1,0,1,0,0,0,0,0] => 12 [1,1,1,1,1,1,0,0,0,0,0,0] => 7 ----------------------------------------------------------------------------- Created: Jun 20, 2018 at 16:24 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Jun 20, 2018 at 16:24 by Rene Marczinzik