***************************************************************************** * 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: St000955 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- 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] => 2 [1,1,0,0,1,0] => 2 [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] => 2 [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] => 2 [1,1,0,0,1,0,1,0] => 2 [1,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,0] => 2 [1,1,0,1,1,0,0,0] => 2 [1,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,1,0,0] => 2 [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] => 2 [1,0,1,0,1,1,0,0,1,0] => 3 [1,0,1,0,1,1,0,1,0,0] => 2 [1,0,1,0,1,1,1,0,0,0] => 2 [1,0,1,1,0,0,1,0,1,0] => 3 [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] => 3 [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] => 2 [1,1,0,0,1,0,1,0,1,0] => 2 [1,1,0,0,1,0,1,1,0,0] => 2 [1,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,1,1,0,0,0] => 2 [1,1,0,1,0,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,1,0,0] => 1 [1,1,0,1,0,1,1,0,0,0] => 3 [1,1,0,1,1,0,0,0,1,0] => 2 [1,1,0,1,1,0,0,1,0,0] => 3 [1,1,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,1,1,0,0,0,0] => 2 [1,1,1,0,0,0,1,0,1,0] => 2 [1,1,1,0,0,0,1,1,0,0] => 2 [1,1,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,0,0,1,0] => 2 [1,1,1,0,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,1,0,0,0] => 2 [1,1,1,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,0,0,0,1,0] => 2 [1,1,1,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,0,0,0] => 2 [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] => 2 [1,0,1,0,1,0,1,1,0,0,1,0] => 3 [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] => 2 [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] => 3 [1,0,1,0,1,1,0,1,0,0,1,0] => 3 [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] => 3 [1,0,1,0,1,1,1,0,0,0,1,0] => 3 [1,0,1,0,1,1,1,0,0,1,0,0] => 3 [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] => 2 [1,0,1,1,0,0,1,0,1,0,1,0] => 3 [1,0,1,1,0,0,1,0,1,1,0,0] => 3 [1,0,1,1,0,0,1,1,0,0,1,0] => 2 [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] => 3 [1,0,1,1,0,1,0,0,1,1,0,0] => 3 [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] => 3 [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] => 4 [1,0,1,1,0,1,1,0,1,0,0,0] => 2 [1,0,1,1,0,1,1,1,0,0,0,0] => 3 [1,0,1,1,1,0,0,0,1,0,1,0] => 3 [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] => 3 [1,0,1,1,1,0,0,1,0,1,0,0] => 3 [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] => 3 [1,0,1,1,1,0,1,0,0,1,0,0] => 3 [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] => 3 [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] => 2 [1,1,0,0,1,0,1,0,1,0,1,0] => 2 [1,1,0,0,1,0,1,0,1,1,0,0] => 2 [1,1,0,0,1,0,1,1,0,0,1,0] => 3 [1,1,0,0,1,0,1,1,0,1,0,0] => 3 [1,1,0,0,1,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,1,0,0,1,0,1,0] => 3 [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] => 3 [1,1,0,0,1,1,0,1,0,1,0,0] => 3 [1,1,0,0,1,1,0,1,1,0,0,0] => 3 [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] => 3 [1,1,0,0,1,1,1,1,0,0,0,0] => 2 [1,1,0,1,0,0,1,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,0,1,1,0,0] => 3 [1,1,0,1,0,0,1,1,0,0,1,0] => 3 [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] => 3 [1,1,0,1,0,1,0,0,1,0,1,0] => 2 [1,1,0,1,0,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,0,1,0,0,1,0] => 2 [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] => 2 [1,1,0,1,0,1,1,0,0,0,1,0] => 3 [1,1,0,1,0,1,1,0,0,1,0,0] => 3 [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] => 3 [1,1,0,1,1,0,0,0,1,0,1,0] => 3 [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] => 4 [1,1,0,1,1,0,0,1,0,1,0,0] => 3 [1,1,0,1,1,0,0,1,1,0,0,0] => 3 [1,1,0,1,1,0,1,0,0,0,1,0] => 3 [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] => 3 [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] => 3 [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] => 2 [1,1,1,0,0,0,1,0,1,0,1,0] => 2 [1,1,1,0,0,0,1,0,1,1,0,0] => 2 [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] => 3 [1,1,1,0,0,0,1,1,1,0,0,0] => 2 [1,1,1,0,0,1,0,0,1,0,1,0] => 3 [1,1,1,0,0,1,0,0,1,1,0,0] => 3 [1,1,1,0,0,1,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,1,0,0] => 2 [1,1,1,0,0,1,0,1,1,0,0,0] => 3 [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] => 3 [1,1,1,0,0,1,1,0,1,0,0,0] => 3 [1,1,1,0,0,1,1,1,0,0,0,0] => 2 [1,1,1,0,1,0,0,0,1,0,1,0] => 2 [1,1,1,0,1,0,0,0,1,1,0,0] => 3 [1,1,1,0,1,0,0,1,0,0,1,0] => 2 [1,1,1,0,1,0,0,1,0,1,0,0] => 2 [1,1,1,0,1,0,0,1,1,0,0,0] => 3 [1,1,1,0,1,0,1,0,0,0,1,0] => 2 [1,1,1,0,1,0,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,1,0,1,0,0,0] => 2 [1,1,1,0,1,0,1,1,0,0,0,0] => 3 [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] => 3 [1,1,1,0,1,1,0,0,1,0,0,0] => 3 [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] => 2 [1,1,1,1,0,0,0,0,1,0,1,0] => 2 [1,1,1,1,0,0,0,0,1,1,0,0] => 2 [1,1,1,1,0,0,0,1,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,0,1,0,0] => 3 [1,1,1,1,0,0,0,1,1,0,0,0] => 2 [1,1,1,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,0,1,0,0,1,0,0] => 3 [1,1,1,1,0,0,1,0,1,0,0,0] => 3 [1,1,1,1,0,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0,1,0] => 2 [1,1,1,1,0,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,1,0,0,0,0] => 2 [1,1,1,1,0,1,1,0,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0,1,0] => 2 [1,1,1,1,1,0,0,0,0,1,0,0] => 2 [1,1,1,1,1,0,0,0,1,0,0,0] => 2 [1,1,1,1,1,0,0,1,0,0,0,0] => 2 [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: Aug 25, 2017 at 21:21 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Aug 25, 2017 at 21:21 by Rene Marczinzik