***************************************************************************** * 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: St000964 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 1 [1,1,0,0] => 3 [1,0,1,0,1,0] => 1 [1,0,1,1,0,0] => 1 [1,1,0,0,1,0] => 1 [1,1,0,1,0,0] => 3 [1,1,1,0,0,0] => 6 [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] => 2 [1,0,1,1,0,1,0,0] => 2 [1,0,1,1,1,0,0,0] => 1 [1,1,0,0,1,0,1,0] => 1 [1,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,0] => 1 [1,1,0,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,0] => 1 [1,1,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,0,0] => 6 [1,1,1,1,0,0,0,0] => 10 [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] => 2 [1,0,1,0,1,1,1,0,0,0] => 1 [1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,1,0,1,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,0] => 1 [1,0,1,1,0,1,1,0,0,0] => 2 [1,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,0,0,0] => 1 [1,1,0,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,0,0] => 1 [1,1,0,1,0,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,0] => 1 [1,1,0,1,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,1,1,0,0,0,0] => 3 [1,1,1,0,0,0,1,0,1,0] => 1 [1,1,1,0,0,0,1,1,0,0] => 1 [1,1,1,0,0,1,0,0,1,0] => 2 [1,1,1,0,0,1,0,1,0,0] => 1 [1,1,1,0,0,1,1,0,0,0] => 3 [1,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,0] => 2 [1,1,1,0,1,0,1,0,0,0] => 1 [1,1,1,0,1,1,0,0,0,0] => 6 [1,1,1,1,0,0,0,0,1,0] => 1 [1,1,1,1,0,0,0,1,0,0] => 3 [1,1,1,1,0,0,1,0,0,0] => 6 [1,1,1,1,0,1,0,0,0,0] => 10 [1,1,1,1,1,0,0,0,0,0] => 15 [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] => 2 [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] => 2 [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] => 1 [1,0,1,0,1,1,0,1,1,0,0,0] => 2 [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] => 3 [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] => 1 [1,0,1,1,0,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,1,0,0,1,0] => 3 [1,0,1,1,0,0,1,1,0,1,0,0] => 2 [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] => 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] => 1 [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] => 1 [1,0,1,1,0,1,1,0,0,0,1,0] => 2 [1,0,1,1,0,1,1,0,0,1,0,0] => 2 [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] => 2 [1,0,1,1,1,0,0,0,1,0,1,0] => 1 [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] => 2 [1,0,1,1,1,0,0,1,0,1,0,0] => 1 [1,0,1,1,1,0,0,1,1,0,0,0] => 4 [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] => 1 [1,0,1,1,1,0,1,0,1,0,0,0] => 1 [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] => 4 [1,0,1,1,1,1,0,0,1,0,0,0] => 7 [1,0,1,1,1,1,0,1,0,0,0,0] => 4 [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] => 1 [1,1,0,0,1,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,0,1,1,0,0,1,0] => 1 [1,1,0,0,1,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,0,1,1,1,0,0,0] => 1 [1,1,0,0,1,1,0,0,1,0,1,0] => 1 [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] => 1 [1,1,0,0,1,1,0,1,0,1,0,0] => 1 [1,1,0,0,1,1,0,1,1,0,0,0] => 2 [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] => 4 [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] => 1 [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] => 2 [1,1,0,1,0,0,1,1,0,0,1,0] => 2 [1,1,0,1,0,0,1,1,0,1,0,0] => 4 [1,1,0,1,0,0,1,1,1,0,0,0] => 2 [1,1,0,1,0,1,0,0,1,0,1,0] => 1 [1,1,0,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,0,1,1,0,0,0] => 3 [1,1,0,1,0,1,1,0,0,0,1,0] => 1 [1,1,0,1,0,1,1,0,0,1,0,0] => 2 [1,1,0,1,0,1,1,0,1,0,0,0] => 4 [1,1,0,1,0,1,1,1,0,0,0,0] => 1 [1,1,0,1,1,0,0,0,1,0,1,0] => 1 [1,1,0,1,1,0,0,0,1,1,0,0] => 4 [1,1,0,1,1,0,0,1,0,0,1,0] => 2 [1,1,0,1,1,0,0,1,0,1,0,0] => 2 [1,1,0,1,1,0,0,1,1,0,0,0] => 4 [1,1,0,1,1,0,1,0,0,0,1,0] => 1 [1,1,0,1,1,0,1,0,0,1,0,0] => 1 [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] => 2 [1,1,0,1,1,1,0,0,0,0,1,0] => 4 [1,1,0,1,1,1,0,0,0,1,0,0] => 6 [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] => 3 [1,1,0,1,1,1,1,0,0,0,0,0] => 3 [1,1,1,0,0,0,1,0,1,0,1,0] => 1 [1,1,1,0,0,0,1,0,1,1,0,0] => 1 [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] => 2 [1,1,1,0,0,0,1,1,1,0,0,0] => 1 [1,1,1,0,0,1,0,0,1,0,1,0] => 2 [1,1,1,0,0,1,0,0,1,1,0,0] => 2 [1,1,1,0,0,1,0,1,0,0,1,0] => 1 [1,1,1,0,0,1,0,1,0,1,0,0] => 3 [1,1,1,0,0,1,0,1,1,0,0,0] => 1 [1,1,1,0,0,1,1,0,0,0,1,0] => 4 [1,1,1,0,0,1,1,0,0,1,0,0] => 4 [1,1,1,0,0,1,1,0,1,0,0,0] => 2 [1,1,1,0,0,1,1,1,0,0,0,0] => 3 [1,1,1,0,1,0,0,0,1,0,1,0] => 3 [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] => 4 [1,1,1,0,1,0,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,1,0,0,0,1,0] => 1 [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] => 3 [1,1,1,0,1,0,1,1,0,0,0,0] => 1 [1,1,1,0,1,1,0,0,0,0,1,0] => 7 [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] => 4 [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] => 6 [1,1,1,1,0,0,0,0,1,0,1,0] => 1 [1,1,1,1,0,0,0,0,1,1,0,0] => 1 [1,1,1,1,0,0,0,1,0,0,1,0] => 2 [1,1,1,1,0,0,0,1,0,1,0,0] => 1 [1,1,1,1,0,0,0,1,1,0,0,0] => 3 [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] => 2 [1,1,1,1,0,0,1,0,1,0,0,0] => 1 [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] => 4 [1,1,1,1,0,1,0,0,0,1,0,0] => 3 [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] => 1 [1,1,1,1,0,1,1,0,0,0,0,0] => 10 [1,1,1,1,1,0,0,0,0,0,1,0] => 1 [1,1,1,1,1,0,0,0,0,1,0,0] => 3 [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] => 10 [1,1,1,1,1,0,1,0,0,0,0,0] => 15 [1,1,1,1,1,1,0,0,0,0,0,0] => 21 ----------------------------------------------------------------------------- Created: Aug 31, 2017 at 11:02 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Aug 31, 2017 at 11:02 by Rene Marczinzik