***************************************************************************** * 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: St001480 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The number of simple summands of the module J^2/J^3. Here J is the Jacobson radical of the Nakayama algebra algebra corresponding to the Dyck path. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0,1,0] => 0 [1,1,0,0] => 1 [1,0,1,0,1,0] => 0 [1,0,1,1,0,0] => 1 [1,1,0,0,1,0] => 1 [1,1,0,1,0,0] => 2 [1,1,1,0,0,0] => 2 [1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,0] => 1 [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] => 1 [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] => 3 [1,1,0,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,0,0] => 3 [1,1,1,1,0,0,0,0] => 3 [1,0,1,0,1,0,1,0,1,0] => 0 [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] => 2 [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] => 2 [1,0,1,1,0,1,0,1,0,0] => 3 [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] => 3 [1,0,1,1,1,0,1,0,0,0] => 3 [1,0,1,1,1,1,0,0,0,0] => 3 [1,1,0,0,1,0,1,0,1,0] => 1 [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] => 3 [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] => 3 [1,1,0,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,1,1,0,0,0] => 4 [1,1,0,1,1,0,0,0,1,0] => 3 [1,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,0,0,0] => 4 [1,1,0,1,1,1,0,0,0,0] => 4 [1,1,1,0,0,0,1,0,1,0] => 2 [1,1,1,0,0,0,1,1,0,0] => 3 [1,1,1,0,0,1,0,0,1,0] => 3 [1,1,1,0,0,1,0,1,0,0] => 4 [1,1,1,0,0,1,1,0,0,0] => 4 [1,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,1,0,0,0] => 4 [1,1,1,0,1,1,0,0,0,0] => 4 [1,1,1,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,0,0,0] => 4 [1,1,1,1,1,0,0,0,0,0] => 4 [1,0,1,0,1,0,1,0,1,0,1,0] => 0 [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] => 2 [1,0,1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,0,1,1,0,0] => 2 [1,0,1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,0,1,1,0,1,0,1,0,0] => 3 [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] => 2 [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] => 3 [1,0,1,0,1,1,1,1,0,0,0,0] => 3 [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] => 2 [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] => 3 [1,0,1,1,0,1,0,0,1,0,1,0] => 2 [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] => 3 [1,0,1,1,0,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,1,0,1,1,0,0,0] => 4 [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] => 4 [1,0,1,1,0,1,1,1,0,0,0,0] => 4 [1,0,1,1,1,0,0,0,1,0,1,0] => 2 [1,0,1,1,1,0,0,0,1,1,0,0] => 3 [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] => 4 [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] => 3 [1,0,1,1,1,0,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,0,1,0,0,0] => 4 [1,0,1,1,1,0,1,1,0,0,0,0] => 4 [1,0,1,1,1,1,0,0,0,0,1,0] => 3 [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] => 4 [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] => 4 [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] => 2 [1,1,0,0,1,0,1,1,0,0,1,0] => 2 [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] => 3 [1,1,0,0,1,1,0,0,1,0,1,0] => 2 [1,1,0,0,1,1,0,0,1,1,0,0] => 3 [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] => 4 [1,1,0,0,1,1,0,1,1,0,0,0] => 4 [1,1,0,0,1,1,1,0,0,0,1,0] => 3 [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] => 4 [1,1,0,0,1,1,1,1,0,0,0,0] => 4 [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] => 4 [1,1,0,1,0,0,1,1,1,0,0,0] => 4 [1,1,0,1,0,1,0,0,1,0,1,0] => 3 [1,1,0,1,0,1,0,0,1,1,0,0] => 4 [1,1,0,1,0,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,0,1,0,1,0,0] => 5 [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] => 4 [1,1,0,1,0,1,1,0,0,1,0,0] => 5 [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] => 5 [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] => 4 [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] => 5 [1,1,0,1,1,0,0,1,1,0,0,0] => 5 [1,1,0,1,1,0,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,1,0,0,1,0,0] => 5 [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] => 5 [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] => 5 [1,1,0,1,1,1,0,0,1,0,0,0] => 5 [1,1,0,1,1,1,0,1,0,0,0,0] => 5 [1,1,0,1,1,1,1,0,0,0,0,0] => 5 [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] => 3 [1,1,1,0,0,0,1,1,0,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,1,0,0] => 4 [1,1,1,0,0,0,1,1,1,0,0,0] => 4 [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] => 4 [1,1,1,0,0,1,0,1,0,0,1,0] => 4 [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] => 5 [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] => 5 [1,1,1,0,0,1,1,0,1,0,0,0] => 5 [1,1,1,0,0,1,1,1,0,0,0,0] => 5 [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] => 4 [1,1,1,0,1,0,0,1,0,0,1,0] => 4 [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] => 5 [1,1,1,0,1,0,1,0,0,0,1,0] => 4 [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] => 5 [1,1,1,0,1,1,0,0,0,0,1,0] => 4 [1,1,1,0,1,1,0,0,0,1,0,0] => 5 [1,1,1,0,1,1,0,0,1,0,0,0] => 5 [1,1,1,0,1,1,0,1,0,0,0,0] => 5 [1,1,1,0,1,1,1,0,0,0,0,0] => 5 [1,1,1,1,0,0,0,0,1,0,1,0] => 3 [1,1,1,1,0,0,0,0,1,1,0,0] => 4 [1,1,1,1,0,0,0,1,0,0,1,0] => 4 [1,1,1,1,0,0,0,1,0,1,0,0] => 5 [1,1,1,1,0,0,0,1,1,0,0,0] => 5 [1,1,1,1,0,0,1,0,0,0,1,0] => 4 [1,1,1,1,0,0,1,0,0,1,0,0] => 5 [1,1,1,1,0,0,1,0,1,0,0,0] => 5 [1,1,1,1,0,0,1,1,0,0,0,0] => 5 [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] => 5 [1,1,1,1,0,1,0,0,1,0,0,0] => 5 [1,1,1,1,0,1,0,1,0,0,0,0] => 5 [1,1,1,1,0,1,1,0,0,0,0,0] => 5 [1,1,1,1,1,0,0,0,0,0,1,0] => 4 [1,1,1,1,1,0,0,0,0,1,0,0] => 5 [1,1,1,1,1,0,0,0,1,0,0,0] => 5 [1,1,1,1,1,0,0,1,0,0,0,0] => 5 [1,1,1,1,1,0,1,0,0,0,0,0] => 5 [1,1,1,1,1,1,0,0,0,0,0,0] => 5 ----------------------------------------------------------------------------- Created: Oct 14, 2019 at 11:23 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Oct 14, 2019 at 11:23 by Rene Marczinzik