***************************************************************************** * 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: St001229 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The vector space dimension of the first extension group between the Jacobson radical J and J^2. The vector space dimension of $Ext_A^1(J,J^2)$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 0 [1,0,1,0] => 0 [1,1,0,0] => 0 [1,0,1,0,1,0] => 0 [1,0,1,1,0,0] => 0 [1,1,0,0,1,0] => 0 [1,1,0,1,0,0] => 1 [1,1,1,0,0,0] => 0 [1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,1,0,0] => 0 [1,0,1,1,0,0,1,0] => 0 [1,0,1,1,0,1,0,0] => 1 [1,0,1,1,1,0,0,0] => 0 [1,1,0,0,1,0,1,0] => 0 [1,1,0,0,1,1,0,0] => 0 [1,1,0,1,0,0,1,0] => 1 [1,1,0,1,0,1,0,0] => 2 [1,1,0,1,1,0,0,0] => 1 [1,1,1,0,0,0,1,0] => 0 [1,1,1,0,0,1,0,0] => 1 [1,1,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,0,0] => 0 [1,0,1,0,1,0,1,0,1,0] => 0 [1,0,1,0,1,0,1,1,0,0] => 0 [1,0,1,0,1,1,0,0,1,0] => 0 [1,0,1,0,1,1,0,1,0,0] => 1 [1,0,1,0,1,1,1,0,0,0] => 0 [1,0,1,1,0,0,1,0,1,0] => 0 [1,0,1,1,0,0,1,1,0,0] => 0 [1,0,1,1,0,1,0,0,1,0] => 1 [1,0,1,1,0,1,0,1,0,0] => 2 [1,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,0] => 0 [1,0,1,1,1,0,0,1,0,0] => 1 [1,0,1,1,1,0,1,0,0,0] => 2 [1,0,1,1,1,1,0,0,0,0] => 0 [1,1,0,0,1,0,1,0,1,0] => 0 [1,1,0,0,1,0,1,1,0,0] => 0 [1,1,0,0,1,1,0,0,1,0] => 0 [1,1,0,0,1,1,0,1,0,0] => 1 [1,1,0,0,1,1,1,0,0,0] => 0 [1,1,0,1,0,0,1,0,1,0] => 1 [1,1,0,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,0] => 2 [1,1,0,1,1,0,0,0,1,0] => 1 [1,1,0,1,1,0,0,1,0,0] => 2 [1,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,0,0,0] => 1 [1,1,1,0,0,0,1,0,1,0] => 0 [1,1,1,0,0,0,1,1,0,0] => 0 [1,1,1,0,0,1,0,0,1,0] => 1 [1,1,1,0,0,1,0,1,0,0] => 2 [1,1,1,0,0,1,1,0,0,0] => 1 [1,1,1,0,1,0,0,0,1,0] => 2 [1,1,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,0,0] => 3 [1,1,1,0,1,1,0,0,0,0] => 2 [1,1,1,1,0,0,0,0,1,0] => 0 [1,1,1,1,0,0,0,1,0,0] => 1 [1,1,1,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,0,0,0] => 3 [1,1,1,1,1,0,0,0,0,0] => 0 [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] => 0 [1,0,1,0,1,0,1,1,0,0,1,0] => 0 [1,0,1,0,1,0,1,1,0,1,0,0] => 1 [1,0,1,0,1,0,1,1,1,0,0,0] => 0 [1,0,1,0,1,1,0,0,1,0,1,0] => 0 [1,0,1,0,1,1,0,0,1,1,0,0] => 0 [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] => 2 [1,0,1,0,1,1,0,1,1,0,0,0] => 1 [1,0,1,0,1,1,1,0,0,0,1,0] => 0 [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] => 2 [1,0,1,0,1,1,1,1,0,0,0,0] => 0 [1,0,1,1,0,0,1,0,1,0,1,0] => 0 [1,0,1,1,0,0,1,0,1,1,0,0] => 0 [1,0,1,1,0,0,1,1,0,0,1,0] => 0 [1,0,1,1,0,0,1,1,0,1,0,0] => 1 [1,0,1,1,0,0,1,1,1,0,0,0] => 0 [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] => 2 [1,0,1,1,0,1,0,1,0,1,0,0] => 3 [1,0,1,1,0,1,0,1,1,0,0,0] => 2 [1,0,1,1,0,1,1,0,0,0,1,0] => 1 [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] => 3 [1,0,1,1,0,1,1,1,0,0,0,0] => 1 [1,0,1,1,1,0,0,0,1,0,1,0] => 0 [1,0,1,1,1,0,0,0,1,1,0,0] => 0 [1,0,1,1,1,0,0,1,0,0,1,0] => 1 [1,0,1,1,1,0,0,1,0,1,0,0] => 2 [1,0,1,1,1,0,0,1,1,0,0,0] => 1 [1,0,1,1,1,0,1,0,0,0,1,0] => 2 [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] => 3 [1,0,1,1,1,0,1,1,0,0,0,0] => 2 [1,0,1,1,1,1,0,0,0,0,1,0] => 0 [1,0,1,1,1,1,0,0,0,1,0,0] => 1 [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] => 3 [1,0,1,1,1,1,1,0,0,0,0,0] => 0 [1,1,0,0,1,0,1,0,1,0,1,0] => 0 [1,1,0,0,1,0,1,0,1,1,0,0] => 0 [1,1,0,0,1,0,1,1,0,0,1,0] => 0 [1,1,0,0,1,0,1,1,0,1,0,0] => 1 [1,1,0,0,1,0,1,1,1,0,0,0] => 0 [1,1,0,0,1,1,0,0,1,0,1,0] => 0 [1,1,0,0,1,1,0,0,1,1,0,0] => 0 [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] => 2 [1,1,0,0,1,1,0,1,1,0,0,0] => 1 [1,1,0,0,1,1,1,0,0,0,1,0] => 0 [1,1,0,0,1,1,1,0,0,1,0,0] => 1 [1,1,0,0,1,1,1,0,1,0,0,0] => 2 [1,1,0,0,1,1,1,1,0,0,0,0] => 0 [1,1,0,1,0,0,1,0,1,0,1,0] => 1 [1,1,0,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,1,0,0,1,0] => 1 [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] => 1 [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] => 2 [1,1,0,1,0,1,0,1,0,0,1,0] => 3 [1,1,0,1,0,1,0,1,0,1,0,0] => 4 [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] => 2 [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] => 4 [1,1,0,1,0,1,1,1,0,0,0,0] => 2 [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] => 1 [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] => 3 [1,1,0,1,1,0,0,1,1,0,0,0] => 2 [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] => 4 [1,1,0,1,1,0,1,0,1,0,0,0] => 4 [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] => 1 [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] => 4 [1,1,0,1,1,1,1,0,0,0,0,0] => 1 [1,1,1,0,0,0,1,0,1,0,1,0] => 0 [1,1,1,0,0,0,1,0,1,1,0,0] => 0 [1,1,1,0,0,0,1,1,0,0,1,0] => 0 [1,1,1,0,0,0,1,1,0,1,0,0] => 1 [1,1,1,0,0,0,1,1,1,0,0,0] => 0 [1,1,1,0,0,1,0,0,1,0,1,0] => 1 [1,1,1,0,0,1,0,0,1,1,0,0] => 1 [1,1,1,0,0,1,0,1,0,0,1,0] => 2 [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] => 2 [1,1,1,0,0,1,1,0,0,0,1,0] => 1 [1,1,1,0,0,1,1,0,0,1,0,0] => 2 [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] => 1 [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] => 2 [1,1,1,0,1,0,0,1,0,0,1,0] => 3 [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] => 3 [1,1,1,0,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,1,0,1,0,0,0] => 4 [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] => 4 [1,1,1,0,1,1,0,1,0,0,0,0] => 4 [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] => 0 [1,1,1,1,0,0,0,0,1,1,0,0] => 0 [1,1,1,1,0,0,0,1,0,0,1,0] => 1 [1,1,1,1,0,0,0,1,0,1,0,0] => 2 [1,1,1,1,0,0,0,1,1,0,0,0] => 1 [1,1,1,1,0,0,1,0,0,0,1,0] => 2 [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] => 3 [1,1,1,1,0,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,1,0,0,0,0] => 4 [1,1,1,1,0,1,1,0,0,0,0,0] => 3 [1,1,1,1,1,0,0,0,0,0,1,0] => 0 [1,1,1,1,1,0,0,0,0,1,0,0] => 1 [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] => 3 [1,1,1,1,1,0,1,0,0,0,0,0] => 4 [1,1,1,1,1,1,0,0,0,0,0,0] => 0 ----------------------------------------------------------------------------- Created: Jul 20, 2018 at 18:14 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Jul 20, 2018 at 18:14 by Rene Marczinzik