***************************************************************************** * 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: St001299 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama algebra. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 2 [1,1,0,0] => 1 [1,0,1,0,1,0] => 6 [1,0,1,1,0,0] => 2 [1,1,0,0,1,0] => 2 [1,1,0,1,0,0] => 2 [1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,0] => 24 [1,0,1,0,1,1,0,0] => 6 [1,0,1,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,0] => 6 [1,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,0,1,0] => 6 [1,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,0,1,0] => 6 [1,1,0,1,0,1,0,0] => 6 [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] => 2 [1,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0] => 120 [1,0,1,0,1,0,1,1,0,0] => 24 [1,0,1,0,1,1,0,0,1,0] => 12 [1,0,1,0,1,1,0,1,0,0] => 24 [1,0,1,0,1,1,1,0,0,0] => 6 [1,0,1,1,0,0,1,0,1,0] => 12 [1,0,1,1,0,0,1,1,0,0] => 4 [1,0,1,1,0,1,0,0,1,0] => 24 [1,0,1,1,0,1,0,1,0,0] => 24 [1,0,1,1,0,1,1,0,0,0] => 6 [1,0,1,1,1,0,0,0,1,0] => 4 [1,0,1,1,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,0,0,0] => 6 [1,0,1,1,1,1,0,0,0,0] => 2 [1,1,0,0,1,0,1,0,1,0] => 24 [1,1,0,0,1,0,1,1,0,0] => 6 [1,1,0,0,1,1,0,0,1,0] => 4 [1,1,0,0,1,1,0,1,0,0] => 6 [1,1,0,0,1,1,1,0,0,0] => 2 [1,1,0,1,0,0,1,0,1,0] => 24 [1,1,0,1,0,0,1,1,0,0] => 6 [1,1,0,1,0,1,0,0,1,0] => 24 [1,1,0,1,0,1,0,1,0,0] => 18 [1,1,0,1,0,1,1,0,0,0] => 6 [1,1,0,1,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,0,0] => 6 [1,1,0,1,1,0,1,0,0,0] => 6 [1,1,0,1,1,1,0,0,0,0] => 2 [1,1,1,0,0,0,1,0,1,0] => 6 [1,1,1,0,0,0,1,1,0,0] => 2 [1,1,1,0,0,1,0,0,1,0] => 6 [1,1,1,0,0,1,0,1,0,0] => 6 [1,1,1,0,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,0,0,1,0] => 6 [1,1,1,0,1,0,0,1,0,0] => 6 [1,1,1,0,1,0,1,0,0,0] => 6 [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] => 2 [1,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0] => 720 [1,0,1,0,1,0,1,0,1,1,0,0] => 120 [1,0,1,0,1,0,1,1,0,0,1,0] => 48 [1,0,1,0,1,0,1,1,0,1,0,0] => 120 [1,0,1,0,1,0,1,1,1,0,0,0] => 24 [1,0,1,0,1,1,0,0,1,0,1,0] => 36 [1,0,1,0,1,1,0,0,1,1,0,0] => 12 [1,0,1,0,1,1,0,1,0,0,1,0] => 120 [1,0,1,0,1,1,0,1,0,1,0,0] => 120 [1,0,1,0,1,1,0,1,1,0,0,0] => 24 [1,0,1,0,1,1,1,0,0,0,1,0] => 12 [1,0,1,0,1,1,1,0,0,1,0,0] => 12 [1,0,1,0,1,1,1,0,1,0,0,0] => 24 [1,0,1,0,1,1,1,1,0,0,0,0] => 6 [1,0,1,1,0,0,1,0,1,0,1,0] => 48 [1,0,1,1,0,0,1,0,1,1,0,0] => 12 [1,0,1,1,0,0,1,1,0,0,1,0] => 8 [1,0,1,1,0,0,1,1,0,1,0,0] => 12 [1,0,1,1,0,0,1,1,1,0,0,0] => 4 [1,0,1,1,0,1,0,0,1,0,1,0] => 120 [1,0,1,1,0,1,0,0,1,1,0,0] => 24 [1,0,1,1,0,1,0,1,0,0,1,0] => 120 [1,0,1,1,0,1,0,1,0,1,0,0] => 72 [1,0,1,1,0,1,0,1,1,0,0,0] => 24 [1,0,1,1,0,1,1,0,0,0,1,0] => 12 [1,0,1,1,0,1,1,0,0,1,0,0] => 24 [1,0,1,1,0,1,1,0,1,0,0,0] => 24 [1,0,1,1,0,1,1,1,0,0,0,0] => 6 [1,0,1,1,1,0,0,0,1,0,1,0] => 12 [1,0,1,1,1,0,0,0,1,1,0,0] => 4 [1,0,1,1,1,0,0,1,0,0,1,0] => 12 [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] => 4 [1,0,1,1,1,0,1,0,0,0,1,0] => 24 [1,0,1,1,1,0,1,0,0,1,0,0] => 24 [1,0,1,1,1,0,1,0,1,0,0,0] => 24 [1,0,1,1,1,0,1,1,0,0,0,0] => 6 [1,0,1,1,1,1,0,0,0,0,1,0] => 4 [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] => 6 [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] => 120 [1,1,0,0,1,0,1,0,1,1,0,0] => 24 [1,1,0,0,1,0,1,1,0,0,1,0] => 12 [1,1,0,0,1,0,1,1,0,1,0,0] => 24 [1,1,0,0,1,0,1,1,1,0,0,0] => 6 [1,1,0,0,1,1,0,0,1,0,1,0] => 12 [1,1,0,0,1,1,0,0,1,1,0,0] => 4 [1,1,0,0,1,1,0,1,0,0,1,0] => 24 [1,1,0,0,1,1,0,1,0,1,0,0] => 24 [1,1,0,0,1,1,0,1,1,0,0,0] => 6 [1,1,0,0,1,1,1,0,0,0,1,0] => 4 [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] => 6 [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] => 120 [1,1,0,1,0,0,1,0,1,1,0,0] => 24 [1,1,0,1,0,0,1,1,0,0,1,0] => 12 [1,1,0,1,0,0,1,1,0,1,0,0] => 24 [1,1,0,1,0,0,1,1,1,0,0,0] => 6 [1,1,0,1,0,1,0,0,1,0,1,0] => 120 [1,1,0,1,0,1,0,0,1,1,0,0] => 24 [1,1,0,1,0,1,0,1,0,0,1,0] => 72 [1,1,0,1,0,1,0,1,0,1,0,0] => 72 [1,1,0,1,0,1,0,1,1,0,0,0] => 18 [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] => 24 [1,1,0,1,0,1,1,0,1,0,0,0] => 18 [1,1,0,1,0,1,1,1,0,0,0,0] => 6 [1,1,0,1,1,0,0,0,1,0,1,0] => 12 [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] => 24 [1,1,0,1,1,0,0,1,0,1,0,0] => 24 [1,1,0,1,1,0,0,1,1,0,0,0] => 6 [1,1,0,1,1,0,1,0,0,0,1,0] => 24 [1,1,0,1,1,0,1,0,0,1,0,0] => 24 [1,1,0,1,1,0,1,0,1,0,0,0] => 18 [1,1,0,1,1,0,1,1,0,0,0,0] => 6 [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] => 4 [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] => 6 [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] => 24 [1,1,1,0,0,0,1,0,1,1,0,0] => 6 [1,1,1,0,0,0,1,1,0,0,1,0] => 4 [1,1,1,0,0,0,1,1,0,1,0,0] => 6 [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] => 24 [1,1,1,0,0,1,0,0,1,1,0,0] => 6 [1,1,1,0,0,1,0,1,0,0,1,0] => 24 [1,1,1,0,0,1,0,1,0,1,0,0] => 18 [1,1,1,0,0,1,0,1,1,0,0,0] => 6 [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] => 6 [1,1,1,0,0,1,1,0,1,0,0,0] => 6 [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] => 24 [1,1,1,0,1,0,0,0,1,1,0,0] => 6 [1,1,1,0,1,0,0,1,0,0,1,0] => 24 [1,1,1,0,1,0,0,1,0,1,0,0] => 18 [1,1,1,0,1,0,0,1,1,0,0,0] => 6 [1,1,1,0,1,0,1,0,0,0,1,0] => 24 [1,1,1,0,1,0,1,0,0,1,0,0] => 18 [1,1,1,0,1,0,1,0,1,0,0,0] => 18 [1,1,1,0,1,0,1,1,0,0,0,0] => 6 [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] => 6 [1,1,1,0,1,1,0,0,1,0,0,0] => 6 [1,1,1,0,1,1,0,1,0,0,0,0] => 6 [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] => 6 [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] => 6 [1,1,1,1,0,0,0,1,0,1,0,0] => 6 [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] => 6 [1,1,1,1,0,0,1,0,0,1,0,0] => 6 [1,1,1,1,0,0,1,0,1,0,0,0] => 6 [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] => 6 [1,1,1,1,0,1,0,0,0,1,0,0] => 6 [1,1,1,1,0,1,0,0,1,0,0,0] => 6 [1,1,1,1,0,1,0,1,0,0,0,0] => 6 [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] => 2 [1,1,1,1,1,1,0,0,0,0,0,0] => 1 ----------------------------------------------------------------------------- Created: Dec 05, 2018 at 13:45 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Dec 05, 2018 at 13:45 by Rene Marczinzik