***************************************************************************** * 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: St001065 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: Number of indecomposable reflexive modules in the corresponding Nakayama algebra. ----------------------------------------------------------------------------- References: [1] [[https://en.wikipedia.org/wiki/Torsionless_module]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 2 [1,0,1,0] => 3 [1,1,0,0] => 3 [1,0,1,0,1,0] => 5 [1,0,1,1,0,0] => 4 [1,1,0,0,1,0] => 4 [1,1,0,1,0,0] => 3 [1,1,1,0,0,0] => 4 [1,0,1,0,1,0,1,0] => 7 [1,0,1,0,1,1,0,0] => 6 [1,0,1,1,0,0,1,0] => 5 [1,0,1,1,0,1,0,0] => 5 [1,0,1,1,1,0,0,0] => 5 [1,1,0,0,1,0,1,0] => 6 [1,1,0,0,1,1,0,0] => 5 [1,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,0] => 6 [1,1,0,1,1,0,0,0] => 4 [1,1,1,0,0,0,1,0] => 5 [1,1,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,0,0] => 3 [1,1,1,1,0,0,0,0] => 5 [1,0,1,0,1,0,1,0,1,0] => 9 [1,0,1,0,1,0,1,1,0,0] => 8 [1,0,1,0,1,1,0,0,1,0] => 7 [1,0,1,0,1,1,0,1,0,0] => 7 [1,0,1,0,1,1,1,0,0,0] => 7 [1,0,1,1,0,0,1,0,1,0] => 7 [1,0,1,1,0,0,1,1,0,0] => 6 [1,0,1,1,0,1,0,0,1,0] => 7 [1,0,1,1,0,1,0,1,0,0] => 8 [1,0,1,1,0,1,1,0,0,0] => 6 [1,0,1,1,1,0,0,0,1,0] => 6 [1,0,1,1,1,0,0,1,0,0] => 5 [1,0,1,1,1,0,1,0,0,0] => 5 [1,0,1,1,1,1,0,0,0,0] => 6 [1,1,0,0,1,0,1,0,1,0] => 8 [1,1,0,0,1,0,1,1,0,0] => 7 [1,1,0,0,1,1,0,0,1,0] => 6 [1,1,0,0,1,1,0,1,0,0] => 6 [1,1,0,0,1,1,1,0,0,0] => 6 [1,1,0,1,0,0,1,0,1,0] => 7 [1,1,0,1,0,0,1,1,0,0] => 6 [1,1,0,1,0,1,0,0,1,0] => 8 [1,1,0,1,0,1,0,1,0,0] => 9 [1,1,0,1,0,1,1,0,0,0] => 7 [1,1,0,1,1,0,0,0,1,0] => 5 [1,1,0,1,1,0,0,1,0,0] => 5 [1,1,0,1,1,0,1,0,0,0] => 6 [1,1,0,1,1,1,0,0,0,0] => 5 [1,1,1,0,0,0,1,0,1,0] => 7 [1,1,1,0,0,0,1,1,0,0] => 6 [1,1,1,0,0,1,0,0,1,0] => 6 [1,1,1,0,0,1,0,1,0,0] => 7 [1,1,1,0,0,1,1,0,0,0] => 5 [1,1,1,0,1,0,0,0,1,0] => 5 [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] => 4 [1,1,1,1,0,0,0,0,1,0] => 6 [1,1,1,1,0,0,0,1,0,0] => 5 [1,1,1,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,0,0,0] => 3 [1,1,1,1,1,0,0,0,0,0] => 6 [1,0,1,0,1,0,1,0,1,0,1,0] => 11 [1,0,1,0,1,0,1,0,1,1,0,0] => 10 [1,0,1,0,1,0,1,1,0,0,1,0] => 9 [1,0,1,0,1,0,1,1,0,1,0,0] => 9 [1,0,1,0,1,0,1,1,1,0,0,0] => 9 [1,0,1,0,1,1,0,0,1,0,1,0] => 9 [1,0,1,0,1,1,0,0,1,1,0,0] => 8 [1,0,1,0,1,1,0,1,0,0,1,0] => 9 [1,0,1,0,1,1,0,1,0,1,0,0] => 10 [1,0,1,0,1,1,0,1,1,0,0,0] => 8 [1,0,1,0,1,1,1,0,0,0,1,0] => 8 [1,0,1,0,1,1,1,0,0,1,0,0] => 7 [1,0,1,0,1,1,1,0,1,0,0,0] => 7 [1,0,1,0,1,1,1,1,0,0,0,0] => 8 [1,0,1,1,0,0,1,0,1,0,1,0] => 9 [1,0,1,1,0,0,1,0,1,1,0,0] => 8 [1,0,1,1,0,0,1,1,0,0,1,0] => 7 [1,0,1,1,0,0,1,1,0,1,0,0] => 7 [1,0,1,1,0,0,1,1,1,0,0,0] => 7 [1,0,1,1,0,1,0,0,1,0,1,0] => 9 [1,0,1,1,0,1,0,0,1,1,0,0] => 8 [1,0,1,1,0,1,0,1,0,0,1,0] => 10 [1,0,1,1,0,1,0,1,0,1,0,0] => 11 [1,0,1,1,0,1,0,1,1,0,0,0] => 9 [1,0,1,1,0,1,1,0,0,0,1,0] => 7 [1,0,1,1,0,1,1,0,0,1,0,0] => 7 [1,0,1,1,0,1,1,0,1,0,0,0] => 8 [1,0,1,1,0,1,1,1,0,0,0,0] => 7 [1,0,1,1,1,0,0,0,1,0,1,0] => 8 [1,0,1,1,1,0,0,0,1,1,0,0] => 7 [1,0,1,1,1,0,0,1,0,0,1,0] => 7 [1,0,1,1,1,0,0,1,0,1,0,0] => 8 [1,0,1,1,1,0,0,1,1,0,0,0] => 6 [1,0,1,1,1,0,1,0,0,0,1,0] => 7 [1,0,1,1,1,0,1,0,0,1,0,0] => 8 [1,0,1,1,1,0,1,0,1,0,0,0] => 8 [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] => 7 [1,0,1,1,1,1,0,0,0,1,0,0] => 6 [1,0,1,1,1,1,0,0,1,0,0,0] => 5 [1,0,1,1,1,1,0,1,0,0,0,0] => 5 [1,0,1,1,1,1,1,0,0,0,0,0] => 7 [1,1,0,0,1,0,1,0,1,0,1,0] => 10 [1,1,0,0,1,0,1,0,1,1,0,0] => 9 [1,1,0,0,1,0,1,1,0,0,1,0] => 8 [1,1,0,0,1,0,1,1,0,1,0,0] => 8 [1,1,0,0,1,0,1,1,1,0,0,0] => 8 [1,1,0,0,1,1,0,0,1,0,1,0] => 8 [1,1,0,0,1,1,0,0,1,1,0,0] => 7 [1,1,0,0,1,1,0,1,0,0,1,0] => 8 [1,1,0,0,1,1,0,1,0,1,0,0] => 9 [1,1,0,0,1,1,0,1,1,0,0,0] => 7 [1,1,0,0,1,1,1,0,0,0,1,0] => 7 [1,1,0,0,1,1,1,0,0,1,0,0] => 6 [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] => 7 [1,1,0,1,0,0,1,0,1,0,1,0] => 9 [1,1,0,1,0,0,1,0,1,1,0,0] => 8 [1,1,0,1,0,0,1,1,0,0,1,0] => 7 [1,1,0,1,0,0,1,1,0,1,0,0] => 7 [1,1,0,1,0,0,1,1,1,0,0,0] => 7 [1,1,0,1,0,1,0,0,1,0,1,0] => 10 [1,1,0,1,0,1,0,0,1,1,0,0] => 9 [1,1,0,1,0,1,0,1,0,0,1,0] => 11 [1,1,0,1,0,1,0,1,0,1,0,0] => 12 [1,1,0,1,0,1,0,1,1,0,0,0] => 10 [1,1,0,1,0,1,1,0,0,0,1,0] => 8 [1,1,0,1,0,1,1,0,0,1,0,0] => 8 [1,1,0,1,0,1,1,0,1,0,0,0] => 9 [1,1,0,1,0,1,1,1,0,0,0,0] => 8 [1,1,0,1,1,0,0,0,1,0,1,0] => 7 [1,1,0,1,1,0,0,0,1,1,0,0] => 6 [1,1,0,1,1,0,0,1,0,0,1,0] => 7 [1,1,0,1,1,0,0,1,0,1,0,0] => 8 [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] => 8 [1,1,0,1,1,0,1,0,0,1,0,0] => 9 [1,1,0,1,1,0,1,0,1,0,0,0] => 9 [1,1,0,1,1,0,1,1,0,0,0,0] => 7 [1,1,0,1,1,1,0,0,0,0,1,0] => 6 [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] => 6 [1,1,0,1,1,1,1,0,0,0,0,0] => 6 [1,1,1,0,0,0,1,0,1,0,1,0] => 9 [1,1,1,0,0,0,1,0,1,1,0,0] => 8 [1,1,1,0,0,0,1,1,0,0,1,0] => 7 [1,1,1,0,0,0,1,1,0,1,0,0] => 7 [1,1,1,0,0,0,1,1,1,0,0,0] => 7 [1,1,1,0,0,1,0,0,1,0,1,0] => 8 [1,1,1,0,0,1,0,0,1,1,0,0] => 7 [1,1,1,0,0,1,0,1,0,0,1,0] => 9 [1,1,1,0,0,1,0,1,0,1,0,0] => 10 [1,1,1,0,0,1,0,1,1,0,0,0] => 8 [1,1,1,0,0,1,1,0,0,0,1,0] => 6 [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] => 7 [1,1,1,0,0,1,1,1,0,0,0,0] => 6 [1,1,1,0,1,0,0,0,1,0,1,0] => 7 [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] => 8 [1,1,1,0,1,0,0,1,0,1,0,0] => 9 [1,1,1,0,1,0,0,1,1,0,0,0] => 7 [1,1,1,0,1,0,1,0,0,0,1,0] => 8 [1,1,1,0,1,0,1,0,0,1,0,0] => 9 [1,1,1,0,1,0,1,0,1,0,0,0] => 10 [1,1,1,0,1,0,1,1,0,0,0,0] => 7 [1,1,1,0,1,1,0,0,0,0,1,0] => 5 [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] => 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] => 5 [1,1,1,1,0,0,0,0,1,0,1,0] => 8 [1,1,1,1,0,0,0,0,1,1,0,0] => 7 [1,1,1,1,0,0,0,1,0,0,1,0] => 7 [1,1,1,1,0,0,0,1,0,1,0,0] => 8 [1,1,1,1,0,0,0,1,1,0,0,0] => 6 [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] => 7 [1,1,1,1,0,0,1,0,1,0,0,0] => 7 [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] => 5 [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] => 4 [1,1,1,1,1,0,0,0,0,0,1,0] => 7 [1,1,1,1,1,0,0,0,0,1,0,0] => 6 [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] => 4 [1,1,1,1,1,0,1,0,0,0,0,0] => 3 [1,1,1,1,1,1,0,0,0,0,0,0] => 7 ----------------------------------------------------------------------------- Created: Dec 30, 2017 at 17:27 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Dec 30, 2017 at 17:27 by Rene Marczinzik