***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * 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: St001218 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. It returns zero in case there is no such k. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 3 [1,0,1,0] => 4 [1,1,0,0] => 4 [1,0,1,0,1,0] => 5 [1,0,1,1,0,0] => 5 [1,1,0,0,1,0] => 5 [1,1,0,1,0,0] => 6 [1,1,1,0,0,0] => 5 [1,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,1,0,0] => 6 [1,0,1,1,0,0,1,0] => 6 [1,0,1,1,0,1,0,0] => 8 [1,0,1,1,1,0,0,0] => 6 [1,1,0,0,1,0,1,0] => 6 [1,1,0,0,1,1,0,0] => 6 [1,1,0,1,0,0,1,0] => 8 [1,1,0,1,0,1,0,0] => 8 [1,1,0,1,1,0,0,0] => 8 [1,1,1,0,0,0,1,0] => 6 [1,1,1,0,0,1,0,0] => 8 [1,1,1,0,1,0,0,0] => 8 [1,1,1,1,0,0,0,0] => 6 [1,0,1,0,1,0,1,0,1,0] => 7 [1,0,1,0,1,0,1,1,0,0] => 7 [1,0,1,0,1,1,0,0,1,0] => 7 [1,0,1,0,1,1,0,1,0,0] => 10 [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] => 7 [1,0,1,1,0,1,0,0,1,0] => 12 [1,0,1,1,0,1,0,1,0,0] => 10 [1,0,1,1,0,1,1,0,0,0] => 12 [1,0,1,1,1,0,0,0,1,0] => 7 [1,0,1,1,1,0,0,1,0,0] => 10 [1,0,1,1,1,0,1,0,0,0] => 12 [1,0,1,1,1,1,0,0,0,0] => 7 [1,1,0,0,1,0,1,0,1,0] => 7 [1,1,0,0,1,0,1,1,0,0] => 7 [1,1,0,0,1,1,0,0,1,0] => 7 [1,1,0,0,1,1,0,1,0,0] => 10 [1,1,0,0,1,1,1,0,0,0] => 7 [1,1,0,1,0,0,1,0,1,0] => 10 [1,1,0,1,0,0,1,1,0,0] => 10 [1,1,0,1,0,1,0,0,1,0] => 10 [1,1,0,1,0,1,0,1,0,0] => 12 [1,1,0,1,0,1,1,0,0,0] => 10 [1,1,0,1,1,0,0,0,1,0] => 10 [1,1,0,1,1,0,0,1,0,0] => 0 [1,1,0,1,1,0,1,0,0,0] => 12 [1,1,0,1,1,1,0,0,0,0] => 10 [1,1,1,0,0,0,1,0,1,0] => 7 [1,1,1,0,0,0,1,1,0,0] => 7 [1,1,1,0,0,1,0,0,1,0] => 12 [1,1,1,0,0,1,0,1,0,0] => 10 [1,1,1,0,0,1,1,0,0,0] => 12 [1,1,1,0,1,0,0,0,1,0] => 12 [1,1,1,0,1,0,0,1,0,0] => 12 [1,1,1,0,1,0,1,0,0,0] => 12 [1,1,1,0,1,1,0,0,0,0] => 12 [1,1,1,1,0,0,0,0,1,0] => 7 [1,1,1,1,0,0,0,1,0,0] => 10 [1,1,1,1,0,0,1,0,0,0] => 12 [1,1,1,1,0,1,0,0,0,0] => 10 [1,1,1,1,1,0,0,0,0,0] => 7 [1,0,1,0,1,0,1,0,1,0,1,0] => 8 [1,0,1,0,1,0,1,0,1,1,0,0] => 8 [1,0,1,0,1,0,1,1,0,0,1,0] => 8 [1,0,1,0,1,0,1,1,0,1,0,0] => 12 [1,0,1,0,1,0,1,1,1,0,0,0] => 8 [1,0,1,0,1,1,0,0,1,0,1,0] => 8 [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] => 18 [1,0,1,0,1,1,0,1,0,1,0,0] => 12 [1,0,1,0,1,1,0,1,1,0,0,0] => 18 [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] => 12 [1,0,1,0,1,1,1,0,1,0,0,0] => 18 [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] => 8 [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] => 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] => 8 [1,0,1,1,0,1,0,0,1,0,1,0] => 18 [1,0,1,1,0,1,0,0,1,1,0,0] => 18 [1,0,1,1,0,1,0,1,0,0,1,0] => 12 [1,0,1,1,0,1,0,1,0,1,0,0] => 18 [1,0,1,1,0,1,0,1,1,0,0,0] => 12 [1,0,1,1,0,1,1,0,0,0,1,0] => 18 [1,0,1,1,0,1,1,0,0,1,0,0] => 0 [1,0,1,1,0,1,1,0,1,0,0,0] => 18 [1,0,1,1,0,1,1,1,0,0,0,0] => 18 [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] => 8 [1,0,1,1,1,0,0,1,0,0,1,0] => 18 [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] => 18 [1,0,1,1,1,0,1,0,0,0,1,0] => 0 [1,0,1,1,1,0,1,0,0,1,0,0] => 18 [1,0,1,1,1,0,1,0,1,0,0,0] => 18 [1,0,1,1,1,0,1,1,0,0,0,0] => 0 [1,0,1,1,1,1,0,0,0,0,1,0] => 8 [1,0,1,1,1,1,0,0,0,1,0,0] => 12 [1,0,1,1,1,1,0,0,1,0,0,0] => 18 [1,0,1,1,1,1,0,1,0,0,0,0] => 18 [1,0,1,1,1,1,1,0,0,0,0,0] => 8 [1,1,0,0,1,0,1,0,1,0,1,0] => 8 [1,1,0,0,1,0,1,0,1,1,0,0] => 8 [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] => 12 [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] => 8 [1,1,0,0,1,1,0,1,0,0,1,0] => 18 [1,1,0,0,1,1,0,1,0,1,0,0] => 12 [1,1,0,0,1,1,0,1,1,0,0,0] => 18 [1,1,0,0,1,1,1,0,0,0,1,0] => 8 [1,1,0,0,1,1,1,0,0,1,0,0] => 12 [1,1,0,0,1,1,1,0,1,0,0,0] => 18 [1,1,0,0,1,1,1,1,0,0,0,0] => 8 [1,1,0,1,0,0,1,0,1,0,1,0] => 12 [1,1,0,1,0,0,1,0,1,1,0,0] => 12 [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] => 0 [1,1,0,1,0,0,1,1,1,0,0,0] => 12 [1,1,0,1,0,1,0,0,1,0,1,0] => 12 [1,1,0,1,0,1,0,0,1,1,0,0] => 12 [1,1,0,1,0,1,0,1,0,0,1,0] => 18 [1,1,0,1,0,1,0,1,0,1,0,0] => 18 [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] => 0 [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] => 12 [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] => 12 [1,1,0,1,1,0,0,1,0,0,1,0] => 0 [1,1,0,1,1,0,0,1,0,1,0,0] => 0 [1,1,0,1,1,0,0,1,1,0,0,0] => 0 [1,1,0,1,1,0,1,0,0,0,1,0] => 18 [1,1,0,1,1,0,1,0,0,1,0,0] => 18 [1,1,0,1,1,0,1,0,1,0,0,0] => 0 [1,1,0,1,1,0,1,1,0,0,0,0] => 18 [1,1,0,1,1,1,0,0,0,0,1,0] => 12 [1,1,0,1,1,1,0,0,0,1,0,0] => 0 [1,1,0,1,1,1,0,0,1,0,0,0] => 0 [1,1,0,1,1,1,0,1,0,0,0,0] => 18 [1,1,0,1,1,1,1,0,0,0,0,0] => 12 [1,1,1,0,0,0,1,0,1,0,1,0] => 8 [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] => 8 [1,1,1,0,0,0,1,1,0,1,0,0] => 12 [1,1,1,0,0,0,1,1,1,0,0,0] => 8 [1,1,1,0,0,1,0,0,1,0,1,0] => 18 [1,1,1,0,0,1,0,0,1,1,0,0] => 18 [1,1,1,0,0,1,0,1,0,0,1,0] => 12 [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] => 12 [1,1,1,0,0,1,1,0,0,0,1,0] => 18 [1,1,1,0,0,1,1,0,0,1,0,0] => 0 [1,1,1,0,0,1,1,0,1,0,0,0] => 18 [1,1,1,0,0,1,1,1,0,0,0,0] => 18 [1,1,1,0,1,0,0,0,1,0,1,0] => 18 [1,1,1,0,1,0,0,0,1,1,0,0] => 18 [1,1,1,0,1,0,0,1,0,0,1,0] => 18 [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] => 18 [1,1,1,0,1,0,1,0,0,0,1,0] => 18 [1,1,1,0,1,0,1,0,0,1,0,0] => 0 [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] => 18 [1,1,1,0,1,1,0,0,0,0,1,0] => 18 [1,1,1,0,1,1,0,0,0,1,0,0] => 0 [1,1,1,0,1,1,0,0,1,0,0,0] => 0 [1,1,1,0,1,1,0,1,0,0,0,0] => 18 [1,1,1,0,1,1,1,0,0,0,0,0] => 18 [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] => 8 [1,1,1,1,0,0,0,1,0,0,1,0] => 18 [1,1,1,1,0,0,0,1,0,1,0,0] => 12 [1,1,1,1,0,0,0,1,1,0,0,0] => 18 [1,1,1,1,0,0,1,0,0,0,1,0] => 0 [1,1,1,1,0,0,1,0,0,1,0,0] => 18 [1,1,1,1,0,0,1,0,1,0,0,0] => 18 [1,1,1,1,0,0,1,1,0,0,0,0] => 0 [1,1,1,1,0,1,0,0,0,0,1,0] => 18 [1,1,1,1,0,1,0,0,0,1,0,0] => 18 [1,1,1,1,0,1,0,0,1,0,0,0] => 18 [1,1,1,1,0,1,0,1,0,0,0,0] => 18 [1,1,1,1,0,1,1,0,0,0,0,0] => 18 [1,1,1,1,1,0,0,0,0,0,1,0] => 8 [1,1,1,1,1,0,0,0,0,1,0,0] => 12 [1,1,1,1,1,0,0,0,1,0,0,0] => 18 [1,1,1,1,1,0,0,1,0,0,0,0] => 18 [1,1,1,1,1,0,1,0,0,0,0,0] => 12 [1,1,1,1,1,1,0,0,0,0,0,0] => 8 ----------------------------------------------------------------------------- Created: Jun 23, 2018 at 15:11 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Jun 24, 2018 at 00:02 by Rene Marczinzik