***************************************************************************** * 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: St000967 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. ----------------------------------------------------------------------------- References: [1] de la Peña, José A. Algebras whose Coxeter polynomials are products of cyclotomic polynomials [[MathSciNet:3254775]] [[DOI:10.1007/s10468-013-9424-0]] ----------------------------------------------------------------------------- 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] => 4 [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] => 4 [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] => 4 [1,1,0,1,0,1,0,0] => 4 [1,1,0,1,1,0,0,0] => 4 [1,1,1,0,0,0,1,0] => 6 [1,1,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,0,0] => 4 [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] => 4 [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] => 3 [1,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,1,1,0,0,0] => 3 [1,0,1,1,1,0,0,0,1,0] => 7 [1,0,1,1,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,0,0,0] => 3 [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] => 4 [1,1,0,0,1,1,1,0,0,0] => 7 [1,1,0,1,0,0,1,0,1,0] => 4 [1,1,0,1,0,0,1,1,0,0] => 4 [1,1,0,1,0,1,0,0,1,0] => 4 [1,1,0,1,0,1,0,1,0,0] => 3 [1,1,0,1,0,1,1,0,0,0] => 4 [1,1,0,1,1,0,0,0,1,0] => 4 [1,1,0,1,1,0,0,1,0,0] => 0 [1,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,0,0,0] => 4 [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] => 3 [1,1,1,0,0,1,0,1,0,0] => 4 [1,1,1,0,0,1,1,0,0,0] => 3 [1,1,1,0,1,0,0,0,1,0] => 3 [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] => 3 [1,1,1,1,0,0,0,0,1,0] => 7 [1,1,1,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,0,0,0] => 3 [1,1,1,1,0,1,0,0,0,0] => 4 [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] => 4 [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] => 2 [1,0,1,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,0,1,1,0,1,1,0,0,0] => 2 [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] => 4 [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] => 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] => 4 [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] => 2 [1,0,1,1,0,1,0,0,1,1,0,0] => 2 [1,0,1,1,0,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,1,0,0] => 2 [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] => 2 [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] => 2 [1,0,1,1,0,1,1,1,0,0,0,0] => 2 [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] => 2 [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] => 2 [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] => 2 [1,0,1,1,1,0,1,0,1,0,0,0] => 2 [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] => 4 [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] => 2 [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] => 4 [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] => 2 [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] => 2 [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] => 4 [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] => 8 [1,1,0,1,0,0,1,0,1,0,1,0] => 4 [1,1,0,1,0,0,1,0,1,1,0,0] => 4 [1,1,0,1,0,0,1,1,0,0,1,0] => 4 [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] => 4 [1,1,0,1,0,1,0,0,1,0,1,0] => 4 [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] => 2 [1,1,0,1,0,1,0,1,0,1,0,0] => 2 [1,1,0,1,0,1,0,1,1,0,0,0] => 2 [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] => 0 [1,1,0,1,0,1,1,0,1,0,0,0] => 2 [1,1,0,1,0,1,1,1,0,0,0,0] => 4 [1,1,0,1,1,0,0,0,1,0,1,0] => 4 [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] => 0 [1,1,0,1,1,0,0,1,1,0,0,0] => -4 [1,1,0,1,1,0,1,0,0,0,1,0] => 2 [1,1,0,1,1,0,1,0,0,1,0,0] => 2 [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] => 2 [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] => 0 [1,1,0,1,1,1,0,0,1,0,0,0] => -4 [1,1,0,1,1,1,0,1,0,0,0,0] => 2 [1,1,0,1,1,1,1,0,0,0,0,0] => 4 [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] => 4 [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] => 2 [1,1,1,0,0,1,0,0,1,1,0,0] => 2 [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] => 2 [1,1,1,0,0,1,0,1,1,0,0,0] => 4 [1,1,1,0,0,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,1,1,0,0,1,0,0] => -4 [1,1,1,0,0,1,1,0,1,0,0,0] => 2 [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] => 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] => 2 [1,1,1,0,1,0,0,1,0,1,0,0] => 2 [1,1,1,0,1,0,0,1,1,0,0,0] => 2 [1,1,1,0,1,0,1,0,0,0,1,0] => 2 [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] => 2 [1,1,1,0,1,0,1,1,0,0,0,0] => 2 [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] => -4 [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] => 2 [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] => 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] => 2 [1,1,1,1,0,0,0,1,0,1,0,0] => 4 [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] => 0 [1,1,1,1,0,0,1,0,0,1,0,0] => 2 [1,1,1,1,0,0,1,0,1,0,0,0] => 2 [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] => 2 [1,1,1,1,0,1,0,0,0,1,0,0] => 2 [1,1,1,1,0,1,0,0,1,0,0,0] => 2 [1,1,1,1,0,1,0,1,0,0,0,0] => 2 [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] => 8 [1,1,1,1,1,0,0,0,0,1,0,0] => 4 [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] => 4 [1,1,1,1,1,1,0,0,0,0,0,0] => 8 ----------------------------------------------------------------------------- Created: Sep 03, 2017 at 14:16 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Sep 03, 2017 at 14:49 by Martin Rubey