***************************************************************************** * 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: St001473 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 3 [1,1,0,0] => 1 [1,0,1,0,1,0] => 3 [1,0,1,1,0,0] => 3 [1,1,0,0,1,0] => 3 [1,1,0,1,0,0] => 4 [1,1,1,0,0,0] => 1 [1,0,1,0,1,0,1,0] => 5 [1,0,1,0,1,1,0,0] => 3 [1,0,1,1,0,0,1,0] => 5 [1,0,1,1,0,1,0,0] => 4 [1,0,1,1,1,0,0,0] => 3 [1,1,0,0,1,0,1,0] => 3 [1,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,0,1,0] => 3 [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] => 3 [1,1,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,0,0] => 5 [1,1,1,1,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0] => 5 [1,0,1,0,1,0,1,1,0,0] => 5 [1,0,1,0,1,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,0] => 6 [1,0,1,0,1,1,1,0,0,0] => 3 [1,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,0,1,1,0,0] => 5 [1,0,1,1,0,1,0,0,1,0] => 5 [1,0,1,1,0,1,0,1,0,0] => 6 [1,0,1,1,0,1,1,0,0,0] => 4 [1,0,1,1,1,0,0,0,1,0] => 5 [1,0,1,1,1,0,0,1,0,0] => 6 [1,0,1,1,1,0,1,0,0,0] => 5 [1,0,1,1,1,1,0,0,0,0] => 3 [1,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,0] => 3 [1,1,0,0,1,1,0,0,1,0] => 5 [1,1,0,0,1,1,0,1,0,0] => 4 [1,1,0,0,1,1,1,0,0,0] => 3 [1,1,0,1,0,0,1,0,1,0] => 6 [1,1,0,1,0,0,1,1,0,0] => 3 [1,1,0,1,0,1,0,0,1,0] => 6 [1,1,0,1,0,1,0,1,0,0] => 4 [1,1,0,1,0,1,1,0,0,0] => 4 [1,1,0,1,1,0,0,0,1,0] => 6 [1,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,0,0,0] => 5 [1,1,0,1,1,1,0,0,0,0] => 4 [1,1,1,0,0,0,1,0,1,0] => 3 [1,1,1,0,0,0,1,1,0,0] => 3 [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] => 4 [1,1,1,0,1,0,0,0,1,0] => 3 [1,1,1,0,1,0,0,1,0,0] => 4 [1,1,1,0,1,0,1,0,0,0] => 5 [1,1,1,0,1,1,0,0,0,0] => 5 [1,1,1,1,0,0,0,0,1,0] => 3 [1,1,1,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,0,0,0] => 5 [1,1,1,1,0,1,0,0,0,0] => 6 [1,1,1,1,1,0,0,0,0,0] => 1 [1,0,1,0,1,0,1,0,1,0,1,0] => 7 [1,0,1,0,1,0,1,0,1,1,0,0] => 5 [1,0,1,0,1,0,1,1,0,0,1,0] => 7 [1,0,1,0,1,0,1,1,0,1,0,0] => 6 [1,0,1,0,1,0,1,1,1,0,0,0] => 5 [1,0,1,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,0,1,1,0,0,1,1,0,0] => 5 [1,0,1,0,1,1,0,1,0,0,1,0] => 5 [1,0,1,0,1,1,0,1,0,1,0,0] => 6 [1,0,1,0,1,1,0,1,1,0,0,0] => 6 [1,0,1,0,1,1,1,0,0,0,1,0] => 5 [1,0,1,0,1,1,1,0,0,1,0,0] => 6 [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] => 3 [1,0,1,1,0,0,1,0,1,0,1,0] => 7 [1,0,1,1,0,0,1,0,1,1,0,0] => 5 [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] => 6 [1,0,1,1,0,0,1,1,1,0,0,0] => 5 [1,0,1,1,0,1,0,0,1,0,1,0] => 6 [1,0,1,1,0,1,0,0,1,1,0,0] => 5 [1,0,1,1,0,1,0,1,0,0,1,0] => 6 [1,0,1,1,0,1,0,1,0,1,0,0] => 6 [1,0,1,1,0,1,0,1,1,0,0,0] => 6 [1,0,1,1,0,1,1,0,0,0,1,0] => 6 [1,0,1,1,0,1,1,0,0,1,0,0] => 6 [1,0,1,1,0,1,1,0,1,0,0,0] => 7 [1,0,1,1,0,1,1,1,0,0,0,0] => 4 [1,0,1,1,1,0,0,0,1,0,1,0] => 5 [1,0,1,1,1,0,0,0,1,1,0,0] => 5 [1,0,1,1,1,0,0,1,0,0,1,0] => 5 [1,0,1,1,1,0,0,1,0,1,0,0] => 6 [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] => 5 [1,0,1,1,1,0,1,0,0,1,0,0] => 6 [1,0,1,1,1,0,1,0,1,0,0,0] => 7 [1,0,1,1,1,0,1,1,0,0,0,0] => 5 [1,0,1,1,1,1,0,0,0,0,1,0] => 5 [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] => 7 [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] => 3 [1,1,0,0,1,0,1,0,1,0,1,0] => 5 [1,1,0,0,1,0,1,0,1,1,0,0] => 5 [1,1,0,0,1,0,1,1,0,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,1,0,0] => 6 [1,1,0,0,1,0,1,1,1,0,0,0] => 3 [1,1,0,0,1,1,0,0,1,0,1,0] => 5 [1,1,0,0,1,1,0,0,1,1,0,0] => 5 [1,1,0,0,1,1,0,1,0,0,1,0] => 5 [1,1,0,0,1,1,0,1,0,1,0,0] => 6 [1,1,0,0,1,1,0,1,1,0,0,0] => 4 [1,1,0,0,1,1,1,0,0,0,1,0] => 5 [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] => 5 [1,1,0,0,1,1,1,1,0,0,0,0] => 3 [1,1,0,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,1,0,0,1,0,1,1,0,0] => 6 [1,1,0,1,0,0,1,1,0,0,1,0] => 5 [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] => 3 [1,1,0,1,0,1,0,0,1,0,1,0] => 6 [1,1,0,1,0,1,0,0,1,1,0,0] => 6 [1,1,0,1,0,1,0,1,0,0,1,0] => 6 [1,1,0,1,0,1,0,1,0,1,0,0] => 7 [1,1,0,1,0,1,0,1,1,0,0,0] => 4 [1,1,0,1,0,1,1,0,0,0,1,0] => 6 [1,1,0,1,0,1,1,0,0,1,0,0] => 7 [1,1,0,1,0,1,1,0,1,0,0,0] => 5 [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] => 6 [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] => 6 [1,1,0,1,1,0,0,1,0,1,0,0] => 7 [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] => 6 [1,1,0,1,1,0,1,0,0,1,0,0] => 7 [1,1,0,1,1,0,1,0,1,0,0,0] => 5 [1,1,0,1,1,0,1,1,0,0,0,0] => 5 [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] => 7 [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] => 4 [1,1,1,0,0,0,1,0,1,0,1,0] => 5 [1,1,1,0,0,0,1,0,1,1,0,0] => 3 [1,1,1,0,0,0,1,1,0,0,1,0] => 5 [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] => 3 [1,1,1,0,0,1,0,0,1,0,1,0] => 6 [1,1,1,0,0,1,0,0,1,1,0,0] => 3 [1,1,1,0,0,1,0,1,0,0,1,0] => 6 [1,1,1,0,0,1,0,1,0,1,0,0] => 4 [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] => 6 [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] => 5 [1,1,1,0,0,1,1,1,0,0,0,0] => 4 [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] => 3 [1,1,1,0,1,0,0,1,0,0,1,0] => 7 [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] => 4 [1,1,1,0,1,0,1,0,0,0,1,0] => 7 [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] => 5 [1,1,1,0,1,0,1,1,0,0,0,0] => 5 [1,1,1,0,1,1,0,0,0,0,1,0] => 7 [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] => 5 [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] => 3 [1,1,1,1,0,0,0,0,1,1,0,0] => 3 [1,1,1,1,0,0,0,1,0,0,1,0] => 3 [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] => 4 [1,1,1,1,0,0,1,0,0,0,1,0] => 3 [1,1,1,1,0,0,1,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,0,1,0,0,0] => 5 [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] => 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] => 5 [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] => 6 [1,1,1,1,1,0,0,0,0,0,1,0] => 3 [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] => 5 [1,1,1,1,1,0,0,1,0,0,0,0] => 6 [1,1,1,1,1,0,1,0,0,0,0,0] => 7 [1,1,1,1,1,1,0,0,0,0,0,0] => 1 ----------------------------------------------------------------------------- Created: Sep 28, 2019 at 09:00 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Sep 28, 2019 at 09:00 by Rene Marczinzik