***************************************************************************** * 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: St001966 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: Half the global dimension of the stable Auslander algebra of a sincere Nakayama algebra (with associated Dyck path). ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 4 [1,1,0,0] => 2 [1,0,1,0,1,0] => 7 [1,0,1,1,0,0] => 4 [1,1,0,0,1,0] => 4 [1,1,0,1,0,0] => 4 [1,1,1,0,0,0] => 2 [1,0,1,0,1,0,1,0] => 10 [1,0,1,0,1,1,0,0] => 7 [1,0,1,1,0,0,1,0] => 7 [1,0,1,1,0,1,0,0] => 7 [1,0,1,1,1,0,0,0] => 4 [1,1,0,0,1,0,1,0] => 7 [1,1,0,0,1,1,0,0] => 4 [1,1,0,1,0,0,1,0] => 7 [1,1,0,1,0,1,0,0] => 5 [1,1,0,1,1,0,0,0] => 4 [1,1,1,0,0,0,1,0] => 4 [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] => 2 [1,0,1,0,1,0,1,0,1,0] => 13 [1,0,1,0,1,0,1,1,0,0] => 10 [1,0,1,0,1,1,0,0,1,0] => 10 [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] => 10 [1,0,1,1,0,0,1,1,0,0] => 7 [1,0,1,1,0,1,0,0,1,0] => 10 [1,0,1,1,0,1,0,1,0,0] => 7 [1,0,1,1,0,1,1,0,0,0] => 7 [1,0,1,1,1,0,0,0,1,0] => 7 [1,0,1,1,1,0,0,1,0,0] => 7 [1,0,1,1,1,0,1,0,0,0] => 7 [1,0,1,1,1,1,0,0,0,0] => 4 [1,1,0,0,1,0,1,0,1,0] => 10 [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] => 7 [1,1,0,0,1,1,1,0,0,0] => 4 [1,1,0,1,0,0,1,0,1,0] => 10 [1,1,0,1,0,0,1,1,0,0] => 7 [1,1,0,1,0,1,0,0,1,0] => 7 [1,1,0,1,0,1,0,1,0,0] => 7 [1,1,0,1,0,1,1,0,0,0] => 5 [1,1,0,1,1,0,0,0,1,0] => 7 [1,1,0,1,1,0,0,1,0,0] => 7 [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] => 7 [1,1,1,0,0,0,1,1,0,0] => 4 [1,1,1,0,0,1,0,0,1,0] => 7 [1,1,1,0,0,1,0,1,0,0] => 5 [1,1,1,0,0,1,1,0,0,0] => 4 [1,1,1,0,1,0,0,0,1,0] => 7 [1,1,1,0,1,0,0,1,0,0] => 5 [1,1,1,0,1,0,1,0,0,0] => 5 [1,1,1,0,1,1,0,0,0,0] => 4 [1,1,1,1,0,0,0,0,1,0] => 4 [1,1,1,1,0,0,0,1,0,0] => 4 [1,1,1,1,0,0,1,0,0,0] => 4 [1,1,1,1,0,1,0,0,0,0] => 4 [1,1,1,1,1,0,0,0,0,0] => 2 [1,0,1,0,1,0,1,0,1,0,1,0] => 16 [1,0,1,0,1,0,1,0,1,1,0,0] => 13 [1,0,1,0,1,0,1,1,0,0,1,0] => 13 [1,0,1,0,1,0,1,1,0,1,0,0] => 13 [1,0,1,0,1,0,1,1,1,0,0,0] => 10 [1,0,1,0,1,1,0,0,1,0,1,0] => 13 [1,0,1,0,1,1,0,0,1,1,0,0] => 10 [1,0,1,0,1,1,0,1,0,0,1,0] => 13 [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] => 10 [1,0,1,0,1,1,1,0,0,0,1,0] => 10 [1,0,1,0,1,1,1,0,0,1,0,0] => 10 [1,0,1,0,1,1,1,0,1,0,0,0] => 10 [1,0,1,0,1,1,1,1,0,0,0,0] => 7 [1,0,1,1,0,0,1,0,1,0,1,0] => 13 [1,0,1,1,0,0,1,0,1,1,0,0] => 10 [1,0,1,1,0,0,1,1,0,0,1,0] => 10 [1,0,1,1,0,0,1,1,0,1,0,0] => 10 [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] => 13 [1,0,1,1,0,1,0,0,1,1,0,0] => 10 [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] => 10 [1,0,1,1,0,1,0,1,1,0,0,0] => 7 [1,0,1,1,0,1,1,0,0,0,1,0] => 10 [1,0,1,1,0,1,1,0,0,1,0,0] => 10 [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] => 7 [1,0,1,1,1,0,0,0,1,0,1,0] => 10 [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] => 10 [1,0,1,1,1,0,0,1,0,1,0,0] => 7 [1,0,1,1,1,0,0,1,1,0,0,0] => 7 [1,0,1,1,1,0,1,0,0,0,1,0] => 10 [1,0,1,1,1,0,1,0,0,1,0,0] => 7 [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] => 7 [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] => 7 [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] => 7 [1,0,1,1,1,1,1,0,0,0,0,0] => 4 [1,1,0,0,1,0,1,0,1,0,1,0] => 13 [1,1,0,0,1,0,1,0,1,1,0,0] => 10 [1,1,0,0,1,0,1,1,0,0,1,0] => 10 [1,1,0,0,1,0,1,1,0,1,0,0] => 10 [1,1,0,0,1,0,1,1,1,0,0,0] => 7 [1,1,0,0,1,1,0,0,1,0,1,0] => 10 [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] => 10 [1,1,0,0,1,1,0,1,0,1,0,0] => 7 [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] => 7 [1,1,0,0,1,1,1,0,1,0,0,0] => 7 [1,1,0,0,1,1,1,1,0,0,0,0] => 4 [1,1,0,1,0,0,1,0,1,0,1,0] => 13 [1,1,0,1,0,0,1,0,1,1,0,0] => 10 [1,1,0,1,0,0,1,1,0,0,1,0] => 10 [1,1,0,1,0,0,1,1,0,1,0,0] => 10 [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] => 7 [1,1,0,1,0,1,0,1,0,0,1,0] => 10 [1,1,0,1,0,1,0,1,0,1,0,0] => 8 [1,1,0,1,0,1,0,1,1,0,0,0] => 7 [1,1,0,1,0,1,1,0,0,0,1,0] => 7 [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] => 7 [1,1,0,1,0,1,1,1,0,0,0,0] => 5 [1,1,0,1,1,0,0,0,1,0,1,0] => 10 [1,1,0,1,1,0,0,0,1,1,0,0] => 7 [1,1,0,1,1,0,0,1,0,0,1,0] => 10 [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] => 7 [1,1,0,1,1,0,1,0,0,0,1,0] => 7 [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] => 7 [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] => 7 [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] => 7 [1,1,0,1,1,1,0,1,0,0,0,0] => 5 [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] => 10 [1,1,1,0,0,0,1,0,1,1,0,0] => 7 [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] => 4 [1,1,1,0,0,1,0,0,1,0,1,0] => 10 [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] => 7 [1,1,1,0,0,1,0,1,0,1,0,0] => 7 [1,1,1,0,0,1,0,1,1,0,0,0] => 5 [1,1,1,0,0,1,1,0,0,0,1,0] => 7 [1,1,1,0,0,1,1,0,0,1,0,0] => 7 [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] => 10 [1,1,1,0,1,0,0,0,1,1,0,0] => 7 [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] => 7 [1,1,1,0,1,0,0,1,1,0,0,0] => 5 [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] => 7 [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] => 7 [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] => 5 [1,1,1,0,1,1,1,0,0,0,0,0] => 4 [1,1,1,1,0,0,0,0,1,0,1,0] => 7 [1,1,1,1,0,0,0,0,1,1,0,0] => 4 [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] => 5 [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] => 7 [1,1,1,1,0,0,1,0,0,1,0,0] => 5 [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] => 4 [1,1,1,1,0,1,0,0,0,0,1,0] => 7 [1,1,1,1,0,1,0,0,0,1,0,0] => 5 [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] => 5 [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] => 4 [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] => 4 [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] => 4 [1,1,1,1,1,1,0,0,0,0,0,0] => 2 ----------------------------------------------------------------------------- Created: Jul 25, 2025 at 16:33 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 25, 2025 at 16:33 by Martin Rubey