***************************************************************************** * 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: St001650 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. ----------------------------------------------------------------------------- References: [1] Ringel, C. M. The finitistic dimension of a Nakayama algebra [[arXiv:2008.10044]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 2 [1,0,1,0] => 3 [1,1,0,0] => 3 [1,0,1,0,1,0] => 4 [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] => 4 [1,0,1,0,1,0,1,0] => 5 [1,0,1,0,1,1,0,0] => 5 [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] => 5 [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] => 5 [1,1,1,0,0,0,1,0] => 5 [1,1,1,0,0,1,0,0] => 5 [1,1,1,0,1,0,0,0] => 5 [1,1,1,1,0,0,0,0] => 5 [1,0,1,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,0,1,1,0,0] => 6 [1,0,1,0,1,1,0,0,1,0] => 6 [1,0,1,0,1,1,0,1,0,0] => 6 [1,0,1,0,1,1,1,0,0,0] => 6 [1,0,1,1,0,0,1,0,1,0] => 6 [1,0,1,1,0,0,1,1,0,0] => 6 [1,0,1,1,0,1,0,0,1,0] => 6 [1,0,1,1,0,1,0,1,0,0] => 4 [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] => 6 [1,0,1,1,1,0,1,0,0,0] => 6 [1,0,1,1,1,1,0,0,0,0] => 6 [1,1,0,0,1,0,1,0,1,0] => 6 [1,1,0,0,1,0,1,1,0,0] => 6 [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] => 6 [1,1,0,1,0,0,1,1,0,0] => 6 [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] => 6 [1,1,0,1,1,0,0,1,0,0] => 6 [1,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,0,0,0] => 6 [1,1,1,0,0,0,1,0,1,0] => 6 [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] => 4 [1,1,1,0,0,1,1,0,0,0] => 6 [1,1,1,0,1,0,0,0,1,0] => 6 [1,1,1,0,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,1,0,0,0] => 4 [1,1,1,0,1,1,0,0,0,0] => 6 [1,1,1,1,0,0,0,0,1,0] => 6 [1,1,1,1,0,0,0,1,0,0] => 6 [1,1,1,1,0,0,1,0,0,0] => 6 [1,1,1,1,0,1,0,0,0,0] => 6 [1,1,1,1,1,0,0,0,0,0] => 6 [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] => 7 [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] => 7 [1,0,1,0,1,0,1,1,1,0,0,0] => 7 [1,0,1,0,1,1,0,0,1,0,1,0] => 7 [1,0,1,0,1,1,0,0,1,1,0,0] => 7 [1,0,1,0,1,1,0,1,0,0,1,0] => 7 [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] => 7 [1,0,1,0,1,1,1,0,0,0,1,0] => 7 [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] => 7 [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] => 7 [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] => 7 [1,0,1,1,0,1,0,0,1,1,0,0] => 7 [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] => 12 [1,0,1,1,0,1,0,1,1,0,0,0] => 10 [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] => 12 [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] => 7 [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] => 10 [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] => 7 [1,0,1,1,1,0,1,0,0,1,0,0] => 12 [1,0,1,1,1,0,1,0,1,0,0,0] => 10 [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] => 7 [1,1,0,0,1,0,1,0,1,0,1,0] => 7 [1,1,0,0,1,0,1,0,1,1,0,0] => 7 [1,1,0,0,1,0,1,1,0,0,1,0] => 7 [1,1,0,0,1,0,1,1,0,1,0,0] => 7 [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] => 7 [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] => 7 [1,1,0,0,1,1,0,1,0,1,0,0] => 10 [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] => 7 [1,1,0,1,0,0,1,0,1,0,1,0] => 7 [1,1,0,1,0,0,1,0,1,1,0,0] => 7 [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] => 10 [1,1,0,1,0,1,0,1,0,0,1,0] => 12 [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] => 12 [1,1,0,1,0,1,1,0,0,0,1,0] => 10 [1,1,0,1,0,1,1,0,0,1,0,0] => 10 [1,1,0,1,0,1,1,0,1,0,0,0] => 12 [1,1,0,1,0,1,1,1,0,0,0,0] => 10 [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] => 7 [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] => 10 [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] => 12 [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] => 12 [1,1,0,1,1,0,1,1,0,0,0,0] => 12 [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] => 12 [1,1,0,1,1,1,1,0,0,0,0,0] => 7 [1,1,1,0,0,0,1,0,1,0,1,0] => 7 [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] => 7 [1,1,1,0,0,1,0,0,1,0,1,0] => 7 [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] => 10 [1,1,1,0,0,1,0,1,0,1,0,0] => 12 [1,1,1,0,0,1,0,1,1,0,0,0] => 10 [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] => 12 [1,1,1,0,0,1,1,1,0,0,0,0] => 7 [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] => 7 [1,1,1,0,1,0,0,1,0,0,1,0] => 12 [1,1,1,0,1,0,0,1,0,1,0,0] => 12 [1,1,1,0,1,0,0,1,1,0,0,0] => 12 [1,1,1,0,1,0,1,0,0,0,1,0] => 10 [1,1,1,0,1,0,1,0,0,1,0,0] => 12 [1,1,1,0,1,0,1,0,1,0,0,0] => 7 [1,1,1,0,1,0,1,1,0,0,0,0] => 10 [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] => 12 [1,1,1,0,1,1,0,1,0,0,0,0] => 12 [1,1,1,0,1,1,1,0,0,0,0,0] => 7 [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] => 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] => 10 [1,1,1,1,0,0,0,1,1,0,0,0] => 7 [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] => 12 [1,1,1,1,0,0,1,0,1,0,0,0] => 10 [1,1,1,1,0,0,1,1,0,0,0,0] => 7 [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] => 12 [1,1,1,1,0,1,0,0,1,0,0,0] => 12 [1,1,1,1,0,1,0,1,0,0,0,0] => 10 [1,1,1,1,0,1,1,0,0,0,0,0] => 7 [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] => 7 [1,1,1,1,1,0,0,0,1,0,0,0] => 7 [1,1,1,1,1,0,0,1,0,0,0,0] => 7 [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] => 7 ----------------------------------------------------------------------------- Created: Nov 29, 2020 at 19:57 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Nov 29, 2020 at 19:57 by Rene Marczinzik