***************************************************************************** * 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: St001258 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. For at most 6 simple modules this statistic coincides with the injective dimension of the regular module as a bimodule. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 2 [1,1,0,0] => 2 [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] => 2 [1,1,1,0,0,0] => 2 [1,0,1,0,1,0,1,0] => 4 [1,0,1,0,1,1,0,0] => 4 [1,0,1,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,0] => 3 [1,0,1,1,1,0,0,0] => 3 [1,1,0,0,1,0,1,0] => 4 [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] => 3 [1,1,0,1,1,0,0,0] => 3 [1,1,1,0,0,0,1,0] => 3 [1,1,1,0,0,1,0,0] => 3 [1,1,1,0,1,0,0,0] => 2 [1,1,1,1,0,0,0,0] => 2 [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] => 4 [1,0,1,0,1,1,1,0,0,0] => 4 [1,0,1,1,0,0,1,0,1,0] => 5 [1,0,1,1,0,0,1,1,0,0] => 4 [1,0,1,1,0,1,0,0,1,0] => 4 [1,0,1,1,0,1,0,1,0,0] => 4 [1,0,1,1,0,1,1,0,0,0] => 4 [1,0,1,1,1,0,0,0,1,0] => 4 [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] => 3 [1,1,0,0,1,0,1,0,1,0] => 5 [1,1,0,0,1,0,1,1,0,0] => 4 [1,1,0,0,1,1,0,0,1,0] => 4 [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] => 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] => 4 [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] => 4 [1,1,0,1,1,0,1,0,0,0] => 3 [1,1,0,1,1,1,0,0,0,0] => 3 [1,1,1,0,0,0,1,0,1,0] => 4 [1,1,1,0,0,0,1,1,0,0] => 3 [1,1,1,0,0,1,0,0,1,0] => 4 [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] => 3 [1,1,1,1,0,0,0,1,0,0] => 3 [1,1,1,1,0,0,1,0,0,0] => 3 [1,1,1,1,0,1,0,0,0,0] => 2 [1,1,1,1,1,0,0,0,0,0] => 2 [1,0,1,0,1,0,1,0,1,0,1,0] => 6 [1,0,1,0,1,0,1,0,1,1,0,0] => 6 [1,0,1,0,1,0,1,1,0,0,1,0] => 6 [1,0,1,0,1,0,1,1,0,1,0,0] => 5 [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] => 6 [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] => 5 [1,0,1,0,1,1,0,1,1,0,0,0] => 5 [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] => 5 [1,0,1,0,1,1,1,0,1,0,0,0] => 4 [1,0,1,0,1,1,1,1,0,0,0,0] => 4 [1,0,1,1,0,0,1,0,1,0,1,0] => 6 [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] => 4 [1,0,1,1,0,0,1,1,0,1,0,0] => 5 [1,0,1,1,0,0,1,1,1,0,0,0] => 4 [1,0,1,1,0,1,0,0,1,0,1,0] => 5 [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] => 5 [1,0,1,1,0,1,0,1,0,1,0,0] => 5 [1,0,1,1,0,1,0,1,1,0,0,0] => 5 [1,0,1,1,0,1,1,0,0,0,1,0] => 5 [1,0,1,1,0,1,1,0,0,1,0,0] => 5 [1,0,1,1,0,1,1,0,1,0,0,0] => 4 [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] => 4 [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] => 5 [1,0,1,1,1,0,0,1,1,0,0,0] => 4 [1,0,1,1,1,0,1,0,0,0,1,0] => 4 [1,0,1,1,1,0,1,0,0,1,0,0] => 4 [1,0,1,1,1,0,1,0,1,0,0,0] => 4 [1,0,1,1,1,0,1,1,0,0,0,0] => 4 [1,0,1,1,1,1,0,0,0,0,1,0] => 4 [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] => 4 [1,0,1,1,1,1,0,1,0,0,0,0] => 3 [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] => 6 [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] => 5 [1,1,0,0,1,0,1,1,1,0,0,0] => 4 [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] => 4 [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] => 5 [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] => 4 [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] => 4 [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] => 5 [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] => 4 [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] => 5 [1,1,0,1,0,1,0,0,1,1,0,0] => 5 [1,1,0,1,0,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,1,0,1,0,0] => 4 [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] => 5 [1,1,0,1,0,1,1,0,0,1,0,0] => 4 [1,1,0,1,0,1,1,0,1,0,0,0] => 4 [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] => 5 [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] => 5 [1,1,0,1,1,0,0,1,0,1,0,0] => 4 [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] => 4 [1,1,0,1,1,0,1,0,0,1,0,0] => 4 [1,1,0,1,1,0,1,0,1,0,0,0] => 4 [1,1,0,1,1,0,1,1,0,0,0,0] => 4 [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] => 4 [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] => 3 [1,1,0,1,1,1,1,0,0,0,0,0] => 3 [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] => 4 [1,1,1,0,0,0,1,1,0,0,1,0] => 4 [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] => 5 [1,1,1,0,0,1,0,0,1,1,0,0] => 4 [1,1,1,0,0,1,0,1,0,0,1,0] => 5 [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] => 4 [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] => 4 [1,1,1,0,0,1,1,1,0,0,0,0] => 3 [1,1,1,0,1,0,0,0,1,0,1,0] => 4 [1,1,1,0,1,0,0,0,1,1,0,0] => 4 [1,1,1,0,1,0,0,1,0,0,1,0] => 4 [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] => 4 [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] => 4 [1,1,1,0,1,0,1,1,0,0,0,0] => 4 [1,1,1,0,1,1,0,0,0,0,1,0] => 4 [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] => 4 [1,1,1,0,1,1,0,1,0,0,0,0] => 3 [1,1,1,0,1,1,1,0,0,0,0,0] => 3 [1,1,1,1,0,0,0,0,1,0,1,0] => 4 [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] => 4 [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] => 3 [1,1,1,1,0,0,1,0,0,0,1,0] => 4 [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] => 4 [1,1,1,1,0,0,1,1,0,0,0,0] => 3 [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] => 3 [1,1,1,1,0,1,0,0,1,0,0,0] => 3 [1,1,1,1,0,1,0,1,0,0,0,0] => 3 [1,1,1,1,0,1,1,0,0,0,0,0] => 3 [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] => 3 [1,1,1,1,1,0,0,0,1,0,0,0] => 3 [1,1,1,1,1,0,0,1,0,0,0,0] => 3 [1,1,1,1,1,0,1,0,0,0,0,0] => 2 [1,1,1,1,1,1,0,0,0,0,0,0] => 2 ----------------------------------------------------------------------------- Created: Sep 19, 2018 at 21:34 by Rene Marczinzik ----------------------------------------------------------------------------- Last Updated: Sep 19, 2018 at 22:12 by Rene Marczinzik