***************************************************************************** * 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: St000079 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- Description: The number of alternating sign matrices for a given Dyck path. The Dyck path is given by the last diagonal of the monotone triangle corresponding to an alternating sign matrix. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(self): return sum( 1 for a in AlternatingSignMatrices(len(list(self))/2) if a.to_dyck_word(algorithm = 'last_diagonal') == self ) ----------------------------------------------------------------------------- Statistic values: [1,0] => 1 [1,0,1,0] => 1 [1,1,0,0] => 1 [1,0,1,0,1,0] => 1 [1,0,1,1,0,0] => 1 [1,1,0,0,1,0] => 1 [1,1,0,1,0,0] => 2 [1,1,1,0,0,0] => 2 [1,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,0] => 1 [1,0,1,1,0,1,0,0] => 2 [1,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,0,1,0] => 1 [1,1,0,0,1,1,0,0] => 1 [1,1,0,1,0,0,1,0] => 2 [1,1,0,1,0,1,0,0] => 5 [1,1,0,1,1,0,0,0] => 5 [1,1,1,0,0,0,1,0] => 2 [1,1,1,0,0,1,0,0] => 5 [1,1,1,0,1,0,0,0] => 7 [1,1,1,1,0,0,0,0] => 7 [1,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,1,0,1,0,0] => 2 [1,0,1,0,1,1,1,0,0,0] => 2 [1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,1,0,0,1,1,0,0] => 1 [1,0,1,1,0,1,0,0,1,0] => 2 [1,0,1,1,0,1,0,1,0,0] => 5 [1,0,1,1,0,1,1,0,0,0] => 5 [1,0,1,1,1,0,0,0,1,0] => 2 [1,0,1,1,1,0,0,1,0,0] => 5 [1,0,1,1,1,0,1,0,0,0] => 7 [1,0,1,1,1,1,0,0,0,0] => 7 [1,1,0,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,1,0,0,1,0] => 1 [1,1,0,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,1,1,0,0,0] => 2 [1,1,0,1,0,0,1,0,1,0] => 2 [1,1,0,1,0,0,1,1,0,0] => 2 [1,1,0,1,0,1,0,0,1,0] => 5 [1,1,0,1,0,1,0,1,0,0] => 14 [1,1,0,1,0,1,1,0,0,0] => 14 [1,1,0,1,1,0,0,0,1,0] => 5 [1,1,0,1,1,0,0,1,0,0] => 14 [1,1,0,1,1,0,1,0,0,0] => 21 [1,1,0,1,1,1,0,0,0,0] => 21 [1,1,1,0,0,0,1,0,1,0] => 2 [1,1,1,0,0,0,1,1,0,0] => 2 [1,1,1,0,0,1,0,0,1,0] => 5 [1,1,1,0,0,1,0,1,0,0] => 14 [1,1,1,0,0,1,1,0,0,0] => 14 [1,1,1,0,1,0,0,0,1,0] => 7 [1,1,1,0,1,0,0,1,0,0] => 21 [1,1,1,0,1,0,1,0,0,0] => 35 [1,1,1,0,1,1,0,0,0,0] => 35 [1,1,1,1,0,0,0,0,1,0] => 7 [1,1,1,1,0,0,0,1,0,0] => 21 [1,1,1,1,0,0,1,0,0,0] => 35 [1,1,1,1,0,1,0,0,0,0] => 42 [1,1,1,1,1,0,0,0,0,0] => 42 [1,0,1,0,1,0,1,0,1,0,1,0] => 1 [1,0,1,0,1,0,1,0,1,1,0,0] => 1 [1,0,1,0,1,0,1,1,0,0,1,0] => 1 [1,0,1,0,1,0,1,1,0,1,0,0] => 2 [1,0,1,0,1,0,1,1,1,0,0,0] => 2 [1,0,1,0,1,1,0,0,1,0,1,0] => 1 [1,0,1,0,1,1,0,0,1,1,0,0] => 1 [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] => 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] => 2 [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] => 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] => 1 [1,0,1,1,0,0,1,0,1,1,0,0] => 1 [1,0,1,1,0,0,1,1,0,0,1,0] => 1 [1,0,1,1,0,0,1,1,0,1,0,0] => 2 [1,0,1,1,0,0,1,1,1,0,0,0] => 2 [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] => 5 [1,0,1,1,0,1,0,1,0,1,0,0] => 14 [1,0,1,1,0,1,0,1,1,0,0,0] => 14 [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] => 14 [1,0,1,1,0,1,1,0,1,0,0,0] => 21 [1,0,1,1,0,1,1,1,0,0,0,0] => 21 [1,0,1,1,1,0,0,0,1,0,1,0] => 2 [1,0,1,1,1,0,0,0,1,1,0,0] => 2 [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] => 14 [1,0,1,1,1,0,0,1,1,0,0,0] => 14 [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] => 21 [1,0,1,1,1,0,1,0,1,0,0,0] => 35 [1,0,1,1,1,0,1,1,0,0,0,0] => 35 [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] => 21 [1,0,1,1,1,1,0,0,1,0,0,0] => 35 [1,0,1,1,1,1,0,1,0,0,0,0] => 42 [1,0,1,1,1,1,1,0,0,0,0,0] => 42 [1,1,0,0,1,0,1,0,1,0,1,0] => 1 [1,1,0,0,1,0,1,0,1,1,0,0] => 1 [1,1,0,0,1,0,1,1,0,0,1,0] => 1 [1,1,0,0,1,0,1,1,0,1,0,0] => 2 [1,1,0,0,1,0,1,1,1,0,0,0] => 2 [1,1,0,0,1,1,0,0,1,0,1,0] => 1 [1,1,0,0,1,1,0,0,1,1,0,0] => 1 [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] => 5 [1,1,0,0,1,1,0,1,1,0,0,0] => 5 [1,1,0,0,1,1,1,0,0,0,1,0] => 2 [1,1,0,0,1,1,1,0,0,1,0,0] => 5 [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] => 2 [1,1,0,1,0,0,1,0,1,1,0,0] => 2 [1,1,0,1,0,0,1,1,0,0,1,0] => 2 [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] => 14 [1,1,0,1,0,1,0,1,0,1,0,0] => 42 [1,1,0,1,0,1,0,1,1,0,0,0] => 42 [1,1,0,1,0,1,1,0,0,0,1,0] => 14 [1,1,0,1,0,1,1,0,0,1,0,0] => 42 [1,1,0,1,0,1,1,0,1,0,0,0] => 65 [1,1,0,1,0,1,1,1,0,0,0,0] => 65 [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] => 5 [1,1,0,1,1,0,0,1,0,0,1,0] => 14 [1,1,0,1,1,0,0,1,0,1,0,0] => 42 [1,1,0,1,1,0,0,1,1,0,0,0] => 42 [1,1,0,1,1,0,1,0,0,0,1,0] => 21 [1,1,0,1,1,0,1,0,0,1,0,0] => 68 [1,1,0,1,1,0,1,0,1,0,0,0] => 119 [1,1,0,1,1,0,1,1,0,0,0,0] => 119 [1,1,0,1,1,1,0,0,0,0,1,0] => 21 [1,1,0,1,1,1,0,0,0,1,0,0] => 68 [1,1,0,1,1,1,0,0,1,0,0,0] => 119 [1,1,0,1,1,1,0,1,0,0,0,0] => 147 [1,1,0,1,1,1,1,0,0,0,0,0] => 147 [1,1,1,0,0,0,1,0,1,0,1,0] => 2 [1,1,1,0,0,0,1,0,1,1,0,0] => 2 [1,1,1,0,0,0,1,1,0,0,1,0] => 2 [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] => 4 [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] => 5 [1,1,1,0,0,1,0,1,0,0,1,0] => 14 [1,1,1,0,0,1,0,1,0,1,0,0] => 42 [1,1,1,0,0,1,0,1,1,0,0,0] => 42 [1,1,1,0,0,1,1,0,0,0,1,0] => 14 [1,1,1,0,0,1,1,0,0,1,0,0] => 42 [1,1,1,0,0,1,1,0,1,0,0,0] => 65 [1,1,1,0,0,1,1,1,0,0,0,0] => 65 [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] => 21 [1,1,1,0,1,0,0,1,0,1,0,0] => 65 [1,1,1,0,1,0,0,1,1,0,0,0] => 65 [1,1,1,0,1,0,1,0,0,0,1,0] => 35 [1,1,1,0,1,0,1,0,0,1,0,0] => 119 [1,1,1,0,1,0,1,0,1,0,0,0] => 219 [1,1,1,0,1,0,1,1,0,0,0,0] => 219 [1,1,1,0,1,1,0,0,0,0,1,0] => 35 [1,1,1,0,1,1,0,0,0,1,0,0] => 119 [1,1,1,0,1,1,0,0,1,0,0,0] => 219 [1,1,1,0,1,1,0,1,0,0,0,0] => 282 [1,1,1,0,1,1,1,0,0,0,0,0] => 282 [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] => 21 [1,1,1,1,0,0,0,1,0,1,0,0] => 65 [1,1,1,1,0,0,0,1,1,0,0,0] => 65 [1,1,1,1,0,0,1,0,0,0,1,0] => 35 [1,1,1,1,0,0,1,0,0,1,0,0] => 119 [1,1,1,1,0,0,1,0,1,0,0,0] => 219 [1,1,1,1,0,0,1,1,0,0,0,0] => 219 [1,1,1,1,0,1,0,0,0,0,1,0] => 42 [1,1,1,1,0,1,0,0,0,1,0,0] => 147 [1,1,1,1,0,1,0,0,1,0,0,0] => 282 [1,1,1,1,0,1,0,1,0,0,0,0] => 387 [1,1,1,1,0,1,1,0,0,0,0,0] => 387 [1,1,1,1,1,0,0,0,0,0,1,0] => 42 [1,1,1,1,1,0,0,0,0,1,0,0] => 147 [1,1,1,1,1,0,0,0,1,0,0,0] => 282 [1,1,1,1,1,0,0,1,0,0,0,0] => 387 [1,1,1,1,1,0,1,0,0,0,0,0] => 429 [1,1,1,1,1,1,0,0,0,0,0,0] => 429 ----------------------------------------------------------------------------- Created: Jun 11, 2013 at 21:17 by Jessica Striker ----------------------------------------------------------------------------- Last Updated: Aug 21, 2017 at 08:49 by Martin Rubey