***************************************************************************** * 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: St001886 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The number of orbits of the rowmotion operator on the root poset of a finite Cartan type. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(ct): return len(ct.root_system().root_poset().rowmotion_orbits()) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 2 ['B',2] => 2 ['G',2] => 2 ['A',3] => 3 ['B',3] => 4 ['C',3] => 4 ['A',4] => 6 ['B',4] => 10 ['C',4] => 10 ['D',4] => 10 ['F',4] => 11 ['A',5] => 14 ['B',5] => 26 ['C',5] => 26 ['D',5] => 17 ['A',6] => 34 ['B',6] => 80 ['C',6] => 80 ['D',6] => 68 ['E',6] => 42 ['A',7] => 95 ['B',7] => 246 ['C',7] => 246 ['D',7] => 146 ['E',7] => 234 ['A',8] => 280 ['B',8] => 810 ['C',8] => 810 ['D',8] => 680 ['E',8] => 844 ----------------------------------------------------------------------------- Created: Jan 06, 2023 at 19:24 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jan 06, 2023 at 19:24 by Martin Rubey