***************************************************************************** * 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: St001146 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The number of Grassmannian elements in the Coxeter group of the given type. An element is Grassmannian if it has at most one descent. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(C): return CoxeterGroup(C, implementation='coxeter3').grassmannian_elements().cardinality() ----------------------------------------------------------------------------- Statistic values: ['A',1] => 2 ['A',2] => 5 ['B',2] => 7 ['G',2] => 11 ['A',3] => 12 ['B',3] => 24 ['C',3] => 24 ['A',4] => 27 ['B',4] => 77 ['C',4] => 77 ['D',4] => 45 ['F',4] => 237 ['A',5] => 58 ['B',5] => 238 ['C',5] => 238 ['D',5] => 158 ['A',6] => 121 ['B',6] => 723 ['C',6] => 723 ['D',6] => 531 ['E',6] => 1273 ['A',7] => 248 ['B',7] => 2180 ['C',7] => 2180 ['D',7] => 1732 ['E',7] => 17636 ----------------------------------------------------------------------------- Created: Apr 19, 2018 at 00:24 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 19, 2018 at 00:24 by Martin Rubey