***************************************************************************** * 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: St001787 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The number of subgroups of the Weyl group of given type. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(C): return len(WeylGroup(C).as_permutation_group().subgroups()) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 2 ['A',2] => 6 ['B',2] => 10 ['G',2] => 16 ['A',3] => 30 ['B',3] => 98 ['C',3] => 98 ['A',4] => 156 ['B',4] => 1659 ['C',4] => 1659 ['D',4] => 605 ['F',4] => 5191 ['A',5] => 1455 ['B',5] => 36430 ['C',5] => 36430 ['D',5] => 6697 ----------------------------------------------------------------------------- Created: Apr 27, 2022 at 10:14 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 27, 2022 at 10:14 by Martin Rubey