***************************************************************************** * 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: St001155 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The number of conjugacy classes of subgroups of the Weyl group of given type. ----------------------------------------------------------------------------- References: [1] Number of permutation groups of degree n; also number of conjugacy classes of subgroups of symmetric group S_n; also number of molecular species of degree n. [[OEIS:A000638]] [2] Number of conjugacy classes of subgroups of the hyperoctahedral group. [[OEIS:A269890]] ----------------------------------------------------------------------------- Code: def statistic(C): return len(WeylGroup(C).as_permutation_group().conjugacy_classes_subgroups()) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 2 ['A',2] => 4 ['B',2] => 8 ['G',2] => 10 ['A',3] => 11 ['B',3] => 33 ['C',3] => 33 ['A',4] => 19 ['B',4] => 193 ['C',4] => 193 ['D',4] => 98 ['F',4] => 246 ['A',5] => 56 ['B',5] => 953 ['C',5] => 953 ['D',5] => 197 ['A',6] => 96 ['B',6] => 7440 ['C',6] => 7440 ['D',6] => 1916 ['E',6] => 350 ['A',7] => 296 ['A',8] => 554 ['A',9] => 1593 ['A',10] => 3094 ----------------------------------------------------------------------------- Created: Apr 21, 2018 at 23:43 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Oct 18, 2020 at 17:52 by Martin Rubey