***************************************************************************** * 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: St001953 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The number of distinct orders of elements in a Weyl group of finite Cartan type. ----------------------------------------------------------------------------- References: [1] Number of distinct orders of permutations of n objects; number of nonisomorphic cyclic subgroups of symmetric group S_n. [[OEIS:A009490]] ----------------------------------------------------------------------------- Code: def statistic(ct): return len(set(w.order() for w in WeylGroup(ct).conjugacy_classes_representatives())) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 2 ['A',2] => 3 ['B',2] => 3 ['G',2] => 4 ['A',3] => 4 ['B',3] => 5 ['C',3] => 5 ['A',4] => 6 ['B',4] => 6 ['C',4] => 6 ['D',4] => 5 ['F',4] => 7 ['A',5] => 6 ['B',5] => 9 ['C',5] => 9 ['D',5] => 8 ['A',6] => 9 ['B',6] => 9 ['C',6] => 9 ['D',6] => 9 ['E',6] => 10 ['A',7] => 11 ['B',7] => 13 ['C',7] => 13 ['D',7] => 12 ['E',7] => 15 ['A',8] => 14 ['B',8] => 16 ['C',8] => 16 ['D',8] => 15 ['E',8] => 17 ----------------------------------------------------------------------------- Created: Jul 09, 2024 at 12:05 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Aug 04, 2024 at 22:05 by Martin Rubey