***************************************************************************** * 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: St001495 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The maximal order of an element in the Weyl group of a given Cartan type. For the symmetric group, this is [[oeis:A000793]] ----------------------------------------------------------------------------- References: [1] user66288 The maximal order of an element in a Coxeter group [[MathOverflow:343118]] ----------------------------------------------------------------------------- Code: def statistic(C): return max(g.order() for g in WeylGroup(C)) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 2 ['A',2] => 3 ['B',2] => 4 ['G',2] => 6 ['A',3] => 4 ['B',3] => 6 ['C',3] => 6 ['A',4] => 6 ['B',4] => 8 ['C',4] => 8 ['D',4] => 6 ['F',4] => 12 ['A',5] => 6 ['B',5] => 12 ['C',5] => 12 ['D',5] => 12 ['A',6] => 12 ['B',6] => 12 ['C',6] => 12 ['D',6] => 12 ['E',6] => 12 ----------------------------------------------------------------------------- Created: Nov 13, 2019 at 08:55 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 13, 2019 at 08:55 by Martin Rubey