***************************************************************************** * 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: St001752 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The number of elements of maximal order in the Weyl group of a finite Cartan type. For the symmetric group $\mathfrak S_n$ this is [[OEIS:A074859]]. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(ct): l = [pi.order() for pi in WeylGroup(ct, implementation="permutation")] m = max(l) return sum(Integer(1) for e in l if e == m) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 2 ['B',2] => 2 ['G',2] => 2 ['A',3] => 6 ['B',3] => 8 ['C',3] => 8 ['A',4] => 20 ['B',4] => 48 ['C',4] => 48 ['D',4] => 32 ['F',4] => 96 ['A',5] => 240 ['B',5] => 320 ['C',5] => 320 ['D',5] => 160 ['A',6] => 420 ['B',6] => 7680 ['C',6] => 7680 ['D',6] => 1920 ['E',6] => 8640 ['A',7] => 2688 ['B',7] => 26880 ['C',7] => 26880 ['D',7] => 13440 ['E',7] => 96768 ['A',8] => 18144 ['B',8] => 516096 ['C',8] => 516096 ['D',8] => 172032 ----------------------------------------------------------------------------- Created: Dec 12, 2021 at 21:05 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 12, 2021 at 21:05 by Martin Rubey