***************************************************************************** * 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: St001952 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The number of conjugacy classes in the Weyl group of finite Cartan type whose elements are involutions. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(ct): return sum(1 for w in WeylGroup(ct).conjugacy_classes_representatives() if w.order() == 2) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 1 ['B',2] => 3 ['G',2] => 3 ['A',3] => 2 ['B',3] => 5 ['C',3] => 5 ['A',4] => 2 ['B',4] => 8 ['C',4] => 8 ['D',4] => 6 ['F',4] => 7 ['A',5] => 3 ['B',5] => 11 ['C',5] => 11 ['D',5] => 5 ['A',6] => 3 ['B',6] => 15 ['C',6] => 15 ['D',6] => 10 ['E',6] => 4 ['A',7] => 4 ['B',7] => 19 ['C',7] => 19 ['D',7] => 9 ['E',7] => 9 ['A',8] => 4 ['B',8] => 24 ['C',8] => 24 ['D',8] => 15 ['E',8] => 9 ----------------------------------------------------------------------------- Created: Jul 09, 2024 at 12:00 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 09, 2024 at 12:00 by Martin Rubey