***************************************************************************** * 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: St001897 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The minimal degree of a faithful permutation representation of a Weyl group. Data are from [1, Table 1]. ----------------------------------------------------------------------------- References: [1] (service unreachable) [[MathSciNet:1862148]] ----------------------------------------------------------------------------- Code: def statistic(ct): if ct.type() == "A": return ct.rank() + 1 if ct.type() in ["B", "C", "D"]: return 2*ct.rank() if ct.type() == "G" and ct.rank() == 2: return 6 if ct.type() == "F" and ct.rank() == 4: return 24 if ct.type() == "E" and ct.rank() == 6: return 27 if ct.type() == "E" and ct.rank() == 7: return 56 if ct.type() == "E" and ct.rank() == 8: return 240 ----------------------------------------------------------------------------- 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] => 5 ['B',4] => 8 ['C',4] => 8 ['D',4] => 8 ['F',4] => 24 ['A',5] => 6 ['B',5] => 10 ['C',5] => 10 ['D',5] => 10 ['A',6] => 7 ['B',6] => 12 ['C',6] => 12 ['D',6] => 12 ['E',6] => 27 ['A',7] => 8 ['B',7] => 14 ['C',7] => 14 ['D',7] => 14 ['E',7] => 56 ['A',8] => 9 ['B',8] => 16 ['C',8] => 16 ['D',8] => 16 ['E',8] => 240 ----------------------------------------------------------------------------- Created: Apr 12, 2023 at 16:12 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 12, 2023 at 16:12 by Martin Rubey