***************************************************************************** * 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: St001154 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The dual Coxeter number of a finite Cartan type. ----------------------------------------------------------------------------- References: [1] Humphreys, J. What role does the "dual Coxeter number" play in Lie theory (and should it be called the "Kac number")? [[MathOverflow:25592]] ----------------------------------------------------------------------------- Code: def statistic(C): return C.dual_coxeter_number() ----------------------------------------------------------------------------- Statistic values: ['A',1] => 2 ['A',2] => 3 ['B',2] => 3 ['G',2] => 4 ['A',3] => 4 ['B',3] => 5 ['C',3] => 4 ['A',4] => 5 ['B',4] => 7 ['C',4] => 5 ['D',4] => 6 ['F',4] => 9 ['A',5] => 6 ['B',5] => 9 ['C',5] => 6 ['D',5] => 8 ['A',6] => 7 ['B',6] => 11 ['C',6] => 7 ['D',6] => 10 ['E',6] => 12 ['A',7] => 8 ['B',7] => 13 ['C',7] => 8 ['D',7] => 12 ['E',7] => 18 ['A',8] => 9 ['B',8] => 15 ['C',8] => 9 ['D',8] => 14 ['E',8] => 30 ----------------------------------------------------------------------------- Created: Apr 20, 2018 at 20:27 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 20, 2018 at 20:27 by Martin Rubey