***************************************************************************** * 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: St001370 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The degree of the largest fundamental representation associated with a Cartan type. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(C): W = WeylCharacterRing(C) return max(W(w).degree() for w in W.fundamental_weights()) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 2 ['A',2] => 3 ['B',2] => 5 ['G',2] => 14 ['A',3] => 6 ['B',3] => 21 ['C',3] => 14 ['A',4] => 10 ['B',4] => 84 ['C',4] => 48 ['D',4] => 28 ['F',4] => 1274 ['A',5] => 20 ['B',5] => 330 ['C',5] => 165 ['D',5] => 120 ['A',6] => 35 ['B',6] => 1287 ['C',6] => 572 ['D',6] => 495 ['E',6] => 2925 ['A',7] => 70 ['B',7] => 5005 ['C',7] => 2002 ['D',7] => 2002 ['E',7] => 365750 ['A',8] => 126 ['B',8] => 19448 ['C',8] => 7072 ['D',8] => 8008 ----------------------------------------------------------------------------- Created: Mar 17, 2019 at 09:42 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 17, 2019 at 09:42 by Martin Rubey