***************************************************************************** * 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: St000113 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The rank of the Cartan type. The rank of a Cartan type $X_n$ is equal to the rank of the corresponding Cartan matrix. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(ct): return ct.rank() ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 2 ['B',2] => 2 ['G',2] => 2 ['A',3] => 3 ['B',3] => 3 ['C',3] => 3 ['A',4] => 4 ['B',4] => 4 ['C',4] => 4 ['F',4] => 4 ['A',5] => 5 ['B',5] => 5 ['C',5] => 5 ['D',5] => 5 ['A',6] => 6 ['B',6] => 6 ['C',6] => 6 ['D',6] => 6 ['E',6] => 6 ['A',7] => 7 ['B',7] => 7 ['C',7] => 7 ['D',7] => 7 ['E',7] => 7 ['A',8] => 8 ['B',8] => 8 ['C',8] => 8 ['D',8] => 8 ['E',8] => 8 ['A',9] => 9 ['A',10] => 10 ['B',9] => 9 ['B',10] => 10 ['C',9] => 9 ['C',10] => 10 ['D',9] => 9 ['D',10] => 10 ----------------------------------------------------------------------------- Created: Jun 15, 2013 at 15:31 by Travis Scrimshaw ----------------------------------------------------------------------------- Last Updated: Dec 28, 2016 at 10:47 by Christian Stump