***************************************************************************** * 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: St001369 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The largest coefficient in the highest root in the root system of a Cartan type. ----------------------------------------------------------------------------- References: [1] Hopkins, S. How big can the index inside the root lattice of the lattice generated by a subset of roots be? [[MathOverflow:310884]] ----------------------------------------------------------------------------- Code: def statistic(C): return max(C.root_system().root_space().highest_root().coefficients()) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 1 ['B',2] => 2 ['G',2] => 3 ['A',3] => 1 ['B',3] => 2 ['C',3] => 2 ['A',4] => 1 ['B',4] => 2 ['C',4] => 2 ['D',4] => 2 ['F',4] => 4 ['A',5] => 1 ['B',5] => 2 ['C',5] => 2 ['D',5] => 2 ['A',6] => 1 ['B',6] => 2 ['C',6] => 2 ['D',6] => 2 ['E',6] => 3 ['A',7] => 1 ['B',7] => 2 ['C',7] => 2 ['D',7] => 2 ['E',7] => 4 ['A',8] => 1 ['B',8] => 2 ['C',8] => 2 ['D',8] => 2 ['E',8] => 6 ----------------------------------------------------------------------------- Created: Mar 17, 2019 at 09:29 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 17, 2019 at 09:29 by Martin Rubey