***************************************************************************** * 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: St001701 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The maximum down-degree of the Hasse diagram of the strong Bruhat order in the Weyl group of the Cartan type. ----------------------------------------------------------------------------- References: [1] Adin, R. M., Roichman, Y. On degrees in the Hasse diagram of the strong Bruhat order [[MathSciNet:2221362]] ----------------------------------------------------------------------------- Code: def statistic(ct): n = ct.rank() if ct.type() == "A": return (n+1)^2//4 return max(WeylGroup(ct).bruhat_poset().hasse_diagram().out_degree()) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 2 ['B',2] => 2 ['G',2] => 2 ['A',3] => 4 ['B',3] => 4 ['C',3] => 4 ['A',4] => 6 ['B',4] => 8 ['C',4] => 8 ['D',4] => 8 ['F',4] => 8 ['A',5] => 9 ['B',5] => 12 ['C',5] => 12 ['D',5] => 12 ----------------------------------------------------------------------------- Created: Mar 08, 2021 at 10:52 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 08, 2021 at 10:52 by Martin Rubey