***************************************************************************** * 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: St001145 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The largest coefficient in a Kazhdan Lusztig polynomial of the Weyl group of given type. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(C): W = CoxeterGroup(C, implementation='coxeter3') r = set([]) for u in W: U = (W(v) for v in W.bruhat_interval(u, W.long_element())) next(U) for v in U: p = W.kazhdan_lusztig_polynomial(u, v) c = set(p.coefficients()) r = r.union(c) return max(r) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 1 ['B',2] => 1 ['G',2] => 1 ['A',3] => 1 ['B',3] => 1 ['C',3] => 1 ['A',4] => 2 ['B',4] => 5 ['C',4] => 5 ['D',4] => 4 ['F',4] => 12 ['A',5] => 4 ----------------------------------------------------------------------------- Created: Apr 19, 2018 at 00:00 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 19, 2018 at 09:07 by Martin Rubey