***************************************************************************** * 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: St001954 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The sum of the entries in the character table of the Weyl group of finite Cartan type. ----------------------------------------------------------------------------- References: [1] Ayyer, A., Dey, H. K., Paul, D. How large is the character degree sum compared to the character table sum for a finite group? [[arXiv:2406.06036]] ----------------------------------------------------------------------------- Code: def statistic(ct): W = WeylGroup(ct, implementation="permutation") t = W.character_table() return sum(sum(t)) ----------------------------------------------------------------------------- Statistic values: ['A',1] => 2 ['A',2] => 5 ['B',2] => 8 ['G',2] => 10 ['A',3] => 13 ['B',3] => 26 ['C',3] => 26 ['A',4] => 31 ['B',4] => 112 ['C',4] => 112 ['D',4] => 70 ['F',4] => 200 ['A',5] => 89 ['B',5] => 410 ['C',5] => 410 ['D',5] => 205 ['A',6] => 259 ['B',6] => 1860 ['C',6] => 1860 ['D',6] => 930 ['E',6] => 995 ['A',7] => 842 ['B',7] => 8074 ['C',7] => 8074 ['D',7] => 4037 ['E',7] => 10734 ----------------------------------------------------------------------------- Created: Jul 23, 2024 at 18:20 by Hiranya Kishore Dey ----------------------------------------------------------------------------- Last Updated: Jul 23, 2024 at 18:20 by Hiranya Kishore Dey