***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew <info@findstat.org> * * * * 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: St001756 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The number of minimal subsets of reflections that generate the group. $~$ This counts the number of minimal subsets $S \subseteq R$ of reflections $R \subseteq W$ that generate the group $W$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 3 ['B',2] => 4 ['G',2] => 6 ['A',3] => 16 ['B',3] => 36 ['C',3] => 36 ['A',4] => 125 ['B',4] => 512 ['C',4] => 512 ['D',4] => 312 ['F',4] => 2160 ['A',5] => 1296 ['B',5] => 10000 ['C',5] => 10000 ['D',5] => 7552 ['A',6] => 16807 ['B',6] => 248832 ['C',6] => 248832 ['D',6] => 220800 ['E',6] => 798985 ['A',7] => 262144 ['B',7] => 7529536 ['C',7] => 7529536 ['D',7] => 7597824 ['E',7] => 196800768 ['A',8] => 4782969 ['C',2] => 4 ----------------------------------------------------------------------------- Created: Dec 13, 2021 at 14:04 by Dennis Jahn ----------------------------------------------------------------------------- Last Updated: Dec 13, 2021 at 14:04 by Dennis Jahn