***************************************************************************** * 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: St001158 ----------------------------------------------------------------------------- Collection: Finite Cartan types ----------------------------------------------------------------------------- Description: The size of the mutation class of quivers of given type. ----------------------------------------------------------------------------- References: [1] Musiker, G., Stump, C. A compendium on the cluster algebra and quiver package in \tt Sage [[MathSciNet:2862990]] ----------------------------------------------------------------------------- Code: def statistic(C): return QuiverMutationType(C.type(), C.rank()).class_size() ----------------------------------------------------------------------------- Statistic values: ['A',1] => 1 ['A',2] => 1 ['B',2] => 2 ['G',2] => 2 ['A',3] => 4 ['B',3] => 5 ['C',3] => 5 ['A',4] => 6 ['B',4] => 14 ['C',4] => 14 ['D',4] => 6 ['F',4] => 15 ['A',5] => 19 ['B',5] => 42 ['C',5] => 42 ['D',5] => 26 ['A',6] => 49 ['B',6] => 132 ['C',6] => 132 ['D',6] => 80 ['E',6] => 67 ['A',7] => 150 ['B',7] => 429 ['C',7] => 429 ['D',7] => 246 ['E',7] => 416 ['A',8] => 442 ['B',8] => 1430 ['C',8] => 1430 ['D',8] => 810 ['E',8] => 1574 ----------------------------------------------------------------------------- Created: Apr 20, 2018 at 22:08 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 20, 2018 at 22:08 by Martin Rubey