***************************************************************************** * 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: St001628 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(mu): s = SymmetricFunctions(QQ).s() F = (species.SimpleGraphSpecies().cycle_index_series()-1).logarithm() return F.coefficient(mu.size()).scalar(s(mu)) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 0 [3] => 2 [2,1] => 1 [1,1,1] => 0 [4] => 6 [3,1] => 5 [2,2] => 5 [2,1,1] => 2 [1,1,1,1] => 1 [5] => 21 [4,1] => 37 [3,2] => 40 [3,1,1] => 27 [2,2,1] => 28 [2,1,1,1] => 13 [1,1,1,1,1] => 5 [6] => 112 [5,1] => 295 [4,2] => 472 [4,1,1] => 375 [3,3] => 208 [3,2,1] => 583 [3,1,1,1] => 292 [2,2,2] => 198 [2,2,1,1] => 242 [2,1,1,1,1] => 128 [1,1,1,1,1,1] => 23 ----------------------------------------------------------------------------- Created: Oct 01, 2020 at 22:40 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Oct 01, 2020 at 22:40 by Martin Rubey