***************************************************************************** * 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: St000088 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The row sums of the character table of the symmetric group. Equivalently, this is the multiplicity of the irreducible representation corresponding to the given partition in the adjoint representation of the symmetric group. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(L): G = SymmetricGroup(sum(L)) rho = SymmetricGroupRepresentation(L) chi = rho.to_character() return sum( chi(pi) for pi in G.conjugacy_classes_representatives() ) ----------------------------------------------------------------------------- Statistic values: [] => 1 [1] => 1 [2] => 2 [1,1] => 0 [3] => 3 [2,1] => 1 [1,1,1] => 1 [4] => 5 [3,1] => 2 [2,2] => 3 [2,1,1] => 2 [1,1,1,1] => 1 [5] => 7 [4,1] => 5 [3,2] => 6 [3,1,1] => 5 [2,2,1] => 4 [2,1,1,1] => 3 [1,1,1,1,1] => 1 [6] => 11 [5,1] => 8 [4,2] => 15 [4,1,1] => 10 [3,3] => 4 [3,2,1] => 13 [3,1,1,1] => 10 [2,2,2] => 8 [2,2,1,1] => 5 [2,1,1,1,1] => 4 [1,1,1,1,1,1] => 1 [7] => 15 [6,1] => 15 [5,2] => 26 [5,1,1] => 19 [4,3] => 18 [4,2,1] => 36 [4,1,1,1] => 21 [3,3,1] => 18 [3,2,2] => 22 [3,2,1,1] => 28 [3,1,1,1,1] => 13 [2,2,2,1] => 12 [2,2,1,1,1] => 10 [2,1,1,1,1,1] => 5 [1,1,1,1,1,1,1] => 1 [8] => 22 [7,1] => 23 [6,2] => 49 [6,1,1] => 33 [5,3] => 39 [5,2,1] => 78 [5,1,1,1] => 44 [4,4] => 25 [4,3,1] => 70 [4,2,2] => 67 [4,2,1,1] => 81 [4,1,1,1,1] => 34 [3,3,2] => 35 [3,3,1,1] => 53 [3,2,2,1] => 58 [3,2,1,1,1] => 52 [3,1,1,1,1,1] => 17 [2,2,2,2] => 19 [2,2,2,1,1] => 19 [2,2,1,1,1,1] => 17 [2,1,1,1,1,1,1] => 5 [1,1,1,1,1,1,1,1] => 2 [9] => 30 [8,1] => 37 [7,2] => 79 [7,1,1] => 57 [6,3] => 87 [6,2,1] => 154 [6,1,1,1] => 82 [5,4] => 64 [5,3,1] => 188 [5,2,2] => 152 [5,2,1,1] => 201 [5,1,1,1,1] => 75 [4,4,1] => 95 [4,3,2] => 168 [4,3,1,1] => 207 [4,2,2,1] => 203 [4,2,1,1,1] => 169 [4,1,1,1,1,1] => 52 [3,3,3] => 41 [3,3,2,1] => 144 [3,3,1,1,1] => 104 [3,2,2,2] => 81 [3,2,2,1,1] => 130 [3,2,1,1,1,1] => 84 [3,1,1,1,1,1,1] => 23 [2,2,2,2,1] => 34 [2,2,2,1,1,1] => 39 [2,2,1,1,1,1,1] => 21 [2,1,1,1,1,1,1,1] => 7 [1,1,1,1,1,1,1,1,1] => 2 ----------------------------------------------------------------------------- Created: Jun 13, 2013 at 12:58 by Chris Berg ----------------------------------------------------------------------------- Last Updated: Apr 17, 2019 at 12:30 by Martin Rubey