***************************************************************************** * 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: St000944 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The 3-degree of an integer partition. For an integer partition $\lambda$, this is given by the exponent of 3 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$. This stupid comment should not be accepted as an edit! ----------------------------------------------------------------------------- References: [1] [[noreference given]] ----------------------------------------------------------------------------- Code: def statistic(L): return L.prime_degree(12) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [2] => 0 [1,1] => 0 [3] => 1 [2,1] => 1 [1,1,1] => 0 [4] => 1 [3,1] => 0 [2,2] => 1 [2,1,1] => 0 [1,1,1,1] => 0 [5] => 1 [4,1] => 4 [3,2] => 1 [3,1,1] => 0 [2,2,1] => 4 [2,1,1,1] => 0 [1,1,1,1,1] => 0 [6] => 2 [5,1] => 9 [4,2] => 0 [4,1,1] => 16 [3,3] => 6 [3,2,1] => 16 [3,1,1,1] => 4 [2,2,2] => 4 [2,2,1,1] => 0 [2,1,1,1,1] => 1 [1,1,1,1,1,1] => 0 [7] => 2 [6,1] => 6 [5,2] => 27 [5,1,1] => 15 [4,3] => 15 [4,2,1] => 42 [4,1,1,1] => 20 [3,3,1] => 6 [3,2,2] => 15 [3,2,1,1] => 28 [3,1,1,1,1] => 0 [2,2,2,1] => 13 [2,2,1,1,1] => 1 [2,1,1,1,1,1] => 0 [1,1,1,1,1,1,1] => 0 [8] => 2 [7,1] => 14 [6,2] => 33 [6,1,1] => 21 [5,3] => 56 [5,2,1] => 99 [5,1,1,1] => 35 [4,4] => 15 [4,3,1] => 49 [4,2,2] => 78 [4,2,1,1] => 0 [4,1,1,1,1] => 35 [3,3,2] => 21 [3,3,1,1] => 34 [3,2,2,1] => 91 [3,2,1,1,1] => 29 [3,1,1,1,1,1] => 0 [2,2,2,2] => 13 [2,2,2,1,1] => 0 [2,2,1,1,1,1] => 7 [2,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1] => 0 [9] => 3 [8,1] => 23 [7,2] => 27 [7,1,1] => 77 [6,3] => 137 [6,2,1] => 238 [6,1,1,1] => 91 [5,4] => 85 [5,3,1] => 0 [5,2,2] => 233 [5,2,1,1] => 189 [5,1,1,1,1] => 105 [4,4,1] => 134 [4,3,2] => 232 [4,3,1,1] => 27 [4,2,2,1] => 189 [4,2,1,1,1] => 0 [4,1,1,1,1,1] => 77 [3,3,3] => 63 [3,3,2,1] => 272 [3,3,1,1,1] => 127 [3,2,2,2] => 118 [3,2,2,1,1] => 0 [3,2,1,1,1,1] => 77 [3,1,1,1,1,1,1] => 7 [2,2,2,2,1] => 41 [2,2,2,1,1,1] => 7 [2,2,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1] => 0 [10] => 4 [9,1] => 18 [8,2] => 138 [8,1,1] => 72 [7,3] => 191 [7,2,1] => 496 [7,1,1,1] => 168 [6,4] => 180 [6,3,1] => 594 [6,2,2] => 351 [6,2,1,1] => 1064 [6,1,1,1,1] => 126 [5,5] => 85 [5,4,1] => 297 [5,3,2] => 297 [5,3,1,1] => 0 [5,2,2,1] => 1232 [5,2,1,1,1] => 896 [5,1,1,1,1,1] => 126 [4,4,2] => 198 [4,4,1,1] => 593 [4,3,3] => 463 [4,3,2,1] => 1152 [4,3,1,1,1] => 343 [4,2,2,2] => 307 [4,2,2,1,1] => 0 [4,2,1,1,1,1] => 336 [4,1,1,1,1,1,1] => 84 [3,3,3,1] => 167 [3,3,2,2] => 306 [3,3,2,1,1] => 603 [3,3,1,1,1,1] => 99 [3,2,2,2,1] => 279 [3,2,2,1,1,1] => 36 [3,2,1,1,1,1,1] => 144 [3,1,1,1,1,1,1,1] => 0 [2,2,2,2,2] => 41 [2,2,2,2,1,1] => 0 [2,2,2,1,1,1,1] => 34 [2,2,1,1,1,1,1,1] => 2 [2,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1] => 0 ----------------------------------------------------------------------------- Created: Aug 22, 2017 at 01:24 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Aug 22, 2017 at 10:43 by Christian Stump