***************************************************************************** * 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: St000706 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The product of the factorials of the multiplicities of an integer partition. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(la): return prod(factorial(p) for p in la.to_exp()) ----------------------------------------------------------------------------- Statistic values: [2] => 1 [1,1] => 2 [3] => 1 [2,1] => 1 [1,1,1] => 6 [4] => 1 [3,1] => 1 [2,2] => 2 [2,1,1] => 2 [1,1,1,1] => 24 [5] => 1 [4,1] => 1 [3,2] => 1 [3,1,1] => 2 [2,2,1] => 2 [2,1,1,1] => 6 [1,1,1,1,1] => 120 [6] => 1 [5,1] => 1 [4,2] => 1 [4,1,1] => 2 [3,3] => 2 [3,2,1] => 1 [3,1,1,1] => 6 [2,2,2] => 6 [2,2,1,1] => 4 [2,1,1,1,1] => 24 [1,1,1,1,1,1] => 720 [7] => 1 [6,1] => 1 [5,2] => 1 [5,1,1] => 2 [4,3] => 1 [4,2,1] => 1 [4,1,1,1] => 6 [3,3,1] => 2 [3,2,2] => 2 [3,2,1,1] => 2 [3,1,1,1,1] => 24 [2,2,2,1] => 6 [2,2,1,1,1] => 12 [2,1,1,1,1,1] => 120 [1,1,1,1,1,1,1] => 5040 [8] => 1 [7,1] => 1 [6,2] => 1 [6,1,1] => 2 [5,3] => 1 [5,2,1] => 1 [5,1,1,1] => 6 [4,4] => 2 [4,3,1] => 1 [4,2,2] => 2 [4,2,1,1] => 2 [4,1,1,1,1] => 24 [3,3,2] => 2 [3,3,1,1] => 4 [3,2,2,1] => 2 [3,2,1,1,1] => 6 [3,1,1,1,1,1] => 120 [2,2,2,2] => 24 [2,2,2,1,1] => 12 [2,2,1,1,1,1] => 48 [2,1,1,1,1,1,1] => 720 [1,1,1,1,1,1,1,1] => 40320 [9] => 1 [8,1] => 1 [7,2] => 1 [7,1,1] => 2 [6,3] => 1 [6,2,1] => 1 [6,1,1,1] => 6 [5,4] => 1 [5,3,1] => 1 [5,2,2] => 2 [5,2,1,1] => 2 [5,1,1,1,1] => 24 [4,4,1] => 2 [4,3,2] => 1 [4,3,1,1] => 2 [4,2,2,1] => 2 [4,2,1,1,1] => 6 [4,1,1,1,1,1] => 120 [3,3,3] => 6 [3,3,2,1] => 2 [3,3,1,1,1] => 12 [3,2,2,2] => 6 [3,2,2,1,1] => 4 [3,2,1,1,1,1] => 24 [3,1,1,1,1,1,1] => 720 [2,2,2,2,1] => 24 [2,2,2,1,1,1] => 36 [2,2,1,1,1,1,1] => 240 [2,1,1,1,1,1,1,1] => 5040 [1,1,1,1,1,1,1,1,1] => 362880 [10] => 1 [9,1] => 1 [8,2] => 1 [8,1,1] => 2 [7,3] => 1 [7,2,1] => 1 [7,1,1,1] => 6 [6,4] => 1 [6,3,1] => 1 [6,2,2] => 2 [6,2,1,1] => 2 [6,1,1,1,1] => 24 [5,5] => 2 [5,4,1] => 1 [5,3,2] => 1 [5,3,1,1] => 2 [5,2,2,1] => 2 [5,2,1,1,1] => 6 [5,1,1,1,1,1] => 120 [4,4,2] => 2 [4,4,1,1] => 4 [4,3,3] => 2 [4,3,2,1] => 1 [4,3,1,1,1] => 6 [4,2,2,2] => 6 [4,2,2,1,1] => 4 [4,2,1,1,1,1] => 24 [4,1,1,1,1,1,1] => 720 [3,3,3,1] => 6 [3,3,2,2] => 4 [3,3,2,1,1] => 4 [3,3,1,1,1,1] => 48 [3,2,2,2,1] => 6 [3,2,2,1,1,1] => 12 [3,2,1,1,1,1,1] => 120 [3,1,1,1,1,1,1,1] => 5040 [2,2,2,2,2] => 120 [2,2,2,2,1,1] => 48 [2,2,2,1,1,1,1] => 144 [2,2,1,1,1,1,1,1] => 1440 [2,1,1,1,1,1,1,1,1] => 40320 [1,1,1,1,1,1,1,1,1,1] => 3628800 [11] => 1 [10,1] => 1 [9,2] => 1 [9,1,1] => 2 [8,3] => 1 [8,2,1] => 1 [8,1,1,1] => 6 [7,4] => 1 [7,3,1] => 1 [7,2,2] => 2 [7,2,1,1] => 2 [7,1,1,1,1] => 24 [6,5] => 1 [6,4,1] => 1 [6,3,2] => 1 [6,3,1,1] => 2 [6,2,2,1] => 2 [6,2,1,1,1] => 6 [6,1,1,1,1,1] => 120 [5,5,1] => 2 [5,4,2] => 1 [5,4,1,1] => 2 [5,3,3] => 2 [5,3,2,1] => 1 [5,3,1,1,1] => 6 [5,2,2,2] => 6 [5,2,2,1,1] => 4 [5,2,1,1,1,1] => 24 [5,1,1,1,1,1,1] => 720 [4,4,3] => 2 [4,4,2,1] => 2 [4,4,1,1,1] => 12 [4,3,3,1] => 2 [4,3,2,2] => 2 [4,3,2,1,1] => 2 [4,3,1,1,1,1] => 24 [4,2,2,2,1] => 6 [4,2,2,1,1,1] => 12 [4,2,1,1,1,1,1] => 120 [4,1,1,1,1,1,1,1] => 5040 [3,3,3,2] => 6 [3,3,3,1,1] => 12 [3,3,2,2,1] => 4 [3,3,2,1,1,1] => 12 [3,3,1,1,1,1,1] => 240 [3,2,2,2,2] => 24 [3,2,2,2,1,1] => 12 [3,2,2,1,1,1,1] => 48 [3,2,1,1,1,1,1,1] => 720 [3,1,1,1,1,1,1,1,1] => 40320 [2,2,2,2,2,1] => 120 [2,2,2,2,1,1,1] => 144 [2,2,2,1,1,1,1,1] => 720 [2,2,1,1,1,1,1,1,1] => 10080 [2,1,1,1,1,1,1,1,1,1] => 362880 [1,1,1,1,1,1,1,1,1,1,1] => 39916800 [12] => 1 [11,1] => 1 [10,2] => 1 [10,1,1] => 2 [9,3] => 1 [9,2,1] => 1 [9,1,1,1] => 6 [8,4] => 1 [8,3,1] => 1 [8,2,2] => 2 [8,2,1,1] => 2 [8,1,1,1,1] => 24 [7,5] => 1 [7,4,1] => 1 [7,3,2] => 1 [7,3,1,1] => 2 [7,2,2,1] => 2 [7,2,1,1,1] => 6 [7,1,1,1,1,1] => 120 [6,6] => 2 [6,5,1] => 1 [6,4,2] => 1 [6,4,1,1] => 2 [6,3,3] => 2 [6,3,2,1] => 1 [6,3,1,1,1] => 6 [6,2,2,2] => 6 [6,2,2,1,1] => 4 [6,2,1,1,1,1] => 24 [6,1,1,1,1,1,1] => 720 [5,5,2] => 2 [5,5,1,1] => 4 [5,4,3] => 1 [5,4,2,1] => 1 [5,4,1,1,1] => 6 [5,3,3,1] => 2 [5,3,2,2] => 2 [5,3,2,1,1] => 2 [5,3,1,1,1,1] => 24 [5,2,2,2,1] => 6 [5,2,2,1,1,1] => 12 [5,2,1,1,1,1,1] => 120 [5,1,1,1,1,1,1,1] => 5040 [4,4,4] => 6 [4,4,3,1] => 2 [4,4,2,2] => 4 [4,4,2,1,1] => 4 [4,4,1,1,1,1] => 48 [4,3,3,2] => 2 [4,3,3,1,1] => 4 [4,3,2,2,1] => 2 [4,3,2,1,1,1] => 6 [4,3,1,1,1,1,1] => 120 [4,2,2,2,2] => 24 [4,2,2,2,1,1] => 12 [4,2,2,1,1,1,1] => 48 [4,2,1,1,1,1,1,1] => 720 [4,1,1,1,1,1,1,1,1] => 40320 [3,3,3,3] => 24 [3,3,3,2,1] => 6 [3,3,3,1,1,1] => 36 [3,3,2,2,2] => 12 [3,3,2,2,1,1] => 8 [3,3,2,1,1,1,1] => 48 [3,3,1,1,1,1,1,1] => 1440 [3,2,2,2,2,1] => 24 [3,2,2,2,1,1,1] => 36 [3,2,2,1,1,1,1,1] => 240 [3,2,1,1,1,1,1,1,1] => 5040 [3,1,1,1,1,1,1,1,1,1] => 362880 [2,2,2,2,2,2] => 720 [2,2,2,2,2,1,1] => 240 [2,2,2,2,1,1,1,1] => 576 [2,2,2,1,1,1,1,1,1] => 4320 [2,2,1,1,1,1,1,1,1,1] => 80640 [2,1,1,1,1,1,1,1,1,1,1] => 3628800 [1,1,1,1,1,1,1,1,1,1,1,1] => 479001600 ----------------------------------------------------------------------------- Created: Mar 07, 2017 at 09:36 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 07, 2017 at 09:36 by Martin Rubey