***************************************************************************** * 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: St000707 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The product of the factorials of the parts. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(la): return prod(factorial(p) for p in la) ----------------------------------------------------------------------------- Statistic values: [2] => 2 [1,1] => 1 [3] => 6 [2,1] => 2 [1,1,1] => 1 [4] => 24 [3,1] => 6 [2,2] => 4 [2,1,1] => 2 [1,1,1,1] => 1 [5] => 120 [4,1] => 24 [3,2] => 12 [3,1,1] => 6 [2,2,1] => 4 [2,1,1,1] => 2 [1,1,1,1,1] => 1 [6] => 720 [5,1] => 120 [4,2] => 48 [4,1,1] => 24 [3,3] => 36 [3,2,1] => 12 [3,1,1,1] => 6 [2,2,2] => 8 [2,2,1,1] => 4 [2,1,1,1,1] => 2 [1,1,1,1,1,1] => 1 [7] => 5040 [6,1] => 720 [5,2] => 240 [5,1,1] => 120 [4,3] => 144 [4,2,1] => 48 [4,1,1,1] => 24 [3,3,1] => 36 [3,2,2] => 24 [3,2,1,1] => 12 [3,1,1,1,1] => 6 [2,2,2,1] => 8 [2,2,1,1,1] => 4 [2,1,1,1,1,1] => 2 [1,1,1,1,1,1,1] => 1 [8] => 40320 [7,1] => 5040 [6,2] => 1440 [6,1,1] => 720 [5,3] => 720 [5,2,1] => 240 [5,1,1,1] => 120 [4,4] => 576 [4,3,1] => 144 [4,2,2] => 96 [4,2,1,1] => 48 [4,1,1,1,1] => 24 [3,3,2] => 72 [3,3,1,1] => 36 [3,2,2,1] => 24 [3,2,1,1,1] => 12 [3,1,1,1,1,1] => 6 [2,2,2,2] => 16 [2,2,2,1,1] => 8 [2,2,1,1,1,1] => 4 [2,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1] => 1 [9] => 362880 [8,1] => 40320 [7,2] => 10080 [7,1,1] => 5040 [6,3] => 4320 [6,2,1] => 1440 [6,1,1,1] => 720 [5,4] => 2880 [5,3,1] => 720 [5,2,2] => 480 [5,2,1,1] => 240 [5,1,1,1,1] => 120 [4,4,1] => 576 [4,3,2] => 288 [4,3,1,1] => 144 [4,2,2,1] => 96 [4,2,1,1,1] => 48 [4,1,1,1,1,1] => 24 [3,3,3] => 216 [3,3,2,1] => 72 [3,3,1,1,1] => 36 [3,2,2,2] => 48 [3,2,2,1,1] => 24 [3,2,1,1,1,1] => 12 [3,1,1,1,1,1,1] => 6 [2,2,2,2,1] => 16 [2,2,2,1,1,1] => 8 [2,2,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1] => 1 [10] => 3628800 [9,1] => 362880 [8,2] => 80640 [8,1,1] => 40320 [7,3] => 30240 [7,2,1] => 10080 [7,1,1,1] => 5040 [6,4] => 17280 [6,3,1] => 4320 [6,2,2] => 2880 [6,2,1,1] => 1440 [6,1,1,1,1] => 720 [5,5] => 14400 [5,4,1] => 2880 [5,3,2] => 1440 [5,3,1,1] => 720 [5,2,2,1] => 480 [5,2,1,1,1] => 240 [5,1,1,1,1,1] => 120 [4,4,2] => 1152 [4,4,1,1] => 576 [4,3,3] => 864 [4,3,2,1] => 288 [4,3,1,1,1] => 144 [4,2,2,2] => 192 [4,2,2,1,1] => 96 [4,2,1,1,1,1] => 48 [4,1,1,1,1,1,1] => 24 [3,3,3,1] => 216 [3,3,2,2] => 144 [3,3,2,1,1] => 72 [3,3,1,1,1,1] => 36 [3,2,2,2,1] => 48 [3,2,2,1,1,1] => 24 [3,2,1,1,1,1,1] => 12 [3,1,1,1,1,1,1,1] => 6 [2,2,2,2,2] => 32 [2,2,2,2,1,1] => 16 [2,2,2,1,1,1,1] => 8 [2,2,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1] => 1 [11] => 39916800 [10,1] => 3628800 [9,2] => 725760 [9,1,1] => 362880 [8,3] => 241920 [8,2,1] => 80640 [8,1,1,1] => 40320 [7,4] => 120960 [7,3,1] => 30240 [7,2,2] => 20160 [7,2,1,1] => 10080 [7,1,1,1,1] => 5040 [6,5] => 86400 [6,4,1] => 17280 [6,3,2] => 8640 [6,3,1,1] => 4320 [6,2,2,1] => 2880 [6,2,1,1,1] => 1440 [6,1,1,1,1,1] => 720 [5,5,1] => 14400 [5,4,2] => 5760 [5,4,1,1] => 2880 [5,3,3] => 4320 [5,3,2,1] => 1440 [5,3,1,1,1] => 720 [5,2,2,2] => 960 [5,2,2,1,1] => 480 [5,2,1,1,1,1] => 240 [5,1,1,1,1,1,1] => 120 [4,4,3] => 3456 [4,4,2,1] => 1152 [4,4,1,1,1] => 576 [4,3,3,1] => 864 [4,3,2,2] => 576 [4,3,2,1,1] => 288 [4,3,1,1,1,1] => 144 [4,2,2,2,1] => 192 [4,2,2,1,1,1] => 96 [4,2,1,1,1,1,1] => 48 [4,1,1,1,1,1,1,1] => 24 [3,3,3,2] => 432 [3,3,3,1,1] => 216 [3,3,2,2,1] => 144 [3,3,2,1,1,1] => 72 [3,3,1,1,1,1,1] => 36 [3,2,2,2,2] => 96 [3,2,2,2,1,1] => 48 [3,2,2,1,1,1,1] => 24 [3,2,1,1,1,1,1,1] => 12 [3,1,1,1,1,1,1,1,1] => 6 [2,2,2,2,2,1] => 32 [2,2,2,2,1,1,1] => 16 [2,2,2,1,1,1,1,1] => 8 [2,2,1,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1] => 1 [12] => 479001600 [11,1] => 39916800 [10,2] => 7257600 [10,1,1] => 3628800 [9,3] => 2177280 [9,2,1] => 725760 [9,1,1,1] => 362880 [8,4] => 967680 [8,3,1] => 241920 [8,2,2] => 161280 [8,2,1,1] => 80640 [8,1,1,1,1] => 40320 [7,5] => 604800 [7,4,1] => 120960 [7,3,2] => 60480 [7,3,1,1] => 30240 [7,2,2,1] => 20160 [7,2,1,1,1] => 10080 [7,1,1,1,1,1] => 5040 [6,6] => 518400 [6,5,1] => 86400 [6,4,2] => 34560 [6,4,1,1] => 17280 [6,3,3] => 25920 [6,3,2,1] => 8640 [6,3,1,1,1] => 4320 [6,2,2,2] => 5760 [6,2,2,1,1] => 2880 [6,2,1,1,1,1] => 1440 [6,1,1,1,1,1,1] => 720 [5,5,2] => 28800 [5,5,1,1] => 14400 [5,4,3] => 17280 [5,4,2,1] => 5760 [5,4,1,1,1] => 2880 [5,3,3,1] => 4320 [5,3,2,2] => 2880 [5,3,2,1,1] => 1440 [5,3,1,1,1,1] => 720 [5,2,2,2,1] => 960 [5,2,2,1,1,1] => 480 [5,2,1,1,1,1,1] => 240 [5,1,1,1,1,1,1,1] => 120 [4,4,4] => 13824 [4,4,3,1] => 3456 [4,4,2,2] => 2304 [4,4,2,1,1] => 1152 [4,4,1,1,1,1] => 576 [4,3,3,2] => 1728 [4,3,3,1,1] => 864 [4,3,2,2,1] => 576 [4,3,2,1,1,1] => 288 [4,3,1,1,1,1,1] => 144 [4,2,2,2,2] => 384 [4,2,2,2,1,1] => 192 [4,2,2,1,1,1,1] => 96 [4,2,1,1,1,1,1,1] => 48 [4,1,1,1,1,1,1,1,1] => 24 [3,3,3,3] => 1296 [3,3,3,2,1] => 432 [3,3,3,1,1,1] => 216 [3,3,2,2,2] => 288 [3,3,2,2,1,1] => 144 [3,3,2,1,1,1,1] => 72 [3,3,1,1,1,1,1,1] => 36 [3,2,2,2,2,1] => 96 [3,2,2,2,1,1,1] => 48 [3,2,2,1,1,1,1,1] => 24 [3,2,1,1,1,1,1,1,1] => 12 [3,1,1,1,1,1,1,1,1,1] => 6 [2,2,2,2,2,2] => 64 [2,2,2,2,2,1,1] => 32 [2,2,2,2,1,1,1,1] => 16 [2,2,2,1,1,1,1,1,1] => 8 [2,2,1,1,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1] => 1 ----------------------------------------------------------------------------- Created: Mar 07, 2017 at 09:36 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 07, 2017 at 09:36 by Martin Rubey