***************************************************************************** * 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: St000933 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of multipartitions of sizes given by an integer partition. This is, for $\lambda = (\lambda_1,\ldots,\lambda_n)$, this is the number of $n$-tuples $(\lambda^{(1)},\ldots,\lambda^{(n)})$ of partitions $\lambda^{(i)}$ such that $\lambda^{(i)} \vdash \lambda_i$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(L): return prod(Partitions(i).cardinality() for i in L) ----------------------------------------------------------------------------- Statistic values: [2] => 2 [1,1] => 1 [3] => 3 [2,1] => 2 [1,1,1] => 1 [4] => 5 [3,1] => 3 [2,2] => 4 [2,1,1] => 2 [1,1,1,1] => 1 [5] => 7 [4,1] => 5 [3,2] => 6 [3,1,1] => 3 [2,2,1] => 4 [2,1,1,1] => 2 [1,1,1,1,1] => 1 [6] => 11 [5,1] => 7 [4,2] => 10 [4,1,1] => 5 [3,3] => 9 [3,2,1] => 6 [3,1,1,1] => 3 [2,2,2] => 8 [2,2,1,1] => 4 [2,1,1,1,1] => 2 [1,1,1,1,1,1] => 1 [7] => 15 [6,1] => 11 [5,2] => 14 [5,1,1] => 7 [4,3] => 15 [4,2,1] => 10 [4,1,1,1] => 5 [3,3,1] => 9 [3,2,2] => 12 [3,2,1,1] => 6 [3,1,1,1,1] => 3 [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] => 22 [7,1] => 15 [6,2] => 22 [6,1,1] => 11 [5,3] => 21 [5,2,1] => 14 [5,1,1,1] => 7 [4,4] => 25 [4,3,1] => 15 [4,2,2] => 20 [4,2,1,1] => 10 [4,1,1,1,1] => 5 [3,3,2] => 18 [3,3,1,1] => 9 [3,2,2,1] => 12 [3,2,1,1,1] => 6 [3,1,1,1,1,1] => 3 [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] => 30 [8,1] => 22 [7,2] => 30 [7,1,1] => 15 [6,3] => 33 [6,2,1] => 22 [6,1,1,1] => 11 [5,4] => 35 [5,3,1] => 21 [5,2,2] => 28 [5,2,1,1] => 14 [5,1,1,1,1] => 7 [4,4,1] => 25 [4,3,2] => 30 [4,3,1,1] => 15 [4,2,2,1] => 20 [4,2,1,1,1] => 10 [4,1,1,1,1,1] => 5 [3,3,3] => 27 [3,3,2,1] => 18 [3,3,1,1,1] => 9 [3,2,2,2] => 24 [3,2,2,1,1] => 12 [3,2,1,1,1,1] => 6 [3,1,1,1,1,1,1] => 3 [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] => 42 [9,1] => 30 [8,2] => 44 [8,1,1] => 22 [7,3] => 45 [7,2,1] => 30 [7,1,1,1] => 15 [6,4] => 55 [6,3,1] => 33 [6,2,2] => 44 [6,2,1,1] => 22 [6,1,1,1,1] => 11 [5,5] => 49 [5,4,1] => 35 [5,3,2] => 42 [5,3,1,1] => 21 [5,2,2,1] => 28 [5,2,1,1,1] => 14 [5,1,1,1,1,1] => 7 [4,4,2] => 50 [4,4,1,1] => 25 [4,3,3] => 45 [4,3,2,1] => 30 [4,3,1,1,1] => 15 [4,2,2,2] => 40 [4,2,2,1,1] => 20 [4,2,1,1,1,1] => 10 [4,1,1,1,1,1,1] => 5 [3,3,3,1] => 27 [3,3,2,2] => 36 [3,3,2,1,1] => 18 [3,3,1,1,1,1] => 9 [3,2,2,2,1] => 24 [3,2,2,1,1,1] => 12 [3,2,1,1,1,1,1] => 6 [3,1,1,1,1,1,1,1] => 3 [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] => 56 [10,1] => 42 [9,2] => 60 [9,1,1] => 30 [8,3] => 66 [8,2,1] => 44 [8,1,1,1] => 22 [7,4] => 75 [7,3,1] => 45 [7,2,2] => 60 [7,2,1,1] => 30 [7,1,1,1,1] => 15 [6,5] => 77 [6,4,1] => 55 [6,3,2] => 66 [6,3,1,1] => 33 [6,2,2,1] => 44 [6,2,1,1,1] => 22 [6,1,1,1,1,1] => 11 [5,5,1] => 49 [5,4,2] => 70 [5,4,1,1] => 35 [5,3,3] => 63 [5,3,2,1] => 42 [5,3,1,1,1] => 21 [5,2,2,2] => 56 [5,2,2,1,1] => 28 [5,2,1,1,1,1] => 14 [5,1,1,1,1,1,1] => 7 [4,4,3] => 75 [4,4,2,1] => 50 [4,4,1,1,1] => 25 [4,3,3,1] => 45 [4,3,2,2] => 60 [4,3,2,1,1] => 30 [4,3,1,1,1,1] => 15 [4,2,2,2,1] => 40 [4,2,2,1,1,1] => 20 [4,2,1,1,1,1,1] => 10 [4,1,1,1,1,1,1,1] => 5 [3,3,3,2] => 54 [3,3,3,1,1] => 27 [3,3,2,2,1] => 36 [3,3,2,1,1,1] => 18 [3,3,1,1,1,1,1] => 9 [3,2,2,2,2] => 48 [3,2,2,2,1,1] => 24 [3,2,2,1,1,1,1] => 12 [3,2,1,1,1,1,1,1] => 6 [3,1,1,1,1,1,1,1,1] => 3 [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] => 77 [11,1] => 56 [10,2] => 84 [10,1,1] => 42 [9,3] => 90 [9,2,1] => 60 [9,1,1,1] => 30 [8,4] => 110 [8,3,1] => 66 [8,2,2] => 88 [8,2,1,1] => 44 [8,1,1,1,1] => 22 [7,5] => 105 [7,4,1] => 75 [7,3,2] => 90 [7,3,1,1] => 45 [7,2,2,1] => 60 [7,2,1,1,1] => 30 [7,1,1,1,1,1] => 15 [6,6] => 121 [6,5,1] => 77 [6,4,2] => 110 [6,4,1,1] => 55 [6,3,3] => 99 [6,3,2,1] => 66 [6,3,1,1,1] => 33 [6,2,2,2] => 88 [6,2,2,1,1] => 44 [6,2,1,1,1,1] => 22 [6,1,1,1,1,1,1] => 11 [5,5,2] => 98 [5,5,1,1] => 49 [5,4,3] => 105 [5,4,2,1] => 70 [5,4,1,1,1] => 35 [5,3,3,1] => 63 [5,3,2,2] => 84 [5,3,2,1,1] => 42 [5,3,1,1,1,1] => 21 [5,2,2,2,1] => 56 [5,2,2,1,1,1] => 28 [5,2,1,1,1,1,1] => 14 [5,1,1,1,1,1,1,1] => 7 [4,4,4] => 125 [4,4,3,1] => 75 [4,4,2,2] => 100 [4,4,2,1,1] => 50 [4,4,1,1,1,1] => 25 [4,3,3,2] => 90 [4,3,3,1,1] => 45 [4,3,2,2,1] => 60 [4,3,2,1,1,1] => 30 [4,3,1,1,1,1,1] => 15 [4,2,2,2,2] => 80 [4,2,2,2,1,1] => 40 [4,2,2,1,1,1,1] => 20 [4,2,1,1,1,1,1,1] => 10 [4,1,1,1,1,1,1,1,1] => 5 [3,3,3,3] => 81 [3,3,3,2,1] => 54 [3,3,3,1,1,1] => 27 [3,3,2,2,2] => 72 [3,3,2,2,1,1] => 36 [3,3,2,1,1,1,1] => 18 [3,3,1,1,1,1,1,1] => 9 [3,2,2,2,2,1] => 48 [3,2,2,2,1,1,1] => 24 [3,2,2,1,1,1,1,1] => 12 [3,2,1,1,1,1,1,1,1] => 6 [3,1,1,1,1,1,1,1,1,1] => 3 [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: Aug 11, 2017 at 16:56 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Aug 11, 2017 at 16:56 by Christian Stump