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Statistic identifier: St000933
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Collection: Integer partitions
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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 $\lambda^{(i)} \vdash \lambda_i$.
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References:
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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
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Last Updated: Aug 11, 2017 at 16:56 by Christian Stump