- FindStat

Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001612

St001612: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1]
 => 1
[2]
 => 2
[1,1]
 => 2
[3]
 => 3
[2,1]
 => 4
[1,1,1]
 => 6
[4]
 => 5
[3,1]
 => 7
[2,2]
 => 10
[2,1,1]
 => 14
[1,1,1,1]
 => 24
[5]
 => 7
[4,1]
 => 12
[3,2]
 => 18
[3,1,1]
 => 28
[2,2,1]
 => 38
[2,1,1,1]
 => 66
[1,1,1,1,1]
 => 120
[6]
 => 11
[5,1]
 => 19
[4,2]
 => 34
[4,1,1]
 => 52
[3,3]
 => 38
[3,2,1]
 => 84
[3,1,1,1]
 => 150
[2,2,2]
 => 120
[2,2,1,1]
 => 208
[2,1,1,1,1]
 => 384
[1,1,1,1,1,1]
 => 720
[7]
 => 15
[6,1]
 => 30
[5,2]
 => 56
[5,1,1]
 => 90
[4,3]
 => 74
[4,2,1]
 => 170
[4,1,1,1]
 => 306
[3,3,1]
 => 206
[3,2,2]
 => 290
[3,2,1,1]
 => 526
[3,1,1,1,1]
 => 984
[2,2,2,1]
 => 744
[2,2,1,1,1]
 => 1392
[2,1,1,1,1,1]
 => 2640
[1,1,1,1,1,1,1]
 => 5040
[8]
 => 22
[7,1]
 => 45
[6,2]
 => 94
[6,1,1]
 => 150
[5,3]
 => 133
[5,2,1]
 => 316

Description

The number of coloured multisets of cycles such that the multiplicities of colours are given by a partition. In particular, the value on the partition

$(n)$ is the number of partitions of

$n$ , whereas the value on the partition

$(1^n)$ is the number of permutations.