Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001385
Mapping
St001385: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 1
[3]
 => 2
[2,1]
 => 1
[1,1,1]
 => 1
[4]
 => 6
[3,1]
 => 2
[2,2]
 => 1
[2,1,1]
 => 1
[1,1,1,1]
 => 1
[5]
 => 6
[4,1]
 => 6
[3,2]
 => 2
[3,1,1]
 => 2
[2,2,1]
 => 1
[2,1,1,1]
 => 1
[1,1,1,1,1]
 => 1
[6]
 => 27
[5,1]
 => 6
[4,2]
 => 6
[4,1,1]
 => 6
[3,3]
 => 4
[3,2,1]
 => 2
[3,1,1,1]
 => 2
[2,2,2]
 => 1
[2,2,1,1]
 => 1
[2,1,1,1,1]
 => 1
[1,1,1,1,1,1]
 => 1
[7]
 => 20
[6,1]
 => 27
[5,2]
 => 6
[5,1,1]
 => 6
[4,3]
 => 12
[4,2,1]
 => 6
[4,1,1,1]
 => 6
[3,3,1]
 => 4
[3,2,2]
 => 2
[3,2,1,1]
 => 2
[3,1,1,1,1]
 => 2
[2,2,2,1]
 => 1
[2,2,1,1,1]
 => 1
[2,1,1,1,1,1]
 => 1
[1,1,1,1,1,1,1]
 => 1
[8]
 => 130
[7,1]
 => 20
[6,2]
 => 27
[6,1,1]
 => 27
[5,3]
 => 12
[5,2,1]
 => 6
Description
The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. Equivalently, given an integer partition $\lambda$, this is the number of molecular combinatorial species that decompose into a product of atomic species of sizes $\lambda_1,\lambda_2,\dots$. In particular, the value on the partition $(n)$ is the number of atomic species of degree $n$, [2].