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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 λ, this is the number of molecular combinatorial species that decompose into a product of atomic species of sizes λ1,λ2,…. In particular, the value on the partition (n) is the number of atomic species of degree n, [2].