Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000565
Mapping
St000565: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => 0
{{1},{2}}
 => 0
{{1,2,3}}
 => 0
{{1,2},{3}}
 => 0
{{1,3},{2}}
 => 1
{{1},{2,3}}
 => 0
{{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => 0
{{1,2,3},{4}}
 => 0
{{1,2,4},{3}}
 => 1
{{1,2},{3,4}}
 => 0
{{1,2},{3},{4}}
 => 0
{{1,3,4},{2}}
 => 2
{{1,3},{2,4}}
 => 1
{{1,3},{2},{4}}
 => 1
{{1,4},{2,3}}
 => 1
{{1},{2,3,4}}
 => 0
{{1},{2,3},{4}}
 => 0
{{1,4},{2},{3}}
 => 1
{{1},{2,4},{3}}
 => 2
{{1},{2},{3,4}}
 => 0
{{1},{2},{3},{4}}
 => 0
{{1,2,3,4,5}}
 => 0
{{1,2,3,4},{5}}
 => 0
{{1,2,3,5},{4}}
 => 1
{{1,2,3},{4,5}}
 => 0
{{1,2,3},{4},{5}}
 => 0
{{1,2,4,5},{3}}
 => 2
{{1,2,4},{3,5}}
 => 1
{{1,2,4},{3},{5}}
 => 1
{{1,2,5},{3,4}}
 => 1
{{1,2},{3,4,5}}
 => 0
{{1,2},{3,4},{5}}
 => 0
{{1,2,5},{3},{4}}
 => 1
{{1,2},{3,5},{4}}
 => 2
{{1,2},{3},{4,5}}
 => 0
{{1,2},{3},{4},{5}}
 => 0
{{1,3,4,5},{2}}
 => 3
{{1,3,4},{2,5}}
 => 2
{{1,3,4},{2},{5}}
 => 2
{{1,3,5},{2,4}}
 => 2
{{1,3},{2,4,5}}
 => 1
{{1,3},{2,4},{5}}
 => 1
{{1,3,5},{2},{4}}
 => 2
{{1,3},{2,5},{4}}
 => 3
{{1,3},{2},{4,5}}
 => 1
{{1,3},{2},{4},{5}}
 => 1
{{1,4,5},{2,3}}
 => 2
{{1,4},{2,3,5}}
 => 1
{{1,4},{2,3},{5}}
 => 1
Description
The major index of a set partition. Let $\pi=B_1/B_2/\dots/B_k$ with $\min B_1<\min B_2<\dots<\min B_k$ a set partition. Let $d_i$ be the number of elements in $B_i$ larger than $\min B_{i+1}$. Then the major index of $\pi$ is $1d_1+2d_2+\dots+(k-1)d_{k-1}$.