Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001781
Mapping
St001781: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => 0
{{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}}
 => 0
{{1,2},{3,4}}
 => 0
{{1,2},{3},{4}}
 => 0
{{1,3,4},{2}}
 => 1
{{1,3},{2,4}}
 => 1
{{1,3},{2},{4}}
 => 1
{{1,4},{2,3}}
 => 0
{{1},{2,3,4}}
 => 0
{{1},{2,3},{4}}
 => 0
{{1,4},{2},{3}}
 => 2
{{1},{2,4},{3}}
 => 1
{{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}}
 => 0
{{1,2,3},{4,5}}
 => 0
{{1,2,3},{4},{5}}
 => 0
{{1,2,4,5},{3}}
 => 0
{{1,2,4},{3,5}}
 => 0
{{1,2,4},{3},{5}}
 => 0
{{1,2,5},{3,4}}
 => 1
{{1,2},{3,4,5}}
 => 0
{{1,2},{3,4},{5}}
 => 0
{{1,2,5},{3},{4}}
 => 0
{{1,2},{3,5},{4}}
 => 1
{{1,2},{3},{4,5}}
 => 0
{{1,2},{3},{4},{5}}
 => 0
{{1,3,4,5},{2}}
 => 1
{{1,3,4},{2,5}}
 => 1
{{1,3,4},{2},{5}}
 => 1
{{1,3,5},{2,4}}
 => 2
{{1,3},{2,4,5}}
 => 1
{{1,3},{2,4},{5}}
 => 1
{{1,3,5},{2},{4}}
 => 1
{{1,3},{2,5},{4}}
 => 2
{{1,3},{2},{4,5}}
 => 1
{{1,3},{2},{4},{5}}
 => 1
{{1,4,5},{2,3}}
 => 0
{{1,4},{2,3,5}}
 => 1
Description
The interlacing number of a set partition. Let $\pi$ be a set partition of $\{1,\dots,n\}$ with $k$ blocks. To each block of $\pi$ we add the element $\infty$, which is larger than $n$. Then, an interlacing of $\pi$ is a pair of blocks $B=(B_1 < \dots < B_b < B_{b+1} = \infty)$ and $C=(C_1 < \dots < C_c < C_{c+1} = \infty)$ together with an index $1\leq i\leq \min(b, c)$, such that $B_i < C_i < B_{i+1} < C_{i+1}$.