Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001641
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Mapping
St001641: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => 0
{{1,2}}
 => 1
{{1},{2}}
 => 1
{{1,2,3}}
 => 2
{{1,2},{3}}
 => 2
{{1,3},{2}}
 => 0
{{1},{2,3}}
 => 2
{{1},{2},{3}}
 => 2
{{1,2,3,4}}
 => 3
{{1,2,3},{4}}
 => 3
{{1,2,4},{3}}
 => 1
{{1,2},{3,4}}
 => 3
{{1,2},{3},{4}}
 => 3
{{1,3,4},{2}}
 => 0
{{1,3},{2,4}}
 => 1
{{1,3},{2},{4}}
 => 1
{{1,4},{2,3}}
 => 1
{{1},{2,3,4}}
 => 3
{{1},{2,3},{4}}
 => 3
{{1,4},{2},{3}}
 => 1
{{1},{2,4},{3}}
 => 1
{{1},{2},{3,4}}
 => 3
{{1},{2},{3},{4}}
 => 3
{{1,2,3,4,5}}
 => 4
{{1,2,3,4},{5}}
 => 4
{{1,2,3,5},{4}}
 => 2
{{1,2,3},{4,5}}
 => 4
{{1,2,3},{4},{5}}
 => 4
{{1,2,4,5},{3}}
 => 1
{{1,2,4},{3,5}}
 => 2
{{1,2,4},{3},{5}}
 => 2
{{1,2,5},{3,4}}
 => 2
{{1,2},{3,4,5}}
 => 4
{{1,2},{3,4},{5}}
 => 4
{{1,2,5},{3},{4}}
 => 2
{{1,2},{3,5},{4}}
 => 2
{{1,2},{3},{4,5}}
 => 4
{{1,2},{3},{4},{5}}
 => 4
{{1,3,4,5},{2}}
 => 0
{{1,3,4},{2,5}}
 => 1
{{1,3,4},{2},{5}}
 => 1
{{1,3,5},{2,4}}
 => 1
{{1,3},{2,4,5}}
 => 2
{{1,3},{2,4},{5}}
 => 2
{{1,3,5},{2},{4}}
 => 1
{{1,3},{2,5},{4}}
 => 0
{{1,3},{2},{4,5}}
 => 2
{{1,3},{2},{4},{5}}
 => 2
{{1,4,5},{2,3}}
 => 1
{{1,4},{2,3,5}}
 => 2
Description
The number of ascent tops in the flattened set partition such that all smaller elements appear before. Let $P$ be a set partition. The flattened set partition is the permutation obtained by sorting the set of blocks of $P$ according to their minimal element and the elements in each block in increasing order. Given a set partition $P$, this statistic is the binary logarithm of the number of set partitions that flatten to the same permutation as $P$.
Matching statistic: St001640
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001640: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => 0
{{1,2}}
 => [2,1] => [1,2] => 1
{{1},{2}}
 => [1,2] => [1,2] => 1
{{1,2,3}}
 => [2,3,1] => [1,2,3] => 2
{{1,2},{3}}
 => [2,1,3] => [1,2,3] => 2
{{1,3},{2}}
 => [3,2,1] => [1,3,2] => 0
{{1},{2,3}}
 => [1,3,2] => [1,2,3] => 2
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 2
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,3,4] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [1,2,3,4] => 3
{{1,2,4},{3}}
 => [2,4,3,1] => [1,2,4,3] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [1,2,3,4] => 3
{{1,2},{3},{4}}
 => [2,1,3,4] => [1,2,3,4] => 3
{{1,3,4},{2}}
 => [3,2,4,1] => [1,3,4,2] => 0
{{1,3},{2,4}}
 => [3,4,1,2] => [1,3,2,4] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [1,3,2,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [1,4,2,3] => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [1,2,3,4] => 3
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,2,3,4] => 3
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,4,2,3] => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,2,4,3] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,3,4] => 3
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 3
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,2,3,4,5] => 4
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [1,2,3,4,5] => 4
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,2,3,5,4] => 2
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [1,2,3,4,5] => 4
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [1,2,3,4,5] => 4
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,2,4,5,3] => 1
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [1,2,4,3,5] => 2
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [1,2,4,3,5] => 2
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [1,2,5,3,4] => 2
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [1,2,3,4,5] => 4
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [1,2,3,4,5] => 4
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [1,2,5,3,4] => 2
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [1,2,3,5,4] => 2
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [1,2,3,4,5] => 4
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [1,2,3,4,5] => 4
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [1,3,4,5,2] => 0
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [1,3,4,2,5] => 1
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [1,3,4,2,5] => 1
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [1,3,5,2,4] => 1
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [1,3,2,4,5] => 2
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [1,3,2,4,5] => 2
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [1,3,5,2,4] => 1
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [1,3,2,5,4] => 0
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [1,3,2,4,5] => 2
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [1,3,2,4,5] => 2
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [1,4,5,2,3] => 1
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [1,4,2,3,5] => 2
Description
The number of ascent tops in the permutation such that all smaller elements appear before.