Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001697
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
St001697: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => [[1]]
 => 0
{{1,2}}
 => [2,1] => [1,2] => [[1,2]]
 => 0
{{1},{2}}
 => [1,2] => [1,2] => [[1,2]]
 => 0
{{1,2,3}}
 => [2,3,1] => [1,2,3] => [[1,2,3]]
 => 0
{{1,2},{3}}
 => [2,1,3] => [1,2,3] => [[1,2,3]]
 => 0
{{1,3},{2}}
 => [3,2,1] => [1,3,2] => [[1,2],[3]]
 => 1
{{1},{2,3}}
 => [1,3,2] => [1,2,3] => [[1,2,3]]
 => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [[1,2,3]]
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,3,4] => [[1,2,3,4]]
 => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [1,2,3,4] => [[1,2,3,4]]
 => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [1,2,4,3] => [[1,2,3],[4]]
 => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [1,2,3,4] => [[1,2,3,4]]
 => 0
{{1,2},{3},{4}}
 => [2,1,3,4] => [1,2,3,4] => [[1,2,3,4]]
 => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [1,3,4,2] => [[1,2,4],[3]]
 => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [1,3,2,4] => [[1,2,4],[3]]
 => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [1,3,2,4] => [[1,2,4],[3]]
 => 2
{{1,4},{2,3}}
 => [4,3,2,1] => [1,4,2,3] => [[1,2,3],[4]]
 => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [1,2,3,4] => [[1,2,3,4]]
 => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,2,3,4] => [[1,2,3,4]]
 => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,4,2,3] => [[1,2,3],[4]]
 => 1
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,2,4,3] => [[1,2,3],[4]]
 => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,3,4] => [[1,2,3,4]]
 => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [[1,2,3,4]]
 => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,2,3,4,5] => [[1,2,3,4,5]]
 => 0
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
 => 0
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,2,3,5,4] => [[1,2,3,4],[5]]
 => 1
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [1,2,3,4,5] => [[1,2,3,4,5]]
 => 0
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
 => 0
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,2,4,5,3] => [[1,2,3,5],[4]]
 => 2
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [1,2,4,3,5] => [[1,2,3,5],[4]]
 => 2
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [1,2,4,3,5] => [[1,2,3,5],[4]]
 => 2
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [1,2,5,3,4] => [[1,2,3,4],[5]]
 => 1
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [1,2,3,4,5] => [[1,2,3,4,5]]
 => 0
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
 => 0
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [1,2,5,3,4] => [[1,2,3,4],[5]]
 => 1
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [1,2,3,5,4] => [[1,2,3,4],[5]]
 => 1
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [1,2,3,4,5] => [[1,2,3,4,5]]
 => 0
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
 => 0
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [1,3,4,5,2] => [[1,2,4,5],[3]]
 => 3
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [1,3,4,2,5] => [[1,2,4,5],[3]]
 => 3
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [1,3,4,2,5] => [[1,2,4,5],[3]]
 => 3
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [1,3,5,2,4] => [[1,2,4],[3,5]]
 => 4
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [1,3,2,4,5] => [[1,2,4,5],[3]]
 => 3
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [1,3,2,4,5] => [[1,2,4,5],[3]]
 => 3
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [1,3,5,2,4] => [[1,2,4],[3,5]]
 => 4
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [1,3,2,5,4] => [[1,2,4],[3,5]]
 => 4
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [1,3,2,4,5] => [[1,2,4,5],[3]]
 => 3
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [1,3,2,4,5] => [[1,2,4,5],[3]]
 => 3
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [1,4,5,2,3] => [[1,2,3],[4,5]]
 => 2
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [1,4,2,3,5] => [[1,2,3,5],[4]]
 => 2
Description
The shifted natural comajor index of a standard Young tableau. A natural descent of a standard tableau $T$ is an entry $i$ such that $i+1$ appears in a higher row than $i$ in English notation. The natural comajor index of a tableau of shape $\lambda$, size $n$ with natural descent set $D$ is then $b(\lambda)+\sum_{d\in D} n-d$, where $b(\lambda) = \sum_i (i-1)\lambda_i$.