Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001804
Mapping
St001804: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => 1
[[1,2]]
 => 1
[[1],[2]]
 => 1
[[1,2,3]]
 => 1
[[1,3],[2]]
 => 2
[[1,2],[3]]
 => 1
[[1],[2],[3]]
 => 1
[[1,2,3,4]]
 => 1
[[1,3,4],[2]]
 => 2
[[1,2,4],[3]]
 => 2
[[1,2,3],[4]]
 => 1
[[1,3],[2,4]]
 => 2
[[1,2],[3,4]]
 => 1
[[1,4],[2],[3]]
 => 3
[[1,3],[2],[4]]
 => 2
[[1,2],[3],[4]]
 => 2
[[1],[2],[3],[4]]
 => 1
[[1,2,3,4,5]]
 => 1
[[1,3,4,5],[2]]
 => 2
[[1,2,4,5],[3]]
 => 2
[[1,2,3,5],[4]]
 => 2
[[1,2,3,4],[5]]
 => 1
[[1,3,5],[2,4]]
 => 2
[[1,2,5],[3,4]]
 => 2
[[1,3,4],[2,5]]
 => 2
[[1,2,4],[3,5]]
 => 2
[[1,2,3],[4,5]]
 => 1
[[1,4,5],[2],[3]]
 => 3
[[1,3,5],[2],[4]]
 => 3
[[1,2,5],[3],[4]]
 => 3
[[1,3,4],[2],[5]]
 => 2
[[1,2,4],[3],[5]]
 => 2
[[1,2,3],[4],[5]]
 => 2
[[1,4],[2,5],[3]]
 => 3
[[1,3],[2,5],[4]]
 => 2
[[1,2],[3,5],[4]]
 => 1
[[1,3],[2,4],[5]]
 => 2
[[1,2],[3,4],[5]]
 => 1
[[1,5],[2],[3],[4]]
 => 4
[[1,4],[2],[3],[5]]
 => 3
[[1,3],[2],[4],[5]]
 => 3
[[1,2],[3],[4],[5]]
 => 3
[[1],[2],[3],[4],[5]]
 => 1
[[1,2,3,4,5,6]]
 => 1
[[1,3,4,5,6],[2]]
 => 2
[[1,2,4,5,6],[3]]
 => 2
[[1,2,3,5,6],[4]]
 => 2
[[1,2,3,4,6],[5]]
 => 2
[[1,2,3,4,5],[6]]
 => 1
[[1,3,5,6],[2,4]]
 => 2
Description
The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. A cylindrical tableau associated with a standard Young tableau $T$ is the skew row-strict tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle. This statistic equals $\max_C\big(\ell(C) - \ell(T)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux.