Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001604
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2,3,4]]
 => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
[[1,2,3,4,5]]
 => [1,2,3,4,5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0
[[1,3,4,5],[2]]
 => [2,1,3,4,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[[1,2,5],[3,4]]
 => [3,4,1,2,5] => [2,2,1]
 => [2,1]
 => 0
[[1,4,5],[2],[3]]
 => [3,2,1,4,5] => [2,1,1,1]
 => [1,1,1]
 => 0
[[1,3],[2,5],[4]]
 => [4,2,5,1,3] => [2,2,1]
 => [2,1]
 => 0
[[1,5],[2],[3],[4]]
 => [4,3,2,1,5] => [2,2,1]
 => [2,1]
 => 0
[[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => [2,2,1]
 => [2,1]
 => 0
[[1,2,3,4,5,6]]
 => [1,2,3,4,5,6] => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
[[1,3,4,5,6],[2]]
 => [2,1,3,4,5,6] => [2,1,1,1,1]
 => [1,1,1,1]
 => 0
[[1,2,4,5,6],[3]]
 => [3,1,2,4,5,6] => [3,1,1,1]
 => [1,1,1]
 => 0
[[1,2,5,6],[3,4]]
 => [3,4,1,2,5,6] => [2,2,1,1]
 => [2,1,1]
 => 0
[[1,2,4,6],[3,5]]
 => [3,5,1,2,4,6] => [3,2,1]
 => [2,1]
 => 0
[[1,2,3,4],[5,6]]
 => [5,6,1,2,3,4] => [3,3]
 => [3]
 => 1
[[1,4,5,6],[2],[3]]
 => [3,2,1,4,5,6] => [2,1,1,1,1]
 => [1,1,1,1]
 => 0
[[1,3,5,6],[2],[4]]
 => [4,2,1,3,5,6] => [3,1,1,1]
 => [1,1,1]
 => 0
[[1,2,3,6],[4],[5]]
 => [5,4,1,2,3,6] => [3,2,1]
 => [2,1]
 => 0
[[1,3,5],[2,4,6]]
 => [2,4,6,1,3,5] => [3,3]
 => [3]
 => 1
[[1,2,3],[4,5,6]]
 => [4,5,6,1,2,3] => [2,2,2]
 => [2,2]
 => 1
[[1,3,6],[2,5],[4]]
 => [4,2,5,1,3,6] => [2,2,1,1]
 => [2,1,1]
 => 0
[[1,2,6],[3,5],[4]]
 => [4,3,5,1,2,6] => [3,2,1]
 => [2,1]
 => 0
[[1,3,5],[2,6],[4]]
 => [4,2,6,1,3,5] => [3,2,1]
 => [2,1]
 => 0
[[1,3,4],[2,5],[6]]
 => [6,2,5,1,3,4] => [3,2,1]
 => [2,1]
 => 0
[[1,2,4],[3,5],[6]]
 => [6,3,5,1,2,4] => [3,3]
 => [3]
 => 1
[[1,5,6],[2],[3],[4]]
 => [4,3,2,1,5,6] => [2,2,1,1]
 => [2,1,1]
 => 0
[[1,4,6],[2],[3],[5]]
 => [5,3,2,1,4,6] => [3,2,1]
 => [2,1]
 => 0
[[1,3,4],[2],[5],[6]]
 => [6,5,2,1,3,4] => [3,3]
 => [3]
 => 1
[[1,2,4],[3],[5],[6]]
 => [6,5,3,1,2,4] => [3,2,1]
 => [2,1]
 => 0
[[1,3],[2,5],[4,6]]
 => [4,6,2,5,1,3] => [3,3]
 => [3]
 => 1
[[1,2],[3,5],[4,6]]
 => [4,6,3,5,1,2] => [3,2,1]
 => [2,1]
 => 0
[[1,3],[2,4],[5,6]]
 => [5,6,2,4,1,3] => [3,2,1]
 => [2,1]
 => 0
[[1,2],[3,4],[5,6]]
 => [5,6,3,4,1,2] => [2,2,1,1]
 => [2,1,1]
 => 0
[[1,4],[2,6],[3],[5]]
 => [5,3,2,6,1,4] => [2,2,2]
 => [2,2]
 => 1
[[1,2],[3,6],[4],[5]]
 => [5,4,3,6,1,2] => [3,2,1]
 => [2,1]
 => 0
[[1,6],[2],[3],[4],[5]]
 => [5,4,3,2,1,6] => [2,2,1,1]
 => [2,1,1]
 => 0
[[1,5],[2],[3],[4],[6]]
 => [6,4,3,2,1,5] => [3,2,1]
 => [2,1]
 => 0
[[1],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1] => [2,2,2]
 => [2,2]
 => 1
[[1,2,3,4,5,6,7]]
 => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 0
[[1,3,4,5,6,7],[2]]
 => [2,1,3,4,5,6,7] => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
[[1,2,4,5,6,7],[3]]
 => [3,1,2,4,5,6,7] => [3,1,1,1,1]
 => [1,1,1,1]
 => 0
[[1,2,3,5,6,7],[4]]
 => [4,1,2,3,5,6,7] => [4,1,1,1]
 => [1,1,1]
 => 0
[[1,3,5,6,7],[2,4]]
 => [2,4,1,3,5,6,7] => [4,1,1,1]
 => [1,1,1]
 => 0
[[1,2,5,6,7],[3,4]]
 => [3,4,1,2,5,6,7] => [2,2,1,1,1]
 => [2,1,1,1]
 => 0
[[1,2,4,6,7],[3,5]]
 => [3,5,1,2,4,6,7] => [3,2,1,1]
 => [2,1,1]
 => 0
[[1,2,4,5,7],[3,6]]
 => [3,6,1,2,4,5,7] => [4,2,1]
 => [2,1]
 => 0
[[1,2,3,4,7],[5,6]]
 => [5,6,1,2,3,4,7] => [3,3,1]
 => [3,1]
 => 0
[[1,2,3,4,6],[5,7]]
 => [5,7,1,2,3,4,6] => [4,3]
 => [3]
 => 1
[[1,4,5,6,7],[2],[3]]
 => [3,2,1,4,5,6,7] => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1
[[1,3,5,6,7],[2],[4]]
 => [4,2,1,3,5,6,7] => [3,1,1,1,1]
 => [1,1,1,1]
 => 0
[[1,2,5,6,7],[3],[4]]
 => [4,3,1,2,5,6,7] => [4,1,1,1]
 => [1,1,1]
 => 0
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.