Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001614
(load all 2 compositions to match this statistic)
Mapping
St001614: Skew partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => 1
[[2],[]]
 => 2
[[1,1],[]]
 => 1
[[2,1],[1]]
 => 2
[[3],[]]
 => 3
[[2,1],[]]
 => 1
[[3,1],[1]]
 => 3
[[2,2],[1]]
 => 1
[[3,2],[2]]
 => 3
[[1,1,1],[]]
 => 3
[[2,2,1],[1,1]]
 => 3
[[2,1,1],[1]]
 => 3
[[3,2,1],[2,1]]
 => 3
[[4],[]]
 => 4
[[3,1],[]]
 => 1
[[4,1],[1]]
 => 4
[[2,2],[]]
 => 4
[[3,2],[1]]
 => 2
[[4,2],[2]]
 => 4
[[2,1,1],[]]
 => 1
[[3,2,1],[1,1]]
 => 4
[[3,1,1],[1]]
 => 1
[[4,2,1],[2,1]]
 => 4
[[3,3],[2]]
 => 1
[[4,3],[3]]
 => 4
[[2,2,1],[1]]
 => 4
[[3,3,1],[2,1]]
 => 4
[[3,2,1],[2]]
 => 4
[[4,3,1],[3,1]]
 => 4
[[2,2,2],[1,1]]
 => 1
[[3,3,2],[2,2]]
 => 1
[[3,2,2],[2,1]]
 => 4
[[4,3,2],[3,2]]
 => 4
[[1,1,1,1],[]]
 => 2
[[2,2,2,1],[1,1,1]]
 => 4
[[2,2,1,1],[1,1]]
 => 4
[[3,3,2,1],[2,2,1]]
 => 4
[[2,1,1,1],[1]]
 => 4
[[3,2,2,1],[2,1,1]]
 => 4
[[3,2,1,1],[2,1]]
 => 4
[[4,3,2,1],[3,2,1]]
 => 4
[[5],[]]
 => 5
[[4,1],[]]
 => 1
[[5,1],[1]]
 => 5
[[3,2],[]]
 => 5
[[4,2],[1]]
 => 1
[[5,2],[2]]
 => 5
[[3,1,1],[]]
 => 5
[[4,2,1],[1,1]]
 => 5
[[4,1,1],[1]]
 => 5
Description
The cyclic permutation representation number of a skew partition. This is the size of the largest cyclic group $C$ such that the fake degree is the character of a permutation representation of $C$. See [[St001527]] for the restriction of this statistic to integer partitions.