Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001527
Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St001527: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0]
 => [[2,2],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => [1]
 => 1
[1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => [1,1]
 => 1
[1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => [1]
 => 1
[1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => [2]
 => 2
[1,1,0,1,1,0,0,0]
 => [[3,3],[1]]
 => [1]
 => 1
[1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => [1,1]
 => 1
[1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1],[2]]
 => [2]
 => 2
[1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1],[1]]
 => [1]
 => 1
[1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => [1]
 => 1
[1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 3
[1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => [1,1]
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => 1
[1,1,0,0,1,1,0,1,0,0]
 => [[4,2],[1]]
 => [1]
 => 1
[1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 1
[1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => [2,2]
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => [2]
 => 2
[1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => [3]
 => 3
[1,1,0,1,0,1,1,0,0,0]
 => [[4,4],[2]]
 => [2]
 => 2
[1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => [2,1]
 => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[4,3],[1]]
 => [1]
 => 1
[1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3],[1,1]]
 => [1,1]
 => 1
[1,1,0,1,1,1,0,0,0,0]
 => [[4,4],[1]]
 => [1]
 => 1
[1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => [1,1]
 => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => [2]
 => 2
[1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2],[1]]
 => [1]
 => 1
[1,1,1,0,1,0,0,0,1,0]
 => [[2,2,2,2],[1]]
 => [1]
 => 1
[1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [[3,3,3],[1]]
 => [1]
 => 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1,1],[2]]
 => [2]
 => 2
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => [1,1]
 => 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => [2,1]
 => 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => [1,1]
 => 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1],[2,2]]
 => [2,2]
 => 4
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => [2]
 => 2
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [[4,4,1],[3]]
 => [3]
 => 3
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [[4,4,1],[2]]
 => [2]
 => 2
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => [2,1]
 => 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => [1]
 => 1
Description
The cyclic permutation representation number of an integer partition. This is the size of the largest cyclic group $C$ such that the fake degree is the character of a permutation representation of $C$.
Matching statistic: St001614
Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001614: Skew partitions ⟶ ℤResult quality: 47% ●values known / values provided: 86%●distinct values known / distinct values provided: 47%
Values
[1,1,0,0,1,0]
 => [[2,2],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => [2]
 => [[2],[]]
 => 2
[1,1,0,1,1,0,0,0]
 => [[3,3],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1],[2]]
 => [2]
 => [[2],[]]
 => 2
[1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => [[1,1,1],[]]
 => 3
[1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => [[2,1],[]]
 => 1
[1,1,0,0,1,1,0,1,0,0]
 => [[4,2],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => [2,2]
 => [[2,2],[]]
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => [2]
 => [[2],[]]
 => 2
[1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => [3]
 => [[3],[]]
 => 3
[1,1,0,1,0,1,1,0,0,0]
 => [[4,4],[2]]
 => [2]
 => [[2],[]]
 => 2
[1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => [2,1]
 => [[2,1],[]]
 => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[4,3],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3],[1,1]]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,1,0,1,1,1,0,0,0,0]
 => [[4,4],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => [2]
 => [[2],[]]
 => 2
[1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,1,0,1,0,0,0,1,0]
 => [[2,2,2,2],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => [[2],[]]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [[3,3,3],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1,1],[2]]
 => [2]
 => [[2],[]]
 => 2
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => [[1,1,1],[]]
 => 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => [2,1]
 => [[2,1],[]]
 => 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => [1,1]
 => [[1,1],[]]
 => 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1],[2,2]]
 => [2,2]
 => [[2,2],[]]
 => 4
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => [2]
 => [[2],[]]
 => 2
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [[4,4,1],[3]]
 => [3]
 => [[3],[]]
 => 3
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [[4,4,1],[2]]
 => [2]
 => [[2],[]]
 => 2
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => [2,1]
 => [[2,1],[]]
 => 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => [1]
 => [[1],[]]
 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => [[3,3,3,3,3],[2,2,2,2]]
 => [2,2,2,2]
 => [[2,2,2,2],[]]
 => ? = 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
 => [[4,4,4,3],[3,3,2]]
 => [3,3,2]
 => [[3,3,2],[]]
 => ? = 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => [[4,4,4,4],[3,3,3]]
 => [3,3,3]
 => [[3,3,3],[]]
 => ? = 9
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [[5,5,5],[4,4]]
 => [4,4]
 => [[4,4],[]]
 => ? = 8
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
 => [[4,4,4,4],[3,3,2]]
 => [3,3,2]
 => [[3,3,2],[]]
 => ? = 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
 => [[4,4,4,3,1],[3,3,2]]
 => [3,3,2]
 => [[3,3,2],[]]
 => ? = 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => [[4,4,4,4,1],[3,3,3]]
 => [3,3,3]
 => [[3,3,3],[]]
 => ? = 9
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[3,3,3,3,2,2],[2,2,2,1,1]]
 => [2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[4,4,4,2,2],[3,3,1,1]]
 => [3,3,1,1]
 => [[3,3,1,1],[]]
 => ? = 8
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [[3,3,3,3,3,2],[2,2,2,2,1]]
 => [2,2,2,2,1]
 => [[2,2,2,2,1],[]]
 => ? = 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[4,4,3,3,2],[3,2,2,1]]
 => [3,2,2,1]
 => [[3,2,2,1],[]]
 => ? = 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[4,4,4,3,2],[3,3,2,1]]
 => [3,3,2,1]
 => [[3,3,2,1],[]]
 => ? = 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [[4,4,4,4,2],[3,3,3,1]]
 => [3,3,3,1]
 => [[3,3,3,1],[]]
 => ? = 10
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [[5,5,4,2],[4,3,1]]
 => [4,3,1]
 => [[4,3,1],[]]
 => ? = 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [[5,5,5,2],[4,4,1]]
 => [4,4,1]
 => [[4,4,1],[]]
 => ? = 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [[3,3,3,3,3,3],[2,2,2,2,2]]
 => [2,2,2,2,2]
 => [[2,2,2,2,2],[]]
 => ? = 10
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => [[4,4,3,3,3],[3,2,2,2]]
 => [3,2,2,2]
 => [[3,2,2,2],[]]
 => ? = 9
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => [[4,4,4,3,3],[3,3,2,2]]
 => [3,3,2,2]
 => [[3,3,2,2],[]]
 => ? = 5
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
 => [[5,5,3,3],[4,2,2]]
 => [4,2,2]
 => [[4,2,2],[]]
 => ? = 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => [[4,4,4,4,3],[3,3,3,2]]
 => [3,3,3,2]
 => [[3,3,3,2],[]]
 => ? = 11
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
 => [[5,4,4,3],[3,3,2]]
 => [3,3,2]
 => [[3,3,2],[]]
 => ? = 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
 => [[5,5,4,3],[4,3,2]]
 => [4,3,2]
 => [[4,3,2],[]]
 => ? = 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
 => [[5,5,5,3],[4,4,2]]
 => [4,4,2]
 => [[4,4,2],[]]
 => ? = 10
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => [[4,4,4,4,4],[3,3,3,3]]
 => [3,3,3,3]
 => [[3,3,3,3],[]]
 => ? = 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
 => [[5,4,4,4],[3,3,3]]
 => [3,3,3]
 => [[3,3,3],[]]
 => ? = 9
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
 => [[5,5,4,4],[4,3,3]]
 => [4,3,3]
 => [[4,3,3],[]]
 => ? = 5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
 => [[5,5,5,4],[4,4,3]]
 => [4,4,3]
 => [[4,4,3],[]]
 => ? = 11
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
 => [[6,6,4],[5,3]]
 => [5,3]
 => [[5,3],[]]
 => ? = 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => [[5,5,5,5],[4,4,4]]
 => [4,4,4]
 => [[4,4,4],[]]
 => ? = 12
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => [[6,6,6],[5,5]]
 => [5,5]
 => [[5,5],[]]
 => ? = 5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
 => [[6,6,6],[5,4]]
 => [5,4]
 => [[5,4],[]]
 => ? = 1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [[6,6,6],[4,4]]
 => [4,4]
 => [[4,4],[]]
 => ? = 8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
 => [[5,5,5,5],[4,4,3]]
 => [4,4,3]
 => [[4,4,3],[]]
 => ? = 11
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
 => [[5,5,5,5],[4,3,3]]
 => [4,3,3]
 => [[4,3,3],[]]
 => ? = 5
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [[5,5,5,5],[3,3,3]]
 => [3,3,3]
 => [[3,3,3],[]]
 => ? = 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
 => [[6,6,6],[5,3]]
 => [5,3]
 => [[5,3],[]]
 => ? = 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
 => [[4,4,4,4,4],[3,3,3,2]]
 => [3,3,3,2]
 => [[3,3,3,2],[]]
 => ? = 11
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
 => [[4,4,4,4,4],[3,3,2,2]]
 => [3,3,2,2]
 => [[3,3,2,2],[]]
 => ? = 5
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
 => [[4,4,4,4,4],[3,2,2,2]]
 => [3,2,2,2]
 => [[3,2,2,2],[]]
 => ? = 9
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
 => [[5,5,5,5],[4,4,2]]
 => [4,4,2]
 => [[4,4,2],[]]
 => ? = 10
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
 => [[5,5,5,5],[4,3,2]]
 => [4,3,2]
 => [[4,3,2],[]]
 => ? = 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
 => [[5,5,5,5],[3,3,2]]
 => [3,3,2]
 => [[3,3,2],[]]
 => ? = 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => [[5,5,5,5],[4,2,2]]
 => [4,2,2]
 => [[4,2,2],[]]
 => ? = 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [[3,3,3,3,3,3],[2,2,2,2,1]]
 => [2,2,2,2,1]
 => [[2,2,2,2,1],[]]
 => ? = 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
 => [[3,3,3,3,3,3],[2,2,2,1,1]]
 => [2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => [[4,4,4,4,4],[3,3,3,1]]
 => [3,3,3,1]
 => [[3,3,3,1],[]]
 => ? = 10
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
 => [[4,4,4,4,4],[3,3,2,1]]
 => [3,3,2,1]
 => [[3,3,2,1],[]]
 => ? = 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
 => [[4,4,4,4,4],[3,2,2,1]]
 => [3,2,2,1]
 => [[3,2,2,1],[]]
 => ? = 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => [[5,5,5,5],[4,4,1]]
 => [4,4,1]
 => [[4,4,1],[]]
 => ? = 9
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
 => [[5,5,5,5],[4,3,1]]
 => [4,3,1]
 => [[4,3,1],[]]
 => ? = 1
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.