Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001527
Mapping
St001527: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 2
[1,1]
 => 1
[3]
 => 3
[2,1]
 => 1
[1,1,1]
 => 3
[4]
 => 4
[3,1]
 => 1
[2,2]
 => 4
[2,1,1]
 => 1
[1,1,1,1]
 => 2
[5]
 => 5
[4,1]
 => 1
[3,2]
 => 5
[3,1,1]
 => 5
[2,2,1]
 => 5
[2,1,1,1]
 => 1
[1,1,1,1,1]
 => 5
[6]
 => 6
[5,1]
 => 1
[4,2]
 => 6
[4,1,1]
 => 3
[3,3]
 => 3
[3,2,1]
 => 2
[3,1,1,1]
 => 3
[2,2,2]
 => 6
[2,2,1,1]
 => 3
[2,1,1,1,1]
 => 2
[1,1,1,1,1,1]
 => 3
[7]
 => 7
[6,1]
 => 1
[5,2]
 => 7
[5,1,1]
 => 7
[4,3]
 => 7
[4,2,1]
 => 7
[4,1,1,1]
 => 1
[3,3,1]
 => 7
[3,2,2]
 => 7
[3,2,1,1]
 => 7
[3,1,1,1,1]
 => 7
[2,2,2,1]
 => 7
[2,2,1,1,1]
 => 7
[2,1,1,1,1,1]
 => 1
[1,1,1,1,1,1,1]
 => 7
[8]
 => 8
[7,1]
 => 1
[6,2]
 => 8
[6,1,1]
 => 1
[5,3]
 => 1
[5,2,1]
 => 8
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
(load all 2 compositions to match this statistic)
Mapping
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001614: Skew partitions ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 41%
Values
[1]
 => [[1],[]]
 => 1
[2]
 => [[2],[]]
 => 2
[1,1]
 => [[1,1],[]]
 => 1
[3]
 => [[3],[]]
 => 3
[2,1]
 => [[2,1],[]]
 => 1
[1,1,1]
 => [[1,1,1],[]]
 => 3
[4]
 => [[4],[]]
 => 4
[3,1]
 => [[3,1],[]]
 => 1
[2,2]
 => [[2,2],[]]
 => 4
[2,1,1]
 => [[2,1,1],[]]
 => 1
[1,1,1,1]
 => [[1,1,1,1],[]]
 => 2
[5]
 => [[5],[]]
 => 5
[4,1]
 => [[4,1],[]]
 => 1
[3,2]
 => [[3,2],[]]
 => 5
[3,1,1]
 => [[3,1,1],[]]
 => 5
[2,2,1]
 => [[2,2,1],[]]
 => 5
[2,1,1,1]
 => [[2,1,1,1],[]]
 => 1
[1,1,1,1,1]
 => [[1,1,1,1,1],[]]
 => 5
[6]
 => [[6],[]]
 => 6
[5,1]
 => [[5,1],[]]
 => 1
[4,2]
 => [[4,2],[]]
 => 6
[4,1,1]
 => [[4,1,1],[]]
 => 3
[3,3]
 => [[3,3],[]]
 => 3
[3,2,1]
 => [[3,2,1],[]]
 => 2
[3,1,1,1]
 => [[3,1,1,1],[]]
 => 3
[2,2,2]
 => [[2,2,2],[]]
 => 6
[2,2,1,1]
 => [[2,2,1,1],[]]
 => 3
[2,1,1,1,1]
 => [[2,1,1,1,1],[]]
 => 2
[1,1,1,1,1,1]
 => [[1,1,1,1,1,1],[]]
 => 3
[7]
 => [[7],[]]
 => 7
[6,1]
 => [[6,1],[]]
 => 1
[5,2]
 => [[5,2],[]]
 => 7
[5,1,1]
 => [[5,1,1],[]]
 => 7
[4,3]
 => [[4,3],[]]
 => 7
[4,2,1]
 => [[4,2,1],[]]
 => 7
[4,1,1,1]
 => [[4,1,1,1],[]]
 => 1
[3,3,1]
 => [[3,3,1],[]]
 => 7
[3,2,2]
 => [[3,2,2],[]]
 => 7
[3,2,1,1]
 => [[3,2,1,1],[]]
 => 7
[3,1,1,1,1]
 => [[3,1,1,1,1],[]]
 => 7
[2,2,2,1]
 => [[2,2,2,1],[]]
 => 7
[2,2,1,1,1]
 => [[2,2,1,1,1],[]]
 => 7
[2,1,1,1,1,1]
 => [[2,1,1,1,1,1],[]]
 => 1
[1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1],[]]
 => 7
[8]
 => [[8],[]]
 => ? = 8
[7,1]
 => [[7,1],[]]
 => ? = 1
[6,2]
 => [[6,2],[]]
 => ? = 8
[6,1,1]
 => [[6,1,1],[]]
 => ? = 1
[5,3]
 => [[5,3],[]]
 => ? = 1
[5,2,1]
 => [[5,2,1],[]]
 => ? = 8
[5,1,1,1]
 => [[5,1,1,1],[]]
 => ? = 2
[4,4]
 => [[4,4],[]]
 => ? = 8
[4,3,1]
 => [[4,3,1],[]]
 => ? = 1
[4,2,2]
 => [[4,2,2],[]]
 => ? = 8
[4,2,1,1]
 => [[4,2,1,1],[]]
 => ? = 1
[4,1,1,1,1]
 => [[4,1,1,1,1],[]]
 => ? = 2
[3,3,2]
 => [[3,3,2],[]]
 => ? = 1
[3,3,1,1]
 => [[3,3,1,1],[]]
 => ? = 8
[3,2,2,1]
 => [[3,2,2,1],[]]
 => ? = 1
[3,2,1,1,1]
 => [[3,2,1,1,1],[]]
 => ? = 8
[3,1,1,1,1,1]
 => [[3,1,1,1,1,1],[]]
 => ? = 1
[2,2,2,2]
 => [[2,2,2,2],[]]
 => ? = 8
[2,2,2,1,1]
 => [[2,2,2,1,1],[]]
 => ? = 1
[2,2,1,1,1,1]
 => [[2,2,1,1,1,1],[]]
 => ? = 8
[2,1,1,1,1,1,1]
 => [[2,1,1,1,1,1,1],[]]
 => ? = 1
[1,1,1,1,1,1,1,1]
 => [[1,1,1,1,1,1,1,1],[]]
 => ? = 4
[9]
 => [[9],[]]
 => ? = 9
[8,1]
 => [[8,1],[]]
 => ? = 1
[7,2]
 => [[7,2],[]]
 => ? = 9
[7,1,1]
 => [[7,1,1],[]]
 => ? = 9
[6,3]
 => [[6,3],[]]
 => ? = 9
[6,2,1]
 => [[6,2,1],[]]
 => ? = 1
[6,1,1,1]
 => [[6,1,1,1],[]]
 => ? = 3
[5,4]
 => [[5,4],[]]
 => ? = 1
[5,3,1]
 => [[5,3,1],[]]
 => ? = 9
[5,2,2]
 => [[5,2,2],[]]
 => ? = 9
[5,2,1,1]
 => [[5,2,1,1],[]]
 => ? = 9
[5,1,1,1,1]
 => [[5,1,1,1,1],[]]
 => ? = 1
[4,4,1]
 => [[4,4,1],[]]
 => ? = 9
[4,3,2]
 => [[4,3,2],[]]
 => ? = 1
[4,3,1,1]
 => [[4,3,1,1],[]]
 => ? = 9
[4,2,2,1]
 => [[4,2,2,1],[]]
 => ? = 9
[4,2,1,1,1]
 => [[4,2,1,1,1],[]]
 => ? = 9
[4,1,1,1,1,1]
 => [[4,1,1,1,1,1],[]]
 => ? = 3
[3,3,3]
 => [[3,3,3],[]]
 => ? = 9
[3,3,2,1]
 => [[3,3,2,1],[]]
 => ? = 1
[3,3,1,1,1]
 => [[3,3,1,1,1],[]]
 => ? = 9
[3,2,2,2]
 => [[3,2,2,2],[]]
 => ? = 9
[3,2,2,1,1]
 => [[3,2,2,1,1],[]]
 => ? = 9
[3,2,1,1,1,1]
 => [[3,2,1,1,1,1],[]]
 => ? = 1
[3,1,1,1,1,1,1]
 => [[3,1,1,1,1,1,1],[]]
 => ? = 9
[2,2,2,2,1]
 => [[2,2,2,2,1],[]]
 => ? = 1
[2,2,2,1,1,1]
 => [[2,2,2,1,1,1],[]]
 => ? = 9
[2,2,1,1,1,1,1]
 => [[2,2,1,1,1,1,1],[]]
 => ? = 9
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.