Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000182
Mapping
St000182: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 1
[3]
 => 2
[2,1]
 => 3
[1,1,1]
 => 1
[4]
 => 6
[3,1]
 => 8
[2,2]
 => 3
[2,1,1]
 => 6
[1,1,1,1]
 => 1
[5]
 => 24
[4,1]
 => 30
[3,2]
 => 20
[3,1,1]
 => 20
[2,2,1]
 => 15
[2,1,1,1]
 => 10
[1,1,1,1,1]
 => 1
[6]
 => 120
[5,1]
 => 144
[4,2]
 => 90
[4,1,1]
 => 90
[3,3]
 => 40
[3,2,1]
 => 120
[3,1,1,1]
 => 40
[2,2,2]
 => 15
[2,2,1,1]
 => 45
[2,1,1,1,1]
 => 15
[1,1,1,1,1,1]
 => 1
[7]
 => 720
[6,1]
 => 840
[5,2]
 => 504
[5,1,1]
 => 504
[4,3]
 => 420
[4,2,1]
 => 630
[4,1,1,1]
 => 210
[3,3,1]
 => 280
[3,2,2]
 => 210
[3,2,1,1]
 => 420
[3,1,1,1,1]
 => 70
[2,2,2,1]
 => 105
[2,2,1,1,1]
 => 105
[2,1,1,1,1,1]
 => 21
[1,1,1,1,1,1,1]
 => 1
[8]
 => 5040
[7,1]
 => 5760
[6,2]
 => 3360
[6,1,1]
 => 3360
[5,3]
 => 2688
[5,2,1]
 => 4032
Description
The number of permutations whose cycle type is the given integer partition. This number is given by $$\{ \pi \in \mathfrak{S}_n : \text{type}(\pi) = \lambda\} = \frac{n!}{\lambda_1 \cdots \lambda_k \mu_1(\lambda)! \cdots \mu_n(\lambda)!}$$ where $\mu_j(\lambda)$ denotes the number of parts of $\lambda$ equal to $j$. All permutations with the same cycle type form a [[wikipedia:Conjugacy class]].
Matching statistic: St000690
Mapping
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00284: Standard tableaux —rows⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
St000690: Permutations ⟶ ℤResult quality: 8% ●values known / values provided: 11%●distinct values known / distinct values provided: 8%
Values
[1]
 => [[1]]
 => {{1}}
 => [1] => ? = 1
[2]
 => [[1,2]]
 => {{1,2}}
 => [2,1] => 1
[1,1]
 => [[1],[2]]
 => {{1},{2}}
 => [1,2] => 1
[3]
 => [[1,2,3]]
 => {{1,2,3}}
 => [2,3,1] => 2
[2,1]
 => [[1,3],[2]]
 => {{1,3},{2}}
 => [3,2,1] => 3
[1,1,1]
 => [[1],[2],[3]]
 => {{1},{2},{3}}
 => [1,2,3] => 1
[4]
 => [[1,2,3,4]]
 => {{1,2,3,4}}
 => [2,3,4,1] => 6
[3,1]
 => [[1,3,4],[2]]
 => {{1,3,4},{2}}
 => [3,2,4,1] => 8
[2,2]
 => [[1,2],[3,4]]
 => {{1,2},{3,4}}
 => [2,1,4,3] => 3
[2,1,1]
 => [[1,4],[2],[3]]
 => {{1,4},{2},{3}}
 => [4,2,3,1] => 6
[1,1,1,1]
 => [[1],[2],[3],[4]]
 => {{1},{2},{3},{4}}
 => [1,2,3,4] => 1
[5]
 => [[1,2,3,4,5]]
 => {{1,2,3,4,5}}
 => [2,3,4,5,1] => 24
[4,1]
 => [[1,3,4,5],[2]]
 => {{1,3,4,5},{2}}
 => [3,2,4,5,1] => 30
[3,2]
 => [[1,2,5],[3,4]]
 => {{1,2,5},{3,4}}
 => [2,5,4,3,1] => 20
[3,1,1]
 => [[1,4,5],[2],[3]]
 => {{1,4,5},{2},{3}}
 => [4,2,3,5,1] => 20
[2,2,1]
 => [[1,3],[2,5],[4]]
 => {{1,3},{2,5},{4}}
 => [3,5,1,4,2] => 15
[2,1,1,1]
 => [[1,5],[2],[3],[4]]
 => {{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => 10
[1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => {{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => 1
[6]
 => [[1,2,3,4,5,6]]
 => {{1,2,3,4,5,6}}
 => [2,3,4,5,6,1] => 120
[5,1]
 => [[1,3,4,5,6],[2]]
 => {{1,3,4,5,6},{2}}
 => [3,2,4,5,6,1] => 144
[4,2]
 => [[1,2,5,6],[3,4]]
 => {{1,2,5,6},{3,4}}
 => [2,5,4,3,6,1] => 90
[4,1,1]
 => [[1,4,5,6],[2],[3]]
 => {{1,4,5,6},{2},{3}}
 => [4,2,3,5,6,1] => 90
[3,3]
 => [[1,2,3],[4,5,6]]
 => {{1,2,3},{4,5,6}}
 => [2,3,1,5,6,4] => 40
[3,2,1]
 => [[1,3,6],[2,5],[4]]
 => {{1,3,6},{2,5},{4}}
 => [3,5,6,4,2,1] => 120
[3,1,1,1]
 => [[1,5,6],[2],[3],[4]]
 => {{1,5,6},{2},{3},{4}}
 => [5,2,3,4,6,1] => 40
[2,2,2]
 => [[1,2],[3,4],[5,6]]
 => {{1,2},{3,4},{5,6}}
 => [2,1,4,3,6,5] => 15
[2,2,1,1]
 => [[1,4],[2,6],[3],[5]]
 => {{1,4},{2,6},{3},{5}}
 => [4,6,3,1,5,2] => 45
[2,1,1,1,1]
 => [[1,6],[2],[3],[4],[5]]
 => {{1,6},{2},{3},{4},{5}}
 => [6,2,3,4,5,1] => 15
[1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => {{1},{2},{3},{4},{5},{6}}
 => [1,2,3,4,5,6] => 1
[7]
 => [[1,2,3,4,5,6,7]]
 => {{1,2,3,4,5,6,7}}
 => [2,3,4,5,6,7,1] => ? = 720
[6,1]
 => [[1,3,4,5,6,7],[2]]
 => {{1,3,4,5,6,7},{2}}
 => [3,2,4,5,6,7,1] => ? = 840
[5,2]
 => [[1,2,5,6,7],[3,4]]
 => {{1,2,5,6,7},{3,4}}
 => [2,5,4,3,6,7,1] => ? = 504
[5,1,1]
 => [[1,4,5,6,7],[2],[3]]
 => {{1,4,5,6,7},{2},{3}}
 => [4,2,3,5,6,7,1] => ? = 504
[4,3]
 => [[1,2,3,7],[4,5,6]]
 => {{1,2,3,7},{4,5,6}}
 => [2,3,7,5,6,4,1] => ? = 420
[4,2,1]
 => [[1,3,6,7],[2,5],[4]]
 => {{1,3,6,7},{2,5},{4}}
 => [3,5,6,4,2,7,1] => ? = 630
[4,1,1,1]
 => [[1,5,6,7],[2],[3],[4]]
 => {{1,5,6,7},{2},{3},{4}}
 => [5,2,3,4,6,7,1] => ? = 210
[3,3,1]
 => [[1,3,4],[2,6,7],[5]]
 => {{1,3,4},{2,6,7},{5}}
 => [3,6,4,1,5,7,2] => ? = 280
[3,2,2]
 => [[1,2,7],[3,4],[5,6]]
 => {{1,2,7},{3,4},{5,6}}
 => [2,7,4,3,6,5,1] => ? = 210
[3,2,1,1]
 => [[1,4,7],[2,6],[3],[5]]
 => {{1,4,7},{2,6},{3},{5}}
 => [4,6,3,7,5,2,1] => ? = 420
[3,1,1,1,1]
 => [[1,6,7],[2],[3],[4],[5]]
 => {{1,6,7},{2},{3},{4},{5}}
 => [6,2,3,4,5,7,1] => ? = 70
[2,2,2,1]
 => [[1,3],[2,5],[4,7],[6]]
 => {{1,3},{2,5},{4,7},{6}}
 => [3,5,1,7,2,6,4] => ? = 105
[2,2,1,1,1]
 => [[1,5],[2,7],[3],[4],[6]]
 => {{1,5},{2,7},{3},{4},{6}}
 => [5,7,3,4,1,6,2] => ? = 105
[2,1,1,1,1,1]
 => [[1,7],[2],[3],[4],[5],[6]]
 => {{1,7},{2},{3},{4},{5},{6}}
 => [7,2,3,4,5,6,1] => ? = 21
[1,1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6],[7]]
 => {{1},{2},{3},{4},{5},{6},{7}}
 => [1,2,3,4,5,6,7] => 1
[8]
 => [[1,2,3,4,5,6,7,8]]
 => {{1,2,3,4,5,6,7,8}}
 => [2,3,4,5,6,7,8,1] => ? = 5040
[7,1]
 => [[1,3,4,5,6,7,8],[2]]
 => {{1,3,4,5,6,7,8},{2}}
 => [3,2,4,5,6,7,8,1] => ? = 5760
[6,2]
 => [[1,2,5,6,7,8],[3,4]]
 => {{1,2,5,6,7,8},{3,4}}
 => [2,5,4,3,6,7,8,1] => ? = 3360
[6,1,1]
 => [[1,4,5,6,7,8],[2],[3]]
 => {{1,4,5,6,7,8},{2},{3}}
 => [4,2,3,5,6,7,8,1] => ? = 3360
[5,3]
 => [[1,2,3,7,8],[4,5,6]]
 => {{1,2,3,7,8},{4,5,6}}
 => [2,3,7,5,6,4,8,1] => ? = 2688
[5,2,1]
 => [[1,3,6,7,8],[2,5],[4]]
 => {{1,3,6,7,8},{2,5},{4}}
 => [3,5,6,4,2,7,8,1] => ? = 4032
[5,1,1,1]
 => [[1,5,6,7,8],[2],[3],[4]]
 => {{1,5,6,7,8},{2},{3},{4}}
 => [5,2,3,4,6,7,8,1] => ? = 1344
[4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => {{1,2,3,4},{5,6,7,8}}
 => [2,3,4,1,6,7,8,5] => ? = 1260
[4,3,1]
 => [[1,3,4,8],[2,6,7],[5]]
 => {{1,3,4,8},{2,6,7},{5}}
 => [3,6,4,8,5,7,2,1] => ? = 3360
[4,2,2]
 => [[1,2,7,8],[3,4],[5,6]]
 => {{1,2,7,8},{3,4},{5,6}}
 => [2,7,4,3,6,5,8,1] => ? = 1260
[4,2,1,1]
 => [[1,4,7,8],[2,6],[3],[5]]
 => {{1,4,7,8},{2,6},{3},{5}}
 => [4,6,3,7,5,2,8,1] => ? = 2520
[4,1,1,1,1]
 => [[1,6,7,8],[2],[3],[4],[5]]
 => {{1,6,7,8},{2},{3},{4},{5}}
 => [6,2,3,4,5,7,8,1] => ? = 420
[3,3,2]
 => [[1,2,5],[3,4,8],[6,7]]
 => {{1,2,5},{3,4,8},{6,7}}
 => [2,5,4,8,1,7,6,3] => ? = 1120
[3,3,1,1]
 => [[1,4,5],[2,7,8],[3],[6]]
 => {{1,4,5},{2,7,8},{3},{6}}
 => [4,7,3,5,1,6,8,2] => ? = 1120
[3,2,2,1]
 => [[1,3,8],[2,5],[4,7],[6]]
 => {{1,3,8},{2,5},{4,7},{6}}
 => [3,5,8,7,2,6,4,1] => ? = 1680
[3,2,1,1,1]
 => [[1,5,8],[2,7],[3],[4],[6]]
 => {{1,5,8},{2,7},{3},{4},{6}}
 => [5,7,3,4,8,6,2,1] => ? = 1120
[3,1,1,1,1,1]
 => [[1,7,8],[2],[3],[4],[5],[6]]
 => {{1,7,8},{2},{3},{4},{5},{6}}
 => [7,2,3,4,5,6,8,1] => ? = 112
[2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => {{1,2},{3,4},{5,6},{7,8}}
 => [2,1,4,3,6,5,8,7] => ? = 105
[2,2,2,1,1]
 => [[1,4],[2,6],[3,8],[5],[7]]
 => {{1,4},{2,6},{3,8},{5},{7}}
 => [4,6,8,1,5,2,7,3] => ? = 420
[2,2,1,1,1,1]
 => [[1,6],[2,8],[3],[4],[5],[7]]
 => {{1,6},{2,8},{3},{4},{5},{7}}
 => [6,8,3,4,5,1,7,2] => ? = 210
[2,1,1,1,1,1,1]
 => [[1,8],[2],[3],[4],[5],[6],[7]]
 => {{1,8},{2},{3},{4},{5},{6},{7}}
 => [8,2,3,4,5,6,7,1] => ? = 28
[1,1,1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6],[7],[8]]
 => {{1},{2},{3},{4},{5},{6},{7},{8}}
 => [1,2,3,4,5,6,7,8] => ? = 1
[9]
 => [[1,2,3,4,5,6,7,8,9]]
 => {{1,2,3,4,5,6,7,8,9}}
 => [2,3,4,5,6,7,8,9,1] => ? = 40320
[8,1]
 => [[1,3,4,5,6,7,8,9],[2]]
 => {{1,3,4,5,6,7,8,9},{2}}
 => [3,2,4,5,6,7,8,9,1] => ? = 45360
[7,2]
 => [[1,2,5,6,7,8,9],[3,4]]
 => {{1,2,5,6,7,8,9},{3,4}}
 => [2,5,4,3,6,7,8,9,1] => ? = 25920
[7,1,1]
 => [[1,4,5,6,7,8,9],[2],[3]]
 => {{1,4,5,6,7,8,9},{2},{3}}
 => [4,2,3,5,6,7,8,9,1] => ? = 25920
[6,3]
 => [[1,2,3,7,8,9],[4,5,6]]
 => {{1,2,3,7,8,9},{4,5,6}}
 => [2,3,7,5,6,4,8,9,1] => ? = 20160
[6,2,1]
 => [[1,3,6,7,8,9],[2,5],[4]]
 => {{1,3,6,7,8,9},{2,5},{4}}
 => [3,5,6,4,2,7,8,9,1] => ? = 30240
[6,1,1,1]
 => [[1,5,6,7,8,9],[2],[3],[4]]
 => {{1,5,6,7,8,9},{2},{3},{4}}
 => [5,2,3,4,6,7,8,9,1] => ? = 10080
[5,4]
 => [[1,2,3,4,9],[5,6,7,8]]
 => {{1,2,3,4,9},{5,6,7,8}}
 => [2,3,4,9,6,7,8,5,1] => ? = 18144
[5,3,1]
 => [[1,3,4,8,9],[2,6,7],[5]]
 => {{1,3,4,8,9},{2,6,7},{5}}
 => [3,6,4,8,5,7,2,9,1] => ? = 24192
[5,2,2]
 => [[1,2,7,8,9],[3,4],[5,6]]
 => {{1,2,7,8,9},{3,4},{5,6}}
 => [2,7,4,3,6,5,8,9,1] => ? = 9072
[5,2,1,1]
 => [[1,4,7,8,9],[2,6],[3],[5]]
 => {{1,4,7,8,9},{2,6},{3},{5}}
 => [4,6,3,7,5,2,8,9,1] => ? = 18144
[5,1,1,1,1]
 => [[1,6,7,8,9],[2],[3],[4],[5]]
 => {{1,6,7,8,9},{2},{3},{4},{5}}
 => [6,2,3,4,5,7,8,9,1] => ? = 3024
[4,4,1]
 => [[1,3,4,5],[2,7,8,9],[6]]
 => {{1,3,4,5},{2,7,8,9},{6}}
 => [3,7,4,5,1,6,8,9,2] => ? = 11340
Description
The size of the conjugacy class of a permutation. Two permutations are conjugate if and only if they have the same cycle type, this statistic is then computed as described in [[St000182]].