Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001899
Mapping
Mp00252: Permutations —restriction⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001899: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1] => [1]
 => [1]
 => 1
[2,1] => [1] => [1]
 => [1]
 => 1
[1,2,3] => [1,2] => [1,1]
 => [2]
 => 1
[1,3,2] => [1,2] => [1,1]
 => [2]
 => 1
[2,1,3] => [2,1] => [2]
 => [1,1]
 => 1
[2,3,1] => [2,1] => [2]
 => [1,1]
 => 1
[3,1,2] => [1,2] => [1,1]
 => [2]
 => 1
[3,2,1] => [2,1] => [2]
 => [1,1]
 => 1
[1,2,3,4] => [1,2,3] => [1,1,1]
 => [3]
 => 1
[1,2,4,3] => [1,2,3] => [1,1,1]
 => [3]
 => 1
[1,3,2,4] => [1,3,2] => [2,1]
 => [2,1]
 => 2
[1,3,4,2] => [1,3,2] => [2,1]
 => [2,1]
 => 2
[1,4,2,3] => [1,2,3] => [1,1,1]
 => [3]
 => 1
[1,4,3,2] => [1,3,2] => [2,1]
 => [2,1]
 => 2
[2,1,3,4] => [2,1,3] => [2,1]
 => [2,1]
 => 2
[2,1,4,3] => [2,1,3] => [2,1]
 => [2,1]
 => 2
[2,3,1,4] => [2,3,1] => [3]
 => [1,1,1]
 => 1
[2,3,4,1] => [2,3,1] => [3]
 => [1,1,1]
 => 1
[2,4,1,3] => [2,1,3] => [2,1]
 => [2,1]
 => 2
[2,4,3,1] => [2,3,1] => [3]
 => [1,1,1]
 => 1
[3,1,2,4] => [3,1,2] => [3]
 => [1,1,1]
 => 1
[3,1,4,2] => [3,1,2] => [3]
 => [1,1,1]
 => 1
[3,2,1,4] => [3,2,1] => [2,1]
 => [2,1]
 => 2
[3,2,4,1] => [3,2,1] => [2,1]
 => [2,1]
 => 2
[3,4,1,2] => [3,1,2] => [3]
 => [1,1,1]
 => 1
[3,4,2,1] => [3,2,1] => [2,1]
 => [2,1]
 => 2
[4,1,2,3] => [1,2,3] => [1,1,1]
 => [3]
 => 1
[4,1,3,2] => [1,3,2] => [2,1]
 => [2,1]
 => 2
[4,2,1,3] => [2,1,3] => [2,1]
 => [2,1]
 => 2
[4,2,3,1] => [2,3,1] => [3]
 => [1,1,1]
 => 1
[4,3,1,2] => [3,1,2] => [3]
 => [1,1,1]
 => 1
[4,3,2,1] => [3,2,1] => [2,1]
 => [2,1]
 => 2
[1,2,3,4,5] => [1,2,3,4] => [1,1,1,1]
 => [4]
 => 2
[1,2,3,5,4] => [1,2,3,4] => [1,1,1,1]
 => [4]
 => 2
[1,2,4,3,5] => [1,2,4,3] => [2,1,1]
 => [3,1]
 => 3
[1,2,4,5,3] => [1,2,4,3] => [2,1,1]
 => [3,1]
 => 3
[1,2,5,3,4] => [1,2,3,4] => [1,1,1,1]
 => [4]
 => 2
[1,2,5,4,3] => [1,2,4,3] => [2,1,1]
 => [3,1]
 => 3
[1,3,2,4,5] => [1,3,2,4] => [2,1,1]
 => [3,1]
 => 3
[1,3,2,5,4] => [1,3,2,4] => [2,1,1]
 => [3,1]
 => 3
[1,3,4,2,5] => [1,3,4,2] => [3,1]
 => [2,1,1]
 => 2
[1,3,4,5,2] => [1,3,4,2] => [3,1]
 => [2,1,1]
 => 2
[1,3,5,2,4] => [1,3,2,4] => [2,1,1]
 => [3,1]
 => 3
[1,3,5,4,2] => [1,3,4,2] => [3,1]
 => [2,1,1]
 => 2
[1,4,2,3,5] => [1,4,2,3] => [3,1]
 => [2,1,1]
 => 2
[1,4,2,5,3] => [1,4,2,3] => [3,1]
 => [2,1,1]
 => 2
[1,4,3,2,5] => [1,4,3,2] => [2,1,1]
 => [3,1]
 => 3
[1,4,3,5,2] => [1,4,3,2] => [2,1,1]
 => [3,1]
 => 3
[1,4,5,2,3] => [1,4,2,3] => [3,1]
 => [2,1,1]
 => 2
[1,4,5,3,2] => [1,4,3,2] => [2,1,1]
 => [3,1]
 => 3
Description
The total number of irreducible representations contained in the higher Lie character for an integer partition.