Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000511
Mapping
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000511: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1]
 => []
 => 1
[1,2] => [1,1]
 => [1]
 => 2
[2,1] => [2]
 => []
 => 1
[1,2,3] => [1,1,1]
 => [1,1]
 => 4
[1,3,2] => [2,1]
 => [1]
 => 2
[2,1,3] => [2,1]
 => [1]
 => 2
[2,3,1] => [3]
 => []
 => 1
[3,1,2] => [3]
 => []
 => 1
[3,2,1] => [2,1]
 => [1]
 => 2
[1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 8
[1,2,4,3] => [2,1,1]
 => [1,1]
 => 4
[1,3,2,4] => [2,1,1]
 => [1,1]
 => 4
[1,3,4,2] => [3,1]
 => [1]
 => 2
[1,4,2,3] => [3,1]
 => [1]
 => 2
[1,4,3,2] => [2,1,1]
 => [1,1]
 => 4
[2,1,3,4] => [2,1,1]
 => [1,1]
 => 4
[2,1,4,3] => [2,2]
 => [2]
 => 2
[2,3,1,4] => [3,1]
 => [1]
 => 2
[2,3,4,1] => [4]
 => []
 => 1
[2,4,1,3] => [4]
 => []
 => 1
[2,4,3,1] => [3,1]
 => [1]
 => 2
[3,1,2,4] => [3,1]
 => [1]
 => 2
[3,1,4,2] => [4]
 => []
 => 1
[3,2,1,4] => [2,1,1]
 => [1,1]
 => 4
[3,2,4,1] => [3,1]
 => [1]
 => 2
[3,4,1,2] => [2,2]
 => [2]
 => 2
[3,4,2,1] => [4]
 => []
 => 1
[4,1,2,3] => [4]
 => []
 => 1
[4,1,3,2] => [3,1]
 => [1]
 => 2
[4,2,1,3] => [3,1]
 => [1]
 => 2
[4,2,3,1] => [2,1,1]
 => [1,1]
 => 4
[4,3,1,2] => [4]
 => []
 => 1
[4,3,2,1] => [2,2]
 => [2]
 => 2
[1,2,3,4,5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 16
[1,2,3,5,4] => [2,1,1,1]
 => [1,1,1]
 => 8
[1,2,4,3,5] => [2,1,1,1]
 => [1,1,1]
 => 8
[1,2,4,5,3] => [3,1,1]
 => [1,1]
 => 4
[1,2,5,3,4] => [3,1,1]
 => [1,1]
 => 4
[1,2,5,4,3] => [2,1,1,1]
 => [1,1,1]
 => 8
[1,3,2,4,5] => [2,1,1,1]
 => [1,1,1]
 => 8
[1,3,2,5,4] => [2,2,1]
 => [2,1]
 => 4
[1,3,4,2,5] => [3,1,1]
 => [1,1]
 => 4
[1,3,4,5,2] => [4,1]
 => [1]
 => 2
[1,3,5,2,4] => [4,1]
 => [1]
 => 2
[1,3,5,4,2] => [3,1,1]
 => [1,1]
 => 4
[1,4,2,3,5] => [3,1,1]
 => [1,1]
 => 4
[1,4,2,5,3] => [4,1]
 => [1]
 => 2
[1,4,3,2,5] => [2,1,1,1]
 => [1,1,1]
 => 8
[1,4,3,5,2] => [3,1,1]
 => [1,1]
 => 4
[1,4,5,2,3] => [2,2,1]
 => [2,1]
 => 4
Description
The number of invariant subsets when acting with a permutation of given cycle type.
Matching statistic: St001661
(load all 32 compositions to match this statistic)
Mapping
St001661: Permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 50%
Values
[1] => 1
[1,2] => 2
[2,1] => 1
[1,2,3] => 4
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 8
[1,2,4,3] => 4
[1,3,2,4] => 4
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 4
[2,1,3,4] => 4
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 1
[3,2,1,4] => 4
[3,2,4,1] => 2
[3,4,1,2] => 2
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 4
[4,3,1,2] => 1
[4,3,2,1] => 2
[1,2,3,4,5] => 16
[1,2,3,5,4] => 8
[1,2,4,3,5] => 8
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 8
[1,3,2,4,5] => 8
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 2
[1,3,5,2,4] => 2
[1,3,5,4,2] => 4
[1,4,2,3,5] => 4
[1,4,2,5,3] => 2
[1,4,3,2,5] => 8
[1,4,3,5,2] => 4
[1,4,5,2,3] => 4
[1,2,3,4,5,6,7] => ? = 64
[1,2,3,4,5,7,6] => ? = 32
[1,2,3,4,6,5,7] => ? = 32
[1,2,3,4,6,7,5] => ? = 16
[1,2,3,4,7,5,6] => ? = 16
[1,2,3,4,7,6,5] => ? = 32
[1,2,3,5,4,6,7] => ? = 32
[1,2,3,5,4,7,6] => ? = 16
[1,2,3,5,6,4,7] => ? = 16
[1,2,3,5,6,7,4] => ? = 8
[1,2,3,5,7,4,6] => ? = 8
[1,2,3,5,7,6,4] => ? = 16
[1,2,3,6,4,5,7] => ? = 16
[1,2,3,6,4,7,5] => ? = 8
[1,2,3,6,5,4,7] => ? = 32
[1,2,3,6,5,7,4] => ? = 16
[1,2,3,6,7,4,5] => ? = 16
[1,2,3,6,7,5,4] => ? = 8
[1,2,3,7,4,5,6] => ? = 8
[1,2,3,7,4,6,5] => ? = 16
[1,2,3,7,5,4,6] => ? = 16
[1,2,3,7,5,6,4] => ? = 32
[1,2,3,7,6,4,5] => ? = 8
[1,2,3,7,6,5,4] => ? = 16
[1,2,4,3,5,6,7] => ? = 32
[1,2,4,3,5,7,6] => ? = 16
[1,2,4,3,6,5,7] => ? = 16
[1,2,4,3,6,7,5] => ? = 8
[1,2,4,3,7,5,6] => ? = 8
[1,2,4,3,7,6,5] => ? = 16
[1,2,4,5,3,6,7] => ? = 16
[1,2,4,5,3,7,6] => ? = 8
[1,2,4,5,6,3,7] => ? = 8
[1,2,4,5,6,7,3] => ? = 4
[1,2,4,5,7,3,6] => ? = 4
[1,2,4,5,7,6,3] => ? = 8
[1,2,4,6,3,5,7] => ? = 8
[1,2,4,6,3,7,5] => ? = 4
[1,2,4,6,5,3,7] => ? = 16
[1,2,4,6,5,7,3] => ? = 8
[1,2,4,6,7,3,5] => ? = 8
[1,2,4,6,7,5,3] => ? = 4
[1,2,4,7,3,5,6] => ? = 4
[1,2,4,7,3,6,5] => ? = 8
[1,2,4,7,5,3,6] => ? = 8
[1,2,4,7,5,6,3] => ? = 16
[1,2,4,7,6,3,5] => ? = 4
[1,2,4,7,6,5,3] => ? = 8
[1,2,5,3,4,6,7] => ? = 16
[1,2,5,3,4,7,6] => ? = 8
Description
Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation.