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Matching statistic: St001806
Mp00252: Permutations —restriction⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St001806: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00252: Permutations —restriction⟶ Permutations
St001806: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [1,2] => [1] => 1
[1,3,2] => [1,2] => [1] => 1
[2,1,3] => [2,1] => [1] => 1
[2,3,1] => [2,1] => [1] => 1
[3,1,2] => [1,2] => [1] => 1
[3,2,1] => [2,1] => [1] => 1
[1,2,3,4] => [1,2,3] => [1,2] => 2
[1,2,4,3] => [1,2,3] => [1,2] => 2
[1,3,2,4] => [1,3,2] => [1,2] => 2
[1,3,4,2] => [1,3,2] => [1,2] => 2
[1,4,2,3] => [1,2,3] => [1,2] => 2
[1,4,3,2] => [1,3,2] => [1,2] => 2
[2,1,3,4] => [2,1,3] => [2,1] => 1
[2,1,4,3] => [2,1,3] => [2,1] => 1
[2,3,1,4] => [2,3,1] => [2,1] => 1
[2,3,4,1] => [2,3,1] => [2,1] => 1
[2,4,1,3] => [2,1,3] => [2,1] => 1
[2,4,3,1] => [2,3,1] => [2,1] => 1
[3,1,2,4] => [3,1,2] => [1,2] => 2
[3,1,4,2] => [3,1,2] => [1,2] => 2
[3,2,1,4] => [3,2,1] => [2,1] => 1
[3,2,4,1] => [3,2,1] => [2,1] => 1
[3,4,1,2] => [3,1,2] => [1,2] => 2
[3,4,2,1] => [3,2,1] => [2,1] => 1
[4,1,2,3] => [1,2,3] => [1,2] => 2
[4,1,3,2] => [1,3,2] => [1,2] => 2
[4,2,1,3] => [2,1,3] => [2,1] => 1
[4,2,3,1] => [2,3,1] => [2,1] => 1
[4,3,1,2] => [3,1,2] => [1,2] => 2
[4,3,2,1] => [3,2,1] => [2,1] => 1
[1,2,3,4,5] => [1,2,3,4] => [1,2,3] => 2
[1,2,3,5,4] => [1,2,3,4] => [1,2,3] => 2
[1,2,4,3,5] => [1,2,4,3] => [1,2,3] => 2
[1,2,4,5,3] => [1,2,4,3] => [1,2,3] => 2
[1,2,5,3,4] => [1,2,3,4] => [1,2,3] => 2
[1,2,5,4,3] => [1,2,4,3] => [1,2,3] => 2
[1,3,2,4,5] => [1,3,2,4] => [1,3,2] => 3
[1,3,2,5,4] => [1,3,2,4] => [1,3,2] => 3
[1,3,4,2,5] => [1,3,4,2] => [1,3,2] => 3
[1,3,4,5,2] => [1,3,4,2] => [1,3,2] => 3
[1,3,5,2,4] => [1,3,2,4] => [1,3,2] => 3
[1,3,5,4,2] => [1,3,4,2] => [1,3,2] => 3
[1,4,2,3,5] => [1,4,2,3] => [1,2,3] => 2
[1,4,2,5,3] => [1,4,2,3] => [1,2,3] => 2
[1,4,3,2,5] => [1,4,3,2] => [1,3,2] => 3
[1,4,3,5,2] => [1,4,3,2] => [1,3,2] => 3
[1,4,5,2,3] => [1,4,2,3] => [1,2,3] => 2
[1,4,5,3,2] => [1,4,3,2] => [1,3,2] => 3
[1,5,2,3,4] => [1,2,3,4] => [1,2,3] => 2
[1,5,2,4,3] => [1,2,4,3] => [1,2,3] => 2
Description
The upper middle entry of a permutation.
This is the entry σ(n+12) when n is odd, and σ(n2+1) when n is even, where n is the size of the permutation σ.
Matching statistic: St001807
Mp00064: Permutations —reverse⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St001807: Permutations ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 100%
Mp00252: Permutations —restriction⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St001807: Permutations ⟶ ℤResult quality: 76% ●values known / values provided: 76%●distinct values known / distinct values provided: 100%
Values
[1,2,3] => [3,2,1] => [2,1] => [1] => 1
[1,3,2] => [2,3,1] => [2,1] => [1] => 1
[2,1,3] => [3,1,2] => [1,2] => [1] => 1
[2,3,1] => [1,3,2] => [1,2] => [1] => 1
[3,1,2] => [2,1,3] => [2,1] => [1] => 1
[3,2,1] => [1,2,3] => [1,2] => [1] => 1
[1,2,3,4] => [4,3,2,1] => [3,2,1] => [2,1] => 2
[1,2,4,3] => [3,4,2,1] => [3,2,1] => [2,1] => 2
[1,3,2,4] => [4,2,3,1] => [2,3,1] => [2,1] => 2
[1,3,4,2] => [2,4,3,1] => [2,3,1] => [2,1] => 2
[1,4,2,3] => [3,2,4,1] => [3,2,1] => [2,1] => 2
[1,4,3,2] => [2,3,4,1] => [2,3,1] => [2,1] => 2
[2,1,3,4] => [4,3,1,2] => [3,1,2] => [1,2] => 1
[2,1,4,3] => [3,4,1,2] => [3,1,2] => [1,2] => 1
[2,3,1,4] => [4,1,3,2] => [1,3,2] => [1,2] => 1
[2,3,4,1] => [1,4,3,2] => [1,3,2] => [1,2] => 1
[2,4,1,3] => [3,1,4,2] => [3,1,2] => [1,2] => 1
[2,4,3,1] => [1,3,4,2] => [1,3,2] => [1,2] => 1
[3,1,2,4] => [4,2,1,3] => [2,1,3] => [2,1] => 2
[3,1,4,2] => [2,4,1,3] => [2,1,3] => [2,1] => 2
[3,2,1,4] => [4,1,2,3] => [1,2,3] => [1,2] => 1
[3,2,4,1] => [1,4,2,3] => [1,2,3] => [1,2] => 1
[3,4,1,2] => [2,1,4,3] => [2,1,3] => [2,1] => 2
[3,4,2,1] => [1,2,4,3] => [1,2,3] => [1,2] => 1
[4,1,2,3] => [3,2,1,4] => [3,2,1] => [2,1] => 2
[4,1,3,2] => [2,3,1,4] => [2,3,1] => [2,1] => 2
[4,2,1,3] => [3,1,2,4] => [3,1,2] => [1,2] => 1
[4,2,3,1] => [1,3,2,4] => [1,3,2] => [1,2] => 1
[4,3,1,2] => [2,1,3,4] => [2,1,3] => [2,1] => 2
[4,3,2,1] => [1,2,3,4] => [1,2,3] => [1,2] => 1
[1,2,3,4,5] => [5,4,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[1,2,3,5,4] => [4,5,3,2,1] => [4,3,2,1] => [3,2,1] => 2
[1,2,4,3,5] => [5,3,4,2,1] => [3,4,2,1] => [3,2,1] => 2
[1,2,4,5,3] => [3,5,4,2,1] => [3,4,2,1] => [3,2,1] => 2
[1,2,5,3,4] => [4,3,5,2,1] => [4,3,2,1] => [3,2,1] => 2
[1,2,5,4,3] => [3,4,5,2,1] => [3,4,2,1] => [3,2,1] => 2
[1,3,2,4,5] => [5,4,2,3,1] => [4,2,3,1] => [2,3,1] => 3
[1,3,2,5,4] => [4,5,2,3,1] => [4,2,3,1] => [2,3,1] => 3
[1,3,4,2,5] => [5,2,4,3,1] => [2,4,3,1] => [2,3,1] => 3
[1,3,4,5,2] => [2,5,4,3,1] => [2,4,3,1] => [2,3,1] => 3
[1,3,5,2,4] => [4,2,5,3,1] => [4,2,3,1] => [2,3,1] => 3
[1,3,5,4,2] => [2,4,5,3,1] => [2,4,3,1] => [2,3,1] => 3
[1,4,2,3,5] => [5,3,2,4,1] => [3,2,4,1] => [3,2,1] => 2
[1,4,2,5,3] => [3,5,2,4,1] => [3,2,4,1] => [3,2,1] => 2
[1,4,3,2,5] => [5,2,3,4,1] => [2,3,4,1] => [2,3,1] => 3
[1,4,3,5,2] => [2,5,3,4,1] => [2,3,4,1] => [2,3,1] => 3
[1,4,5,2,3] => [3,2,5,4,1] => [3,2,4,1] => [3,2,1] => 2
[1,4,5,3,2] => [2,3,5,4,1] => [2,3,4,1] => [2,3,1] => 3
[1,5,2,3,4] => [4,3,2,5,1] => [4,3,2,1] => [3,2,1] => 2
[1,5,2,4,3] => [3,4,2,5,1] => [3,4,2,1] => [3,2,1] => 2
[7,8,5,6,4,3,2,1] => [1,2,3,4,6,5,8,7] => ? => ? => ? = 3
[7,5,6,8,4,3,2,1] => [1,2,3,4,8,6,5,7] => ? => ? => ? = 3
[6,5,7,8,4,3,2,1] => [1,2,3,4,8,7,5,6] => ? => ? => ? = 3
[7,8,6,4,5,3,2,1] => [1,2,3,5,4,6,8,7] => ? => ? => ? = 3
[7,6,4,5,8,3,2,1] => [1,2,3,8,5,4,6,7] => ? => ? => ? = 3
[7,5,4,6,8,3,2,1] => [1,2,3,8,6,4,5,7] => ? => ? => ? = 3
[7,4,5,6,8,3,2,1] => [1,2,3,8,6,5,4,7] => ? => ? => ? = 3
[8,7,6,5,3,4,2,1] => [1,2,4,3,5,6,7,8] => ? => ? => ? = 4
[7,8,6,5,3,4,2,1] => [1,2,4,3,5,6,8,7] => ? => ? => ? = 4
[8,6,7,5,3,4,2,1] => [1,2,4,3,5,7,6,8] => ? => ? => ? = 4
[6,7,8,3,4,5,2,1] => [1,2,5,4,3,8,7,6] => ? => ? => ? = 5
[8,7,5,4,3,6,2,1] => [1,2,6,3,4,5,7,8] => ? => ? => ? = 6
[7,6,5,4,3,8,2,1] => [1,2,8,3,4,5,6,7] => ? => ? => ? = 3
[6,4,5,7,3,8,2,1] => [1,2,8,3,7,5,4,6] => ? => ? => ? = 3
[7,6,4,3,5,8,2,1] => [1,2,8,5,3,4,6,7] => ? => ? => ? = 5
[6,3,4,5,7,8,2,1] => [1,2,8,7,5,4,3,6] => ? => ? => ? = 5
[4,3,5,6,7,8,2,1] => [1,2,8,7,6,5,3,4] => ? => ? => ? = 6
[7,8,6,5,4,2,3,1] => [1,3,2,4,5,6,8,7] => ? => ? => ? = 2
[8,7,5,6,4,2,3,1] => [1,3,2,4,6,5,7,8] => ? => ? => ? = 2
[8,7,6,5,2,3,4,1] => [1,4,3,2,5,6,7,8] => ? => ? => ? = 3
[6,7,8,5,2,3,4,1] => [1,4,3,2,5,8,7,6] => ? => ? => ? = 3
[6,5,3,4,7,2,8,1] => [1,8,2,7,4,3,5,6] => ? => ? => ? = 4
[7,6,5,3,2,4,8,1] => [1,8,4,2,3,5,6,7] => ? => ? => ? = 2
[7,6,5,2,3,4,8,1] => [1,8,4,3,2,5,6,7] => ? => ? => ? = 3
[3,4,5,2,6,7,8,1] => [1,8,7,6,2,5,4,3] => ? => ? => ? = 2
[4,3,2,5,6,7,8,1] => [1,8,7,6,5,2,3,4] => ? => ? => ? = 5
[3,4,2,5,6,7,8,1] => [1,8,7,6,5,2,4,3] => ? => ? => ? = 5
[4,2,3,5,6,7,8,1] => [1,8,7,6,5,3,2,4] => ? => ? => ? = 5
[8,6,7,5,4,3,1,2] => [2,1,3,4,5,7,6,8] => ? => ? => ? = 3
[8,7,5,6,4,3,1,2] => [2,1,3,4,6,5,7,8] => ? => ? => ? = 3
[6,5,7,8,4,3,1,2] => [2,1,3,4,8,7,5,6] => ? => ? => ? = 3
[8,7,6,4,5,3,1,2] => [2,1,3,5,4,6,7,8] => ? => ? => ? = 3
[7,8,6,4,5,3,1,2] => [2,1,3,5,4,6,8,7] => ? => ? => ? = 3
[8,7,6,5,3,4,1,2] => [2,1,4,3,5,6,7,8] => ? => ? => ? = 4
[8,7,5,6,3,4,1,2] => [2,1,4,3,6,5,7,8] => ? => ? => ? = 4
[8,3,4,5,6,7,1,2] => [2,1,7,6,5,4,3,8] => ? => ? => ? = 6
[6,5,7,4,3,8,1,2] => [2,1,8,3,4,7,5,6] => ? => ? => ? = 3
[5,4,6,3,7,8,1,2] => [2,1,8,7,3,6,4,5] => ? => ? => ? = 3
[6,5,7,8,4,1,2,3] => [3,2,1,4,8,7,5,6] => ? => ? => ? = 1
[8,7,6,4,5,1,2,3] => [3,2,1,5,4,6,7,8] => ? => ? => ? = 1
[8,7,4,5,6,1,2,3] => [3,2,1,6,5,4,7,8] => ? => ? => ? = 1
[7,8,4,5,6,1,2,3] => [3,2,1,6,5,4,8,7] => ? => ? => ? = 1
[8,7,6,5,3,1,2,4] => [4,2,1,3,5,6,7,8] => ? => ? => ? = 1
[8,7,6,5,2,1,3,4] => [4,3,1,2,5,6,7,8] => ? => ? => ? = 1
[6,7,8,4,3,2,1,5] => [5,1,2,3,4,8,7,6] => ? => ? => ? = 2
[6,7,8,3,4,2,1,5] => [5,1,2,4,3,8,7,6] => ? => ? => ? = 2
[8,7,6,4,2,3,1,5] => [5,1,3,2,4,6,7,8] => ? => ? => ? = 3
[6,7,8,4,2,3,1,5] => [5,1,3,2,4,8,7,6] => ? => ? => ? = 3
[8,7,6,3,2,4,1,5] => [5,1,4,2,3,6,7,8] => ? => ? => ? = 4
[6,7,8,3,2,4,1,5] => [5,1,4,2,3,8,7,6] => ? => ? => ? = 4
Description
The lower middle entry of a permutation.
This is the entry σ(n+12) when n is odd, and σ(n2) when n is even, where n is the size of the permutation σ.
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