Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St000431
(load all 5 compositions to match this statistic)
Mapping
St000431: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 0
[2,1,3] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 1
[1,3,4,2] => 0
[1,4,2,3] => 0
[1,4,3,2] => 1
[2,1,3,4] => 2
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 0
[2,4,1,3] => 1
[2,4,3,1] => 1
[3,1,2,4] => 2
[3,1,4,2] => 1
[3,2,1,4] => 4
[3,2,4,1] => 2
[3,4,1,2] => 0
[3,4,2,1] => 2
[4,1,2,3] => 0
[4,1,3,2] => 1
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 2
[4,3,2,1] => 4
[1,2,3,4,5] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 1
[1,2,4,5,3] => 0
[1,2,5,3,4] => 0
[1,2,5,4,3] => 1
[1,3,2,4,5] => 2
[1,3,2,5,4] => 2
[1,3,4,2,5] => 2
[1,3,4,5,2] => 0
[1,3,5,2,4] => 1
[1,3,5,4,2] => 1
[1,4,2,3,5] => 2
[1,4,2,5,3] => 1
[1,4,3,2,5] => 4
[1,4,3,5,2] => 2
[1,4,5,2,3] => 0
Description
The number of occurrences of the pattern 213 or of the pattern 321 in a permutation.
Matching statistic: St000433
(load all 2 compositions to match this statistic)
Mapping
Mp00064: Permutations —reverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
St000433: Permutations ⟶ ℤResult quality: 55% ●values known / values provided: 55%●distinct values known / distinct values provided: 58%
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [2,1] => [2,1] => [1,2] => 0
[2,1] => [1,2] => [1,2] => [2,1] => 0
[1,2,3] => [3,2,1] => [3,2,1] => [1,2,3] => 0
[1,3,2] => [2,3,1] => [3,1,2] => [2,1,3] => 0
[2,1,3] => [3,1,2] => [2,3,1] => [1,3,2] => 1
[2,3,1] => [1,3,2] => [1,3,2] => [2,3,1] => 0
[3,1,2] => [2,1,3] => [2,1,3] => [3,1,2] => 0
[3,2,1] => [1,2,3] => [1,2,3] => [3,2,1] => 1
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => [1,2,3,4] => 0
[1,2,4,3] => [3,4,2,1] => [4,3,1,2] => [2,1,3,4] => 0
[1,3,2,4] => [4,2,3,1] => [4,2,3,1] => [1,3,2,4] => 1
[1,3,4,2] => [2,4,3,1] => [4,1,3,2] => [2,3,1,4] => 0
[1,4,2,3] => [3,2,4,1] => [4,2,1,3] => [3,1,2,4] => 0
[1,4,3,2] => [2,3,4,1] => [4,1,2,3] => [3,2,1,4] => 1
[2,1,3,4] => [4,3,1,2] => [3,4,2,1] => [1,2,4,3] => 2
[2,1,4,3] => [3,4,1,2] => [3,4,1,2] => [2,1,4,3] => 2
[2,3,1,4] => [4,1,3,2] => [2,4,3,1] => [1,3,4,2] => 2
[2,3,4,1] => [1,4,3,2] => [1,4,3,2] => [2,3,4,1] => 0
[2,4,1,3] => [3,1,4,2] => [2,4,1,3] => [3,1,4,2] => 1
[2,4,3,1] => [1,3,4,2] => [1,4,2,3] => [3,2,4,1] => 1
[3,1,2,4] => [4,2,1,3] => [3,2,4,1] => [1,4,2,3] => 2
[3,1,4,2] => [2,4,1,3] => [3,1,4,2] => [2,4,1,3] => 1
[3,2,1,4] => [4,1,2,3] => [2,3,4,1] => [1,4,3,2] => 4
[3,2,4,1] => [1,4,2,3] => [1,3,4,2] => [2,4,3,1] => 2
[3,4,1,2] => [2,1,4,3] => [2,1,4,3] => [3,4,1,2] => 0
[3,4,2,1] => [1,2,4,3] => [1,2,4,3] => [3,4,2,1] => 2
[4,1,2,3] => [3,2,1,4] => [3,2,1,4] => [4,1,2,3] => 0
[4,1,3,2] => [2,3,1,4] => [3,1,2,4] => [4,2,1,3] => 1
[4,2,1,3] => [3,1,2,4] => [2,3,1,4] => [4,1,3,2] => 2
[4,2,3,1] => [1,3,2,4] => [1,3,2,4] => [4,2,3,1] => 2
[4,3,1,2] => [2,1,3,4] => [2,1,3,4] => [4,3,1,2] => 2
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [4,3,2,1] => 4
[1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [4,5,3,2,1] => [5,4,3,1,2] => [2,1,3,4,5] => 0
[1,2,4,3,5] => [5,3,4,2,1] => [5,4,2,3,1] => [1,3,2,4,5] => 1
[1,2,4,5,3] => [3,5,4,2,1] => [5,4,1,3,2] => [2,3,1,4,5] => 0
[1,2,5,3,4] => [4,3,5,2,1] => [5,4,2,1,3] => [3,1,2,4,5] => 0
[1,2,5,4,3] => [3,4,5,2,1] => [5,4,1,2,3] => [3,2,1,4,5] => 1
[1,3,2,4,5] => [5,4,2,3,1] => [5,3,4,2,1] => [1,2,4,3,5] => 2
[1,3,2,5,4] => [4,5,2,3,1] => [5,3,4,1,2] => [2,1,4,3,5] => 2
[1,3,4,2,5] => [5,2,4,3,1] => [5,2,4,3,1] => [1,3,4,2,5] => 2
[1,3,4,5,2] => [2,5,4,3,1] => [5,1,4,3,2] => [2,3,4,1,5] => 0
[1,3,5,2,4] => [4,2,5,3,1] => [5,2,4,1,3] => [3,1,4,2,5] => 1
[1,3,5,4,2] => [2,4,5,3,1] => [5,1,4,2,3] => [3,2,4,1,5] => 1
[1,4,2,3,5] => [5,3,2,4,1] => [5,3,2,4,1] => [1,4,2,3,5] => 2
[1,4,2,5,3] => [3,5,2,4,1] => [5,3,1,4,2] => [2,4,1,3,5] => 1
[1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => [1,4,3,2,5] => 4
[1,4,3,5,2] => [2,5,3,4,1] => [5,1,3,4,2] => [2,4,3,1,5] => 2
[1,4,5,2,3] => [3,2,5,4,1] => [5,2,1,4,3] => [3,4,1,2,5] => 0
[1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => [7,6,5,3,4,1,2] => [2,1,4,3,5,6,7] => ? = 2
[1,2,3,5,7,4,6] => [6,4,7,5,3,2,1] => [7,6,5,2,4,1,3] => [3,1,4,2,5,6,7] => ? = 1
[1,2,3,5,7,6,4] => [4,6,7,5,3,2,1] => [7,6,5,1,4,2,3] => [3,2,4,1,5,6,7] => ? = 1
[1,2,3,6,5,7,4] => [4,7,5,6,3,2,1] => [7,6,5,1,3,4,2] => [2,4,3,1,5,6,7] => ? = 2
[1,2,3,6,7,5,4] => [4,5,7,6,3,2,1] => [7,6,5,1,2,4,3] => [3,4,2,1,5,6,7] => ? = 2
[1,2,3,7,4,6,5] => [5,6,4,7,3,2,1] => [7,6,5,3,1,2,4] => [4,2,1,3,5,6,7] => ? = 1
[1,2,3,7,5,4,6] => [6,4,5,7,3,2,1] => [7,6,5,2,3,1,4] => [4,1,3,2,5,6,7] => ? = 2
[1,2,3,7,5,6,4] => [4,6,5,7,3,2,1] => [7,6,5,1,3,2,4] => [4,2,3,1,5,6,7] => ? = 2
[1,2,3,7,6,4,5] => [5,4,6,7,3,2,1] => [7,6,5,2,1,3,4] => [4,3,1,2,5,6,7] => ? = 2
[1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => [7,6,4,5,3,1,2] => [2,1,3,5,4,6,7] => ? = 3
[1,2,4,3,6,7,5] => [5,7,6,3,4,2,1] => [7,6,4,5,1,3,2] => [2,3,1,5,4,6,7] => ? = 3
[1,2,4,3,7,5,6] => [6,5,7,3,4,2,1] => [7,6,4,5,2,1,3] => [3,1,2,5,4,6,7] => ? = 3
[1,2,4,3,7,6,5] => [5,6,7,3,4,2,1] => [7,6,4,5,1,2,3] => [3,2,1,5,4,6,7] => ? = 4
[1,2,4,5,3,7,6] => [6,7,3,5,4,2,1] => [7,6,3,5,4,1,2] => [2,1,4,5,3,6,7] => ? = 4
[1,2,4,5,7,3,6] => [6,3,7,5,4,2,1] => [7,6,2,5,4,1,3] => [3,1,4,5,2,6,7] => ? = 2
[1,2,4,5,7,6,3] => [3,6,7,5,4,2,1] => [7,6,1,5,4,2,3] => [3,2,4,5,1,6,7] => ? = 1
[1,2,4,6,3,7,5] => [5,7,3,6,4,2,1] => [7,6,3,5,1,4,2] => [2,4,1,5,3,6,7] => ? = 3
[1,2,4,6,5,7,3] => [3,7,5,6,4,2,1] => [7,6,1,5,3,4,2] => [2,4,3,5,1,6,7] => ? = 2
[1,2,4,6,7,3,5] => [5,3,7,6,4,2,1] => [7,6,2,5,1,4,3] => [3,4,1,5,2,6,7] => ? = 1
[1,2,4,6,7,5,3] => [3,5,7,6,4,2,1] => [7,6,1,5,2,4,3] => [3,4,2,5,1,6,7] => ? = 2
[1,2,4,7,3,5,6] => [6,5,3,7,4,2,1] => [7,6,3,5,2,1,4] => [4,1,2,5,3,6,7] => ? = 2
[1,2,4,7,3,6,5] => [5,6,3,7,4,2,1] => [7,6,3,5,1,2,4] => [4,2,1,5,3,6,7] => ? = 3
[1,2,4,7,5,3,6] => [6,3,5,7,4,2,1] => [7,6,2,5,3,1,4] => [4,1,3,5,2,6,7] => ? = 3
[1,2,4,7,5,6,3] => [3,6,5,7,4,2,1] => [7,6,1,5,3,2,4] => [4,2,3,5,1,6,7] => ? = 2
[1,2,4,7,6,3,5] => [5,3,6,7,4,2,1] => [7,6,2,5,1,3,4] => [4,3,1,5,2,6,7] => ? = 3
[1,2,4,7,6,5,3] => [3,5,6,7,4,2,1] => [7,6,1,5,2,3,4] => [4,3,2,5,1,6,7] => ? = 4
[1,2,5,3,4,7,6] => [6,7,4,3,5,2,1] => [7,6,4,3,5,1,2] => [2,1,5,3,4,6,7] => ? = 4
[1,2,5,3,6,7,4] => [4,7,6,3,5,2,1] => [7,6,4,1,5,3,2] => [2,3,5,1,4,6,7] => ? = 2
[1,2,5,3,7,4,6] => [6,4,7,3,5,2,1] => [7,6,4,2,5,1,3] => [3,1,5,2,4,6,7] => ? = 3
[1,2,5,3,7,6,4] => [4,6,7,3,5,2,1] => [7,6,4,1,5,2,3] => [3,2,5,1,4,6,7] => ? = 3
[1,2,5,4,3,7,6] => [6,7,3,4,5,2,1] => [7,6,3,4,5,1,2] => [2,1,5,4,3,6,7] => ? = 7
[1,2,5,4,6,7,3] => [3,7,6,4,5,2,1] => [7,6,1,4,5,3,2] => [2,3,5,4,1,6,7] => ? = 3
[1,2,5,4,7,3,6] => [6,3,7,4,5,2,1] => [7,6,2,4,5,1,3] => [3,1,5,4,2,6,7] => ? = 5
[1,2,5,4,7,6,3] => [3,6,7,4,5,2,1] => [7,6,1,4,5,2,3] => [3,2,5,4,1,6,7] => ? = 4
[1,2,5,6,3,7,4] => [4,7,3,6,5,2,1] => [7,6,3,1,5,4,2] => [2,4,5,1,3,6,7] => ? = 2
[1,2,5,6,4,7,3] => [3,7,4,6,5,2,1] => [7,6,1,3,5,4,2] => [2,4,5,3,1,6,7] => ? = 4
[1,2,5,6,7,3,4] => [4,3,7,6,5,2,1] => [7,6,2,1,5,4,3] => [3,4,5,1,2,6,7] => ? = 0
[1,2,5,6,7,4,3] => [3,4,7,6,5,2,1] => [7,6,1,2,5,4,3] => [3,4,5,2,1,6,7] => ? = 3
[1,2,5,7,3,4,6] => [6,4,3,7,5,2,1] => [7,6,3,2,5,1,4] => [4,1,5,2,3,6,7] => ? = 2
[1,2,5,7,4,3,6] => [6,3,4,7,5,2,1] => [7,6,2,3,5,1,4] => [4,1,5,3,2,6,7] => ? = 5
[1,2,5,7,4,6,3] => [3,6,4,7,5,2,1] => [7,6,1,3,5,2,4] => [4,2,5,3,1,6,7] => ? = 4
[1,2,5,7,6,3,4] => [4,3,6,7,5,2,1] => [7,6,2,1,5,3,4] => [4,3,5,1,2,6,7] => ? = 2
[1,2,5,7,6,4,3] => [3,4,6,7,5,2,1] => [7,6,1,2,5,3,4] => [4,3,5,2,1,6,7] => ? = 5
[1,2,6,3,4,5,7] => [7,5,4,3,6,2,1] => [7,6,4,3,2,5,1] => [1,5,2,3,4,6,7] => ? = 3
[1,2,6,3,5,4,7] => [7,4,5,3,6,2,1] => [7,6,4,2,3,5,1] => [1,5,3,2,4,6,7] => ? = 5
[1,2,6,3,5,7,4] => [4,7,5,3,6,2,1] => [7,6,4,1,3,5,2] => [2,5,3,1,4,6,7] => ? = 3
[1,2,6,3,7,4,5] => [5,4,7,3,6,2,1] => [7,6,4,2,1,5,3] => [3,5,1,2,4,6,7] => ? = 1
[1,2,6,3,7,5,4] => [4,5,7,3,6,2,1] => [7,6,4,1,2,5,3] => [3,5,2,1,4,6,7] => ? = 3
[1,2,6,4,3,5,7] => [7,5,3,4,6,2,1] => [7,6,3,4,2,5,1] => [1,5,2,4,3,6,7] => ? = 6
[1,2,6,4,3,7,5] => [5,7,3,4,6,2,1] => [7,6,3,4,1,5,2] => [2,5,1,4,3,6,7] => ? = 5
Description
The number of occurrences of the pattern 132 or of the pattern 321 in a permutation.
Matching statistic: St000430
(load all 3 compositions to match this statistic)
Mapping
Mp00329: Permutations —Tanimoto⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
St000430: Permutations ⟶ ℤResult quality: 21% ●values known / values provided: 30%●distinct values known / distinct values provided: 21%
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [2,1] => [1,2] => 0
[2,1] => [2,1] => [1,2] => [2,1] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [1,3,2] => 0
[1,3,2] => [2,1,3] => [1,3,2] => [2,3,1] => 0
[2,1,3] => [1,3,2] => [3,2,1] => [1,2,3] => 1
[2,3,1] => [3,1,2] => [3,1,2] => [2,1,3] => 0
[3,1,2] => [2,3,1] => [1,2,3] => [3,2,1] => 0
[3,2,1] => [3,2,1] => [2,1,3] => [3,1,2] => 1
[1,2,3,4] => [1,2,3,4] => [2,3,4,1] => [1,4,3,2] => 0
[1,2,4,3] => [2,3,1,4] => [1,2,4,3] => [3,4,2,1] => 0
[1,3,2,4] => [1,2,4,3] => [2,4,3,1] => [1,3,4,2] => 1
[1,3,4,2] => [2,4,1,3] => [1,4,2,3] => [3,2,4,1] => 0
[1,4,2,3] => [2,1,3,4] => [1,3,4,2] => [2,4,3,1] => 0
[1,4,3,2] => [2,1,4,3] => [1,4,3,2] => [2,3,4,1] => 1
[2,1,3,4] => [1,3,2,4] => [3,2,4,1] => [1,4,2,3] => 2
[2,1,4,3] => [3,2,1,4] => [2,1,4,3] => [3,4,1,2] => 2
[2,3,1,4] => [1,3,4,2] => [4,2,3,1] => [1,3,2,4] => 2
[2,3,4,1] => [3,4,1,2] => [4,1,2,3] => [3,2,1,4] => 0
[2,4,1,3] => [3,1,2,4] => [3,1,4,2] => [2,4,1,3] => 1
[2,4,3,1] => [3,1,4,2] => [4,1,3,2] => [2,3,1,4] => 1
[3,1,2,4] => [1,4,2,3] => [3,4,2,1] => [1,2,4,3] => 2
[3,1,4,2] => [4,2,1,3] => [2,4,1,3] => [3,1,4,2] => 1
[3,2,1,4] => [1,4,3,2] => [4,3,2,1] => [1,2,3,4] => 4
[3,2,4,1] => [4,3,1,2] => [4,2,1,3] => [3,1,2,4] => 2
[3,4,1,2] => [4,1,2,3] => [3,4,1,2] => [2,1,4,3] => 0
[3,4,2,1] => [4,1,3,2] => [4,3,1,2] => [2,1,3,4] => 2
[4,1,2,3] => [2,3,4,1] => [1,2,3,4] => [4,3,2,1] => 0
[4,1,3,2] => [2,4,3,1] => [1,3,2,4] => [4,2,3,1] => 1
[4,2,1,3] => [3,2,4,1] => [2,1,3,4] => [4,3,1,2] => 2
[4,2,3,1] => [3,4,2,1] => [3,1,2,4] => [4,2,1,3] => 2
[4,3,1,2] => [4,2,3,1] => [2,3,1,4] => [4,1,3,2] => 2
[4,3,2,1] => [4,3,2,1] => [3,2,1,4] => [4,1,2,3] => 4
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,1] => [1,5,4,3,2] => 0
[1,2,3,5,4] => [2,3,4,1,5] => [1,2,3,5,4] => [4,5,3,2,1] => 0
[1,2,4,3,5] => [1,2,3,5,4] => [2,3,5,4,1] => [1,4,5,3,2] => 1
[1,2,4,5,3] => [2,3,5,1,4] => [1,2,5,3,4] => [4,3,5,2,1] => 0
[1,2,5,3,4] => [2,3,1,4,5] => [1,2,4,5,3] => [3,5,4,2,1] => 0
[1,2,5,4,3] => [2,3,1,5,4] => [1,2,5,4,3] => [3,4,5,2,1] => 1
[1,3,2,4,5] => [1,2,4,3,5] => [2,4,3,5,1] => [1,5,3,4,2] => 2
[1,3,2,5,4] => [2,4,3,1,5] => [1,3,2,5,4] => [4,5,2,3,1] => 2
[1,3,4,2,5] => [1,2,4,5,3] => [2,5,3,4,1] => [1,4,3,5,2] => 2
[1,3,4,5,2] => [2,4,5,1,3] => [1,5,2,3,4] => [4,3,2,5,1] => 0
[1,3,5,2,4] => [2,4,1,3,5] => [1,4,2,5,3] => [3,5,2,4,1] => 1
[1,3,5,4,2] => [2,4,1,5,3] => [1,5,2,4,3] => [3,4,2,5,1] => 1
[1,4,2,3,5] => [1,2,5,3,4] => [2,4,5,3,1] => [1,3,5,4,2] => 2
[1,4,2,5,3] => [2,5,3,1,4] => [1,3,5,2,4] => [4,2,5,3,1] => 1
[1,4,3,2,5] => [1,2,5,4,3] => [2,5,4,3,1] => [1,3,4,5,2] => 4
[1,4,3,5,2] => [2,5,4,1,3] => [1,5,3,2,4] => [4,2,3,5,1] => 2
[1,4,5,2,3] => [2,5,1,3,4] => [1,4,5,2,3] => [3,2,5,4,1] => 0
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => ? = 0
[1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => [1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => ? = 0
[1,2,3,4,6,5,7] => [1,2,3,4,5,7,6] => [2,3,4,5,7,6,1] => [1,6,7,5,4,3,2] => ? = 1
[1,2,3,4,6,7,5] => [2,3,4,5,7,1,6] => [1,2,3,4,7,5,6] => [6,5,7,4,3,2,1] => ? = 0
[1,2,3,4,7,5,6] => [2,3,4,5,1,6,7] => [1,2,3,4,6,7,5] => [5,7,6,4,3,2,1] => ? = 0
[1,2,3,4,7,6,5] => [2,3,4,5,1,7,6] => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => ? = 1
[1,2,3,5,4,6,7] => [1,2,3,4,6,5,7] => [2,3,4,6,5,7,1] => [1,7,5,6,4,3,2] => ? = 2
[1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => ? = 2
[1,2,3,5,6,4,7] => [1,2,3,4,6,7,5] => [2,3,4,7,5,6,1] => [1,6,5,7,4,3,2] => ? = 2
[1,2,3,5,6,7,4] => [2,3,4,6,7,1,5] => [1,2,3,7,4,5,6] => [6,5,4,7,3,2,1] => ? = 0
[1,2,3,5,7,4,6] => [2,3,4,6,1,5,7] => [1,2,3,6,4,7,5] => [5,7,4,6,3,2,1] => ? = 1
[1,2,3,5,7,6,4] => [2,3,4,6,1,7,5] => [1,2,3,7,4,6,5] => [5,6,4,7,3,2,1] => ? = 1
[1,2,3,6,4,5,7] => [1,2,3,4,7,5,6] => [2,3,4,6,7,5,1] => [1,5,7,6,4,3,2] => ? = 2
[1,2,3,6,4,7,5] => [2,3,4,7,5,1,6] => [1,2,3,5,7,4,6] => [6,4,7,5,3,2,1] => ? = 1
[1,2,3,6,5,4,7] => [1,2,3,4,7,6,5] => [2,3,4,7,6,5,1] => [1,5,6,7,4,3,2] => ? = 4
[1,2,3,6,5,7,4] => [2,3,4,7,6,1,5] => [1,2,3,7,5,4,6] => [6,4,5,7,3,2,1] => ? = 2
[1,2,3,6,7,4,5] => [2,3,4,7,1,5,6] => [1,2,3,6,7,4,5] => [5,4,7,6,3,2,1] => ? = 0
[1,2,3,6,7,5,4] => [2,3,4,7,1,6,5] => [1,2,3,7,6,4,5] => [5,4,6,7,3,2,1] => ? = 2
[1,2,3,7,4,5,6] => [2,3,4,1,5,6,7] => [1,2,3,5,6,7,4] => [4,7,6,5,3,2,1] => ? = 0
[1,2,3,7,4,6,5] => [2,3,4,1,5,7,6] => [1,2,3,5,7,6,4] => [4,6,7,5,3,2,1] => ? = 1
[1,2,3,7,5,4,6] => [2,3,4,1,6,5,7] => [1,2,3,6,5,7,4] => [4,7,5,6,3,2,1] => ? = 2
[1,2,3,7,5,6,4] => [2,3,4,1,6,7,5] => [1,2,3,7,5,6,4] => [4,6,5,7,3,2,1] => ? = 2
[1,2,3,7,6,4,5] => [2,3,4,1,7,5,6] => [1,2,3,6,7,5,4] => [4,5,7,6,3,2,1] => ? = 2
[1,2,3,7,6,5,4] => [2,3,4,1,7,6,5] => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => ? = 4
[1,2,4,3,5,6,7] => [1,2,3,5,4,6,7] => [2,3,5,4,6,7,1] => [1,7,6,4,5,3,2] => ? = 3
[1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => [1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => ? = 3
[1,2,4,3,6,5,7] => [1,2,3,5,4,7,6] => [2,3,5,4,7,6,1] => [1,6,7,4,5,3,2] => ? = 4
[1,2,4,3,6,7,5] => [2,3,5,4,7,1,6] => [1,2,4,3,7,5,6] => [6,5,7,3,4,2,1] => ? = 3
[1,2,4,3,7,5,6] => [2,3,5,4,1,6,7] => [1,2,4,3,6,7,5] => [5,7,6,3,4,2,1] => ? = 3
[1,2,4,3,7,6,5] => [2,3,5,4,1,7,6] => [1,2,4,3,7,6,5] => [5,6,7,3,4,2,1] => ? = 4
[1,2,4,5,3,6,7] => [1,2,3,5,6,4,7] => [2,3,6,4,5,7,1] => [1,7,5,4,6,3,2] => ? = 4
[1,2,4,5,3,7,6] => [2,3,5,6,4,1,7] => [1,2,5,3,4,7,6] => [6,7,4,3,5,2,1] => ? = 4
[1,2,4,5,6,3,7] => [1,2,3,5,6,7,4] => [2,3,7,4,5,6,1] => [1,6,5,4,7,3,2] => ? = 3
[1,2,4,5,6,7,3] => [2,3,5,6,7,1,4] => [1,2,7,3,4,5,6] => [6,5,4,3,7,2,1] => ? = 0
[1,2,4,5,7,3,6] => [2,3,5,6,1,4,7] => [1,2,6,3,4,7,5] => [5,7,4,3,6,2,1] => ? = 2
[1,2,4,5,7,6,3] => [2,3,5,6,1,7,4] => [1,2,7,3,4,6,5] => [5,6,4,3,7,2,1] => ? = 1
[1,2,4,6,3,5,7] => [1,2,3,5,7,4,6] => [2,3,6,4,7,5,1] => [1,5,7,4,6,3,2] => ? = 4
[1,2,4,6,3,7,5] => [2,3,5,7,4,1,6] => [1,2,5,3,7,4,6] => [6,4,7,3,5,2,1] => ? = 3
[1,2,4,6,5,3,7] => [1,2,3,5,7,6,4] => [2,3,7,4,6,5,1] => [1,5,6,4,7,3,2] => ? = 5
[1,2,4,6,5,7,3] => [2,3,5,7,6,1,4] => [1,2,7,3,5,4,6] => [6,4,5,3,7,2,1] => ? = 2
[1,2,4,6,7,3,5] => [2,3,5,7,1,4,6] => [1,2,6,3,7,4,5] => [5,4,7,3,6,2,1] => ? = 1
[1,2,4,6,7,5,3] => [2,3,5,7,1,6,4] => [1,2,7,3,6,4,5] => [5,4,6,3,7,2,1] => ? = 2
[1,2,4,7,3,5,6] => [2,3,5,1,4,6,7] => [1,2,5,3,6,7,4] => [4,7,6,3,5,2,1] => ? = 2
[1,2,4,7,3,6,5] => [2,3,5,1,4,7,6] => [1,2,5,3,7,6,4] => [4,6,7,3,5,2,1] => ? = 3
[1,2,4,7,5,3,6] => [2,3,5,1,6,4,7] => [1,2,6,3,5,7,4] => [4,7,5,3,6,2,1] => ? = 3
[1,2,4,7,5,6,3] => [2,3,5,1,6,7,4] => [1,2,7,3,5,6,4] => [4,6,5,3,7,2,1] => ? = 2
[1,2,4,7,6,3,5] => [2,3,5,1,7,4,6] => [1,2,6,3,7,5,4] => [4,5,7,3,6,2,1] => ? = 3
[1,2,4,7,6,5,3] => [2,3,5,1,7,6,4] => [1,2,7,3,6,5,4] => [4,5,6,3,7,2,1] => ? = 4
[1,2,5,3,4,6,7] => [1,2,3,6,4,5,7] => [2,3,5,6,4,7,1] => [1,7,4,6,5,3,2] => ? = 4
[1,2,5,3,4,7,6] => [2,3,6,4,5,1,7] => [1,2,4,5,3,7,6] => [6,7,3,5,4,2,1] => ? = 4
Description
The number of occurrences of the pattern 123 or of the pattern 312 in a permutation.
Matching statistic: St000427
(load all 4 compositions to match this statistic)
Mapping
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00329: Permutations —Tanimoto⟶ Permutations
St000427: Permutations ⟶ ℤResult quality: 22% ●values known / values provided: 30%●distinct values known / distinct values provided: 22%
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [2,1] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [2,1] => [2,1] => 0
[1,2,3] => [2,3,1] => [2,1,3] => [1,3,2] => 0
[1,3,2] => [2,1,3] => [2,3,1] => [3,1,2] => 0
[2,1,3] => [3,2,1] => [1,2,3] => [1,2,3] => 1
[2,3,1] => [1,2,3] => [3,2,1] => [3,2,1] => 0
[3,1,2] => [3,1,2] => [1,3,2] => [2,1,3] => 0
[3,2,1] => [1,3,2] => [3,1,2] => [2,3,1] => 1
[1,2,3,4] => [2,3,4,1] => [3,2,1,4] => [1,4,3,2] => 0
[1,2,4,3] => [2,3,1,4] => [3,2,4,1] => [4,3,1,2] => 0
[1,3,2,4] => [2,4,3,1] => [3,1,2,4] => [1,4,2,3] => 1
[1,3,4,2] => [2,1,3,4] => [3,4,2,1] => [4,1,3,2] => 0
[1,4,2,3] => [2,4,1,3] => [3,1,4,2] => [4,2,1,3] => 0
[1,4,3,2] => [2,1,4,3] => [3,4,1,2] => [4,1,2,3] => 1
[2,1,3,4] => [3,2,4,1] => [2,3,1,4] => [1,3,4,2] => 2
[2,1,4,3] => [3,2,1,4] => [2,3,4,1] => [3,4,1,2] => 2
[2,3,1,4] => [4,2,3,1] => [1,3,2,4] => [1,2,4,3] => 2
[2,3,4,1] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[2,4,1,3] => [4,2,1,3] => [1,3,4,2] => [2,4,1,3] => 1
[2,4,3,1] => [1,2,4,3] => [4,3,1,2] => [4,2,3,1] => 1
[3,1,2,4] => [3,4,2,1] => [2,1,3,4] => [1,3,2,4] => 2
[3,1,4,2] => [3,1,2,4] => [2,4,3,1] => [3,1,4,2] => 1
[3,2,1,4] => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 4
[3,2,4,1] => [1,3,2,4] => [4,2,3,1] => [3,4,2,1] => 2
[3,4,1,2] => [4,1,2,3] => [1,4,3,2] => [2,1,4,3] => 0
[3,4,2,1] => [1,4,2,3] => [4,1,3,2] => [2,4,3,1] => 2
[4,1,2,3] => [3,4,1,2] => [2,1,4,3] => [3,2,1,4] => 0
[4,1,3,2] => [3,1,4,2] => [2,4,1,3] => [3,1,2,4] => 1
[4,2,1,3] => [4,3,1,2] => [1,2,4,3] => [2,3,1,4] => 2
[4,2,3,1] => [1,3,4,2] => [4,2,1,3] => [3,2,4,1] => 2
[4,3,1,2] => [4,1,3,2] => [1,4,2,3] => [2,1,3,4] => 2
[4,3,2,1] => [1,4,3,2] => [4,1,2,3] => [2,3,4,1] => 4
[1,2,3,4,5] => [2,3,4,5,1] => [4,3,2,1,5] => [1,5,4,3,2] => 0
[1,2,3,5,4] => [2,3,4,1,5] => [4,3,2,5,1] => [5,4,3,1,2] => 0
[1,2,4,3,5] => [2,3,5,4,1] => [4,3,1,2,5] => [1,5,4,2,3] => 1
[1,2,4,5,3] => [2,3,1,4,5] => [4,3,5,2,1] => [5,4,1,3,2] => 0
[1,2,5,3,4] => [2,3,5,1,4] => [4,3,1,5,2] => [5,4,2,1,3] => 0
[1,2,5,4,3] => [2,3,1,5,4] => [4,3,5,1,2] => [5,4,1,2,3] => 1
[1,3,2,4,5] => [2,4,3,5,1] => [4,2,3,1,5] => [1,5,3,4,2] => 2
[1,3,2,5,4] => [2,4,3,1,5] => [4,2,3,5,1] => [5,3,4,1,2] => 2
[1,3,4,2,5] => [2,5,3,4,1] => [4,1,3,2,5] => [1,5,2,4,3] => 2
[1,3,4,5,2] => [2,1,3,4,5] => [4,5,3,2,1] => [5,1,4,3,2] => 0
[1,3,5,2,4] => [2,5,3,1,4] => [4,1,3,5,2] => [5,2,4,1,3] => 1
[1,3,5,4,2] => [2,1,3,5,4] => [4,5,3,1,2] => [5,1,4,2,3] => 1
[1,4,2,3,5] => [2,4,5,3,1] => [4,2,1,3,5] => [1,5,3,2,4] => 2
[1,4,2,5,3] => [2,4,1,3,5] => [4,2,5,3,1] => [5,3,1,4,2] => 1
[1,4,3,2,5] => [2,5,4,3,1] => [4,1,2,3,5] => [1,5,2,3,4] => 4
[1,4,3,5,2] => [2,1,4,3,5] => [4,5,2,3,1] => [5,1,3,4,2] => 2
[1,4,5,2,3] => [2,5,1,3,4] => [4,1,5,3,2] => [5,2,1,4,3] => 0
[1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => [1,7,6,5,4,3,2] => ? = 0
[1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => [6,5,4,3,2,7,1] => [7,6,5,4,3,1,2] => ? = 0
[1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => [6,5,4,3,1,2,7] => [1,7,6,5,4,2,3] => ? = 1
[1,2,3,4,6,7,5] => [2,3,4,5,1,6,7] => [6,5,4,3,7,2,1] => [7,6,5,4,1,3,2] => ? = 0
[1,2,3,4,7,5,6] => [2,3,4,5,7,1,6] => [6,5,4,3,1,7,2] => [7,6,5,4,2,1,3] => ? = 0
[1,2,3,4,7,6,5] => [2,3,4,5,1,7,6] => [6,5,4,3,7,1,2] => [7,6,5,4,1,2,3] => ? = 1
[1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => [6,5,4,2,3,1,7] => [1,7,6,5,3,4,2] => ? = 2
[1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => [6,5,4,2,3,7,1] => [7,6,5,3,4,1,2] => ? = 2
[1,2,3,5,6,4,7] => [2,3,4,7,5,6,1] => [6,5,4,1,3,2,7] => [1,7,6,5,2,4,3] => ? = 2
[1,2,3,5,6,7,4] => [2,3,4,1,5,6,7] => [6,5,4,7,3,2,1] => [7,6,5,1,4,3,2] => ? = 0
[1,2,3,5,7,4,6] => [2,3,4,7,5,1,6] => [6,5,4,1,3,7,2] => [7,6,5,2,4,1,3] => ? = 1
[1,2,3,5,7,6,4] => [2,3,4,1,5,7,6] => [6,5,4,7,3,1,2] => [7,6,5,1,4,2,3] => ? = 1
[1,2,3,6,4,5,7] => [2,3,4,6,7,5,1] => [6,5,4,2,1,3,7] => [1,7,6,5,3,2,4] => ? = 2
[1,2,3,6,4,7,5] => [2,3,4,6,1,5,7] => [6,5,4,2,7,3,1] => [7,6,5,3,1,4,2] => ? = 1
[1,2,3,6,5,4,7] => [2,3,4,7,6,5,1] => [6,5,4,1,2,3,7] => [1,7,6,5,2,3,4] => ? = 4
[1,2,3,6,5,7,4] => [2,3,4,1,6,5,7] => [6,5,4,7,2,3,1] => [7,6,5,1,3,4,2] => ? = 2
[1,2,3,6,7,4,5] => [2,3,4,7,1,5,6] => [6,5,4,1,7,3,2] => [7,6,5,2,1,4,3] => ? = 0
[1,2,3,6,7,5,4] => [2,3,4,1,7,5,6] => [6,5,4,7,1,3,2] => [7,6,5,1,2,4,3] => ? = 2
[1,2,3,7,4,5,6] => [2,3,4,6,7,1,5] => [6,5,4,2,1,7,3] => [7,6,5,3,2,1,4] => ? = 0
[1,2,3,7,4,6,5] => [2,3,4,6,1,7,5] => [6,5,4,2,7,1,3] => [7,6,5,3,1,2,4] => ? = 1
[1,2,3,7,5,4,6] => [2,3,4,7,6,1,5] => [6,5,4,1,2,7,3] => [7,6,5,2,3,1,4] => ? = 2
[1,2,3,7,5,6,4] => [2,3,4,1,6,7,5] => [6,5,4,7,2,1,3] => [7,6,5,1,3,2,4] => ? = 2
[1,2,3,7,6,4,5] => [2,3,4,7,1,6,5] => [6,5,4,1,7,2,3] => [7,6,5,2,1,3,4] => ? = 2
[1,2,3,7,6,5,4] => [2,3,4,1,7,6,5] => [6,5,4,7,1,2,3] => [7,6,5,1,2,3,4] => ? = 4
[1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => [6,5,3,4,2,1,7] => [1,7,6,4,5,3,2] => ? = 3
[1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => [6,5,3,4,2,7,1] => [7,6,4,5,3,1,2] => ? = 3
[1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => [6,5,3,4,1,2,7] => [1,7,6,4,5,2,3] => ? = 4
[1,2,4,3,6,7,5] => [2,3,5,4,1,6,7] => [6,5,3,4,7,2,1] => [7,6,4,5,1,3,2] => ? = 3
[1,2,4,3,7,5,6] => [2,3,5,4,7,1,6] => [6,5,3,4,1,7,2] => [7,6,4,5,2,1,3] => ? = 3
[1,2,4,3,7,6,5] => [2,3,5,4,1,7,6] => [6,5,3,4,7,1,2] => [7,6,4,5,1,2,3] => ? = 4
[1,2,4,5,3,6,7] => [2,3,6,4,5,7,1] => [6,5,2,4,3,1,7] => [1,7,6,3,5,4,2] => ? = 4
[1,2,4,5,3,7,6] => [2,3,6,4,5,1,7] => [6,5,2,4,3,7,1] => [7,6,3,5,4,1,2] => ? = 4
[1,2,4,5,6,3,7] => [2,3,7,4,5,6,1] => [6,5,1,4,3,2,7] => [1,7,6,2,5,4,3] => ? = 3
[1,2,4,5,6,7,3] => [2,3,1,4,5,6,7] => [6,5,7,4,3,2,1] => [7,6,1,5,4,3,2] => ? = 0
[1,2,4,5,7,3,6] => [2,3,7,4,5,1,6] => [6,5,1,4,3,7,2] => [7,6,2,5,4,1,3] => ? = 2
[1,2,4,5,7,6,3] => [2,3,1,4,5,7,6] => [6,5,7,4,3,1,2] => [7,6,1,5,4,2,3] => ? = 1
[1,2,4,6,3,5,7] => [2,3,6,4,7,5,1] => [6,5,2,4,1,3,7] => [1,7,6,3,5,2,4] => ? = 4
[1,2,4,6,3,7,5] => [2,3,6,4,1,5,7] => [6,5,2,4,7,3,1] => [7,6,3,5,1,4,2] => ? = 3
[1,2,4,6,5,3,7] => [2,3,7,4,6,5,1] => [6,5,1,4,2,3,7] => [1,7,6,2,5,3,4] => ? = 5
[1,2,4,6,5,7,3] => [2,3,1,4,6,5,7] => [6,5,7,4,2,3,1] => [7,6,1,5,3,4,2] => ? = 2
[1,2,4,6,7,3,5] => [2,3,7,4,1,5,6] => [6,5,1,4,7,3,2] => [7,6,2,5,1,4,3] => ? = 1
[1,2,4,6,7,5,3] => [2,3,1,4,7,5,6] => [6,5,7,4,1,3,2] => [7,6,1,5,2,4,3] => ? = 2
[1,2,4,7,3,5,6] => [2,3,6,4,7,1,5] => [6,5,2,4,1,7,3] => [7,6,3,5,2,1,4] => ? = 2
[1,2,4,7,3,6,5] => [2,3,6,4,1,7,5] => [6,5,2,4,7,1,3] => [7,6,3,5,1,2,4] => ? = 3
[1,2,4,7,5,3,6] => [2,3,7,4,6,1,5] => [6,5,1,4,2,7,3] => [7,6,2,5,3,1,4] => ? = 3
[1,2,4,7,5,6,3] => [2,3,1,4,6,7,5] => [6,5,7,4,2,1,3] => [7,6,1,5,3,2,4] => ? = 2
[1,2,4,7,6,3,5] => [2,3,7,4,1,6,5] => [6,5,1,4,7,2,3] => [7,6,2,5,1,3,4] => ? = 3
[1,2,4,7,6,5,3] => [2,3,1,4,7,6,5] => [6,5,7,4,1,2,3] => [7,6,1,5,2,3,4] => ? = 4
[1,2,5,3,4,6,7] => [2,3,5,6,4,7,1] => [6,5,3,2,4,1,7] => [1,7,6,4,3,5,2] => ? = 4
[1,2,5,3,4,7,6] => [2,3,5,6,4,1,7] => [6,5,3,2,4,7,1] => [7,6,4,3,5,1,2] => ? = 4
Description
The number of occurrences of the pattern 123 or of the pattern 231 in a permutation.