Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000837
(load all 2 compositions to match this statistic)
Mapping
St000837: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => 0
[2,1] => 0
[1,2,3] => 1
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 2
[1,2,4,3] => 2
[1,3,2,4] => 2
[1,3,4,2] => 1
[1,4,2,3] => 1
[1,4,3,2] => 1
[2,1,3,4] => 2
[2,1,4,3] => 2
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 0
[2,4,3,1] => 1
[3,1,2,4] => 1
[3,1,4,2] => 2
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 1
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 0
[1,2,3,4,5] => 3
[1,2,3,5,4] => 3
[1,2,4,3,5] => 3
[1,2,4,5,3] => 2
[1,2,5,3,4] => 2
[1,2,5,4,3] => 2
[1,3,2,4,5] => 3
[1,3,2,5,4] => 3
[1,3,4,2,5] => 2
[1,3,4,5,2] => 2
[1,3,5,2,4] => 1
[1,3,5,4,2] => 2
[1,4,2,3,5] => 2
[1,4,2,5,3] => 3
[1,4,3,2,5] => 2
[1,4,3,5,2] => 2
[1,4,5,2,3] => 1
[1,4,5,3,2] => 1
Description
The number of ascents of distance 2 of a permutation. This is, $\operatorname{asc}_2(\pi) = | \{ i : \pi(i) < \pi(i+2) \} |$.
Matching statistic: St000836
(load all 2 compositions to match this statistic)
Mapping
Mp00069: Permutations —complement⟶ Permutations
St000836: Permutations ⟶ ℤResult quality: 73% ●values known / values provided: 73%●distinct values known / distinct values provided: 83%
Values
[1,2] => [2,1] => 0
[2,1] => [1,2] => 0
[1,2,3] => [3,2,1] => 1
[1,3,2] => [3,1,2] => 1
[2,1,3] => [2,3,1] => 1
[2,3,1] => [2,1,3] => 0
[3,1,2] => [1,3,2] => 0
[3,2,1] => [1,2,3] => 0
[1,2,3,4] => [4,3,2,1] => 2
[1,2,4,3] => [4,3,1,2] => 2
[1,3,2,4] => [4,2,3,1] => 2
[1,3,4,2] => [4,2,1,3] => 1
[1,4,2,3] => [4,1,3,2] => 1
[1,4,3,2] => [4,1,2,3] => 1
[2,1,3,4] => [3,4,2,1] => 2
[2,1,4,3] => [3,4,1,2] => 2
[2,3,1,4] => [3,2,4,1] => 1
[2,3,4,1] => [3,2,1,4] => 1
[2,4,1,3] => [3,1,4,2] => 0
[2,4,3,1] => [3,1,2,4] => 1
[3,1,2,4] => [2,4,3,1] => 1
[3,1,4,2] => [2,4,1,3] => 2
[3,2,1,4] => [2,3,4,1] => 1
[3,2,4,1] => [2,3,1,4] => 1
[3,4,1,2] => [2,1,4,3] => 0
[3,4,2,1] => [2,1,3,4] => 0
[4,1,2,3] => [1,4,3,2] => 1
[4,1,3,2] => [1,4,2,3] => 1
[4,2,1,3] => [1,3,4,2] => 1
[4,2,3,1] => [1,3,2,4] => 0
[4,3,1,2] => [1,2,4,3] => 0
[4,3,2,1] => [1,2,3,4] => 0
[1,2,3,4,5] => [5,4,3,2,1] => 3
[1,2,3,5,4] => [5,4,3,1,2] => 3
[1,2,4,3,5] => [5,4,2,3,1] => 3
[1,2,4,5,3] => [5,4,2,1,3] => 2
[1,2,5,3,4] => [5,4,1,3,2] => 2
[1,2,5,4,3] => [5,4,1,2,3] => 2
[1,3,2,4,5] => [5,3,4,2,1] => 3
[1,3,2,5,4] => [5,3,4,1,2] => 3
[1,3,4,2,5] => [5,3,2,4,1] => 2
[1,3,4,5,2] => [5,3,2,1,4] => 2
[1,3,5,2,4] => [5,3,1,4,2] => 1
[1,3,5,4,2] => [5,3,1,2,4] => 2
[1,4,2,3,5] => [5,2,4,3,1] => 2
[1,4,2,5,3] => [5,2,4,1,3] => 3
[1,4,3,2,5] => [5,2,3,4,1] => 2
[1,4,3,5,2] => [5,2,3,1,4] => 2
[1,4,5,2,3] => [5,2,1,4,3] => 1
[1,4,5,3,2] => [5,2,1,3,4] => 1
[1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => ? = 5
[1,2,3,4,5,7,6] => [7,6,5,4,3,1,2] => ? = 5
[1,2,3,4,6,5,7] => [7,6,5,4,2,3,1] => ? = 5
[1,2,3,4,6,7,5] => [7,6,5,4,2,1,3] => ? = 4
[1,2,3,4,7,5,6] => [7,6,5,4,1,3,2] => ? = 4
[1,2,3,4,7,6,5] => [7,6,5,4,1,2,3] => ? = 4
[1,2,3,5,4,6,7] => [7,6,5,3,4,2,1] => ? = 5
[1,2,3,5,4,7,6] => [7,6,5,3,4,1,2] => ? = 5
[1,2,3,5,6,4,7] => [7,6,5,3,2,4,1] => ? = 4
[1,2,3,5,6,7,4] => [7,6,5,3,2,1,4] => ? = 4
[1,2,3,5,7,4,6] => [7,6,5,3,1,4,2] => ? = 3
[1,2,3,5,7,6,4] => [7,6,5,3,1,2,4] => ? = 4
[1,2,3,6,4,5,7] => [7,6,5,2,4,3,1] => ? = 4
[1,2,3,6,4,7,5] => [7,6,5,2,4,1,3] => ? = 5
[1,2,3,6,5,4,7] => [7,6,5,2,3,4,1] => ? = 4
[1,2,3,6,5,7,4] => [7,6,5,2,3,1,4] => ? = 4
[1,2,3,6,7,4,5] => [7,6,5,2,1,4,3] => ? = 3
[1,2,3,6,7,5,4] => [7,6,5,2,1,3,4] => ? = 3
[1,2,3,7,4,5,6] => [7,6,5,1,4,3,2] => ? = 4
[1,2,3,7,4,6,5] => [7,6,5,1,4,2,3] => ? = 4
[1,2,3,7,5,4,6] => [7,6,5,1,3,4,2] => ? = 4
[1,2,3,7,5,6,4] => [7,6,5,1,3,2,4] => ? = 3
[1,2,3,7,6,4,5] => [7,6,5,1,2,4,3] => ? = 3
[1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3
[1,2,4,3,5,6,7] => [7,6,4,5,3,2,1] => ? = 5
[1,2,4,3,5,7,6] => [7,6,4,5,3,1,2] => ? = 5
[1,2,4,3,6,5,7] => [7,6,4,5,2,3,1] => ? = 5
[1,2,4,3,6,7,5] => [7,6,4,5,2,1,3] => ? = 4
[1,2,4,3,7,5,6] => [7,6,4,5,1,3,2] => ? = 4
[1,2,4,3,7,6,5] => [7,6,4,5,1,2,3] => ? = 4
[1,2,4,5,3,6,7] => [7,6,4,3,5,2,1] => ? = 4
[1,2,4,5,3,7,6] => [7,6,4,3,5,1,2] => ? = 4
[1,2,4,5,6,3,7] => [7,6,4,3,2,5,1] => ? = 4
[1,2,4,5,6,7,3] => [7,6,4,3,2,1,5] => ? = 4
[1,2,4,5,7,3,6] => [7,6,4,3,1,5,2] => ? = 3
[1,2,4,5,7,6,3] => [7,6,4,3,1,2,5] => ? = 4
[1,2,4,6,3,5,7] => [7,6,4,2,5,3,1] => ? = 3
[1,2,4,6,3,7,5] => [7,6,4,2,5,1,3] => ? = 4
[1,2,4,6,5,3,7] => [7,6,4,2,3,5,1] => ? = 4
[1,2,4,6,5,7,3] => [7,6,4,2,3,1,5] => ? = 4
[1,2,4,6,7,3,5] => [7,6,4,2,1,5,3] => ? = 3
[1,2,4,6,7,5,3] => [7,6,4,2,1,3,5] => ? = 3
[1,2,4,7,3,5,6] => [7,6,4,1,5,3,2] => ? = 3
[1,2,4,7,3,6,5] => [7,6,4,1,5,2,3] => ? = 3
[1,2,4,7,5,3,6] => [7,6,4,1,3,5,2] => ? = 4
[1,2,4,7,5,6,3] => [7,6,4,1,3,2,5] => ? = 3
[1,2,4,7,6,3,5] => [7,6,4,1,2,5,3] => ? = 3
[1,2,4,7,6,5,3] => [7,6,4,1,2,3,5] => ? = 3
[1,2,5,3,4,6,7] => [7,6,3,5,4,2,1] => ? = 4
[1,2,5,3,4,7,6] => [7,6,3,5,4,1,2] => ? = 4
Description
The number of descents of distance 2 of a permutation. This is, $\operatorname{des}_2(\pi) = | \{ i : \pi(i) > \pi(i+2) \} |$.