Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001087
Mapping
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001087: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1] => [1] => [1] => 0
[1,0,1,0]
 => [2,1] => [2,1] => [1,2] => 0
[1,1,0,0]
 => [1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0]
 => [2,3,1] => [3,2,1] => [1,3,2] => 0
[1,0,1,1,0,0]
 => [2,1,3] => [2,1,3] => [1,2,3] => 1
[1,1,0,0,1,0]
 => [1,3,2] => [1,3,2] => [1,2,3] => 1
[1,1,0,1,0,0]
 => [3,1,2] => [3,1,2] => [1,3,2] => 0
[1,1,1,0,0,0]
 => [1,2,3] => [1,2,3] => [1,2,3] => 1
[1,0,1,0,1,0,1,0]
 => [2,3,4,1] => [4,2,3,1] => [1,4,2,3] => 1
[1,0,1,0,1,1,0,0]
 => [2,3,1,4] => [3,2,1,4] => [1,3,2,4] => 1
[1,0,1,1,0,0,1,0]
 => [2,1,4,3] => [2,1,4,3] => [1,2,3,4] => 2
[1,0,1,1,0,1,0,0]
 => [2,4,1,3] => [4,2,1,3] => [1,4,3,2] => 0
[1,0,1,1,1,0,0,0]
 => [2,1,3,4] => [2,1,3,4] => [1,2,3,4] => 2
[1,1,0,0,1,0,1,0]
 => [1,3,4,2] => [1,4,3,2] => [1,2,4,3] => 1
[1,1,0,0,1,1,0,0]
 => [1,3,2,4] => [1,3,2,4] => [1,2,3,4] => 2
[1,1,0,1,0,0,1,0]
 => [3,1,4,2] => [4,1,3,2] => [1,4,2,3] => 1
[1,1,0,1,0,1,0,0]
 => [3,4,1,2] => [4,3,2,1] => [1,4,2,3] => 1
[1,1,0,1,1,0,0,0]
 => [3,1,2,4] => [3,1,2,4] => [1,3,2,4] => 1
[1,1,1,0,0,0,1,0]
 => [1,2,4,3] => [1,2,4,3] => [1,2,3,4] => 2
[1,1,1,0,0,1,0,0]
 => [1,4,2,3] => [1,4,2,3] => [1,2,4,3] => 1
[1,1,1,0,1,0,0,0]
 => [4,1,2,3] => [4,1,2,3] => [1,4,3,2] => 0
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 2
[1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,1] => [5,2,3,4,1] => [1,5,2,3,4] => 2
[1,0,1,0,1,0,1,1,0,0]
 => [2,3,4,1,5] => [4,2,3,1,5] => [1,4,2,3,5] => 2
[1,0,1,0,1,1,0,0,1,0]
 => [2,3,1,5,4] => [3,2,1,5,4] => [1,3,2,4,5] => 2
[1,0,1,0,1,1,0,1,0,0]
 => [2,3,5,1,4] => [5,2,3,1,4] => [1,5,4,2,3] => 1
[1,0,1,0,1,1,1,0,0,0]
 => [2,3,1,4,5] => [3,2,1,4,5] => [1,3,2,4,5] => 2
[1,0,1,1,0,0,1,0,1,0]
 => [2,1,4,5,3] => [2,1,5,4,3] => [1,2,3,5,4] => 2
[1,0,1,1,0,0,1,1,0,0]
 => [2,1,4,3,5] => [2,1,4,3,5] => [1,2,3,4,5] => 3
[1,0,1,1,0,1,0,0,1,0]
 => [2,4,1,5,3] => [5,2,1,4,3] => [1,5,3,2,4] => 1
[1,0,1,1,0,1,0,1,0,0]
 => [2,4,5,1,3] => [5,2,4,3,1] => [1,5,2,3,4] => 2
[1,0,1,1,0,1,1,0,0,0]
 => [2,4,1,3,5] => [4,2,1,3,5] => [1,4,3,2,5] => 1
[1,0,1,1,1,0,0,0,1,0]
 => [2,1,3,5,4] => [2,1,3,5,4] => [1,2,3,4,5] => 3
[1,0,1,1,1,0,0,1,0,0]
 => [2,1,5,3,4] => [2,1,5,3,4] => [1,2,3,5,4] => 2
[1,0,1,1,1,0,1,0,0,0]
 => [2,5,1,3,4] => [5,2,1,3,4] => [1,5,4,3,2] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [2,1,3,4,5] => [2,1,3,4,5] => [1,2,3,4,5] => 3
[1,1,0,0,1,0,1,0,1,0]
 => [1,3,4,5,2] => [1,5,3,4,2] => [1,2,5,3,4] => 2
[1,1,0,0,1,0,1,1,0,0]
 => [1,3,4,2,5] => [1,4,3,2,5] => [1,2,4,3,5] => 2
[1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4] => [1,3,2,5,4] => [1,2,3,4,5] => 3
[1,1,0,0,1,1,0,1,0,0]
 => [1,3,5,2,4] => [1,5,3,2,4] => [1,2,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,4,5] => [1,3,2,4,5] => [1,2,3,4,5] => 3
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,4,5,2] => [5,1,3,4,2] => [1,5,2,3,4] => 2
[1,1,0,1,0,0,1,1,0,0]
 => [3,1,4,2,5] => [4,1,3,2,5] => [1,4,2,3,5] => 2
[1,1,0,1,0,1,0,0,1,0]
 => [3,4,1,5,2] => [5,3,2,4,1] => [1,5,2,3,4] => 2
[1,1,0,1,0,1,0,1,0,0]
 => [3,4,5,1,2] => [5,4,3,2,1] => [1,5,2,4,3] => 1
[1,1,0,1,0,1,1,0,0,0]
 => [3,4,1,2,5] => [4,3,2,1,5] => [1,4,2,3,5] => 2
[1,1,0,1,1,0,0,0,1,0]
 => [3,1,2,5,4] => [3,1,2,5,4] => [1,3,2,4,5] => 2
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,5,2,4] => [5,1,3,2,4] => [1,5,4,2,3] => 1
[1,1,0,1,1,0,1,0,0,0]
 => [3,5,1,2,4] => [5,3,2,1,4] => [1,5,4,2,3] => 1
[1,1,0,1,1,1,0,0,0,0]
 => [3,1,2,4,5] => [3,1,2,4,5] => [1,3,2,4,5] => 2
Description
The number of occurrences of the vincular pattern |12-3 in a permutation. This is the number of occurrences of the pattern $123$, where the first matched entry is the first entry of the permutation and the other two matched entries are consecutive. In other words, this is the number of ascents whose bottom value is strictly larger than the first entry of the permutation.
Matching statistic: St000837
Mapping
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
St000837: Permutations ⟶ ℤResult quality: 34% ●values known / values provided: 34%●distinct values known / distinct values provided: 67%
Values
[1,0]
 => [1] => [1] => [1] => ? = 0
[1,0,1,0]
 => [2,1] => [2,1] => [2,1] => 0
[1,1,0,0]
 => [1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0]
 => [2,3,1] => [3,1,2] => [3,1,2] => 0
[1,0,1,1,0,0]
 => [2,1,3] => [2,1,3] => [2,1,3] => 1
[1,1,0,0,1,0]
 => [1,3,2] => [1,3,2] => [1,3,2] => 1
[1,1,0,1,0,0]
 => [3,1,2] => [2,3,1] => [3,2,1] => 0
[1,1,1,0,0,0]
 => [1,2,3] => [1,2,3] => [1,2,3] => 1
[1,0,1,0,1,0,1,0]
 => [2,3,4,1] => [4,1,2,3] => [4,1,2,3] => 1
[1,0,1,0,1,1,0,0]
 => [2,3,1,4] => [3,1,2,4] => [3,1,2,4] => 1
[1,0,1,1,0,0,1,0]
 => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2
[1,0,1,1,0,1,0,0]
 => [2,4,1,3] => [3,1,4,2] => [4,3,1,2] => 0
[1,0,1,1,1,0,0,0]
 => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 2
[1,1,0,0,1,0,1,0]
 => [1,3,4,2] => [1,4,2,3] => [1,4,2,3] => 1
[1,1,0,0,1,1,0,0]
 => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 2
[1,1,0,1,0,0,1,0]
 => [3,1,4,2] => [2,4,1,3] => [4,2,1,3] => 1
[1,1,0,1,0,1,0,0]
 => [3,4,1,2] => [3,4,1,2] => [4,1,3,2] => 1
[1,1,0,1,1,0,0,0]
 => [3,1,2,4] => [2,3,1,4] => [3,2,1,4] => 1
[1,1,1,0,0,0,1,0]
 => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 2
[1,1,1,0,0,1,0,0]
 => [1,4,2,3] => [1,3,4,2] => [1,4,3,2] => 1
[1,1,1,0,1,0,0,0]
 => [4,1,2,3] => [2,3,4,1] => [4,3,2,1] => 0
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 2
[1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,1] => [5,1,2,3,4] => [5,1,2,3,4] => 2
[1,0,1,0,1,0,1,1,0,0]
 => [2,3,4,1,5] => [4,1,2,3,5] => [4,1,2,3,5] => 2
[1,0,1,0,1,1,0,0,1,0]
 => [2,3,1,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => 2
[1,0,1,0,1,1,0,1,0,0]
 => [2,3,5,1,4] => [4,1,2,5,3] => [5,4,1,2,3] => 1
[1,0,1,0,1,1,1,0,0,0]
 => [2,3,1,4,5] => [3,1,2,4,5] => [3,1,2,4,5] => 2
[1,0,1,1,0,0,1,0,1,0]
 => [2,1,4,5,3] => [2,1,5,3,4] => [2,1,5,3,4] => 2
[1,0,1,1,0,0,1,1,0,0]
 => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 3
[1,0,1,1,0,1,0,0,1,0]
 => [2,4,1,5,3] => [3,1,5,2,4] => [5,3,1,2,4] => 1
[1,0,1,1,0,1,0,1,0,0]
 => [2,4,5,1,3] => [4,1,5,2,3] => [5,1,2,4,3] => 2
[1,0,1,1,0,1,1,0,0,0]
 => [2,4,1,3,5] => [3,1,4,2,5] => [4,3,1,2,5] => 1
[1,0,1,1,1,0,0,0,1,0]
 => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 3
[1,0,1,1,1,0,0,1,0,0]
 => [2,1,5,3,4] => [2,1,4,5,3] => [2,1,5,4,3] => 2
[1,0,1,1,1,0,1,0,0,0]
 => [2,5,1,3,4] => [3,1,4,5,2] => [5,4,3,1,2] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 3
[1,1,0,0,1,0,1,0,1,0]
 => [1,3,4,5,2] => [1,5,2,3,4] => [1,5,2,3,4] => 2
[1,1,0,0,1,0,1,1,0,0]
 => [1,3,4,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => 2
[1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 3
[1,1,0,0,1,1,0,1,0,0]
 => [1,3,5,2,4] => [1,4,2,5,3] => [1,5,4,2,3] => 1
[1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 3
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,4,5,2] => [2,5,1,3,4] => [5,2,1,3,4] => 2
[1,1,0,1,0,0,1,1,0,0]
 => [3,1,4,2,5] => [2,4,1,3,5] => [4,2,1,3,5] => 2
[1,1,0,1,0,1,0,0,1,0]
 => [3,4,1,5,2] => [3,5,1,2,4] => [5,1,3,2,4] => 2
[1,1,0,1,0,1,0,1,0,0]
 => [3,4,5,1,2] => [4,5,1,2,3] => [5,1,4,2,3] => 1
[1,1,0,1,0,1,1,0,0,0]
 => [3,4,1,2,5] => [3,4,1,2,5] => [4,1,3,2,5] => 2
[1,1,0,1,1,0,0,0,1,0]
 => [3,1,2,5,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,5,2,4] => [2,4,1,5,3] => [5,4,2,1,3] => 1
[1,1,0,1,1,0,1,0,0,0]
 => [3,5,1,2,4] => [3,4,1,5,2] => [5,4,1,3,2] => 1
[1,1,0,1,1,1,0,0,0,0]
 => [3,1,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 2
[1,1,1,0,0,0,1,0,1,0]
 => [1,2,4,5,3] => [1,2,5,3,4] => [1,2,5,3,4] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => ? = 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [2,3,4,1,6,7,5] => [4,1,2,3,7,5,6] => [4,1,2,3,7,5,6] => ? = 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [2,3,4,1,6,5,7] => [4,1,2,3,6,5,7] => [4,1,2,3,6,5,7] => ? = 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [2,3,4,6,7,1,5] => [6,1,2,3,7,4,5] => [7,1,2,3,4,6,5] => ? = 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [2,3,4,1,5,7,6] => [4,1,2,3,5,7,6] => [4,1,2,3,5,7,6] => ? = 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [2,3,4,1,7,5,6] => [4,1,2,3,6,7,5] => [4,1,2,3,7,6,5] => ? = 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => ? = 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => [3,1,2,7,4,5,6] => ? = 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => [3,1,2,6,4,5,7] => ? = 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [3,1,2,5,4,7,6] => ? = 4
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [2,3,1,5,7,4,6] => [3,1,2,6,4,7,5] => [3,1,2,7,6,4,5] => ? = 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [3,1,2,5,4,6,7] => ? = 4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [2,3,5,6,1,7,4] => [5,1,2,7,3,4,6] => [7,1,2,3,5,4,6] => ? = 4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => [3,1,2,4,7,5,6] => ? = 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [3,1,2,4,6,5,7] => ? = 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [2,3,1,6,4,7,5] => [3,1,2,5,7,4,6] => [3,1,2,7,5,4,6] => ? = 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [2,3,1,6,7,4,5] => [3,1,2,6,7,4,5] => [3,1,2,7,4,6,5] => ? = 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [2,3,1,6,4,5,7] => [3,1,2,5,6,4,7] => [3,1,2,6,5,4,7] => ? = 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [3,1,2,4,5,7,6] => ? = 4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [2,3,1,4,7,5,6] => [3,1,2,4,6,7,5] => [3,1,2,4,7,6,5] => ? = 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [2,3,1,7,4,5,6] => [3,1,2,5,6,7,4] => [3,1,2,7,6,5,4] => ? = 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => ? = 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [2,1,4,5,6,7,3] => [2,1,7,3,4,5,6] => [2,1,7,3,4,5,6] => ? = 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [2,1,4,5,6,3,7] => [2,1,6,3,4,5,7] => [2,1,6,3,4,5,7] => ? = 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,1,4,5,3,7,6] => [2,1,5,3,4,7,6] => [2,1,5,3,4,7,6] => ? = 4
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [2,1,4,5,7,3,6] => [2,1,6,3,4,7,5] => [2,1,7,6,3,4,5] => ? = 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,4,5,3,6,7] => [2,1,5,3,4,6,7] => [2,1,5,3,4,6,7] => ? = 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,1,4,3,6,7,5] => [2,1,4,3,7,5,6] => [2,1,4,3,7,5,6] => ? = 4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => [2,1,4,3,6,5,7] => ? = 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,1,4,6,3,7,5] => [2,1,5,3,7,4,6] => [2,1,7,5,3,4,6] => ? = 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [2,1,4,6,7,3,5] => [2,1,6,3,7,4,5] => [2,1,7,3,4,6,5] => ? = 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
 => [2,1,4,6,3,5,7] => [2,1,5,3,6,4,7] => [2,1,6,5,3,4,7] => ? = 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => [2,1,4,3,5,7,6] => ? = 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
 => [2,1,4,3,7,5,6] => [2,1,4,3,6,7,5] => [2,1,4,3,7,6,5] => ? = 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
 => [2,1,4,7,3,5,6] => [2,1,5,3,6,7,4] => [2,1,7,6,5,3,4] => ? = 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => [2,1,4,3,5,6,7] => ? = 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => [2,4,5,1,6,7,3] => [4,1,7,2,3,5,6] => [7,1,2,4,3,5,6] => ? = 4
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
 => [2,4,1,3,6,7,5] => [3,1,4,2,7,5,6] => [4,3,1,2,7,5,6] => ? = 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
 => [2,4,1,3,6,5,7] => [3,1,4,2,6,5,7] => [4,3,1,2,6,5,7] => ? = 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
 => [2,4,6,1,7,3,5] => [4,1,6,2,7,3,5] => [7,1,2,4,3,6,5] => ? = 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [2,4,1,3,5,7,6] => [3,1,4,2,5,7,6] => [4,3,1,2,5,7,6] => ? = 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
 => [2,4,1,3,7,5,6] => [3,1,4,2,6,7,5] => [4,3,1,2,7,6,5] => ? = 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,4,1,3,5,6,7] => [3,1,4,2,5,6,7] => [4,3,1,2,5,6,7] => ? = 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => [2,1,3,7,4,5,6] => ? = 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
 => [2,1,3,5,6,4,7] => [2,1,3,6,4,5,7] => [2,1,3,6,4,5,7] => ? = 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
 => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => [2,1,3,5,4,7,6] => ? = 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
 => [2,1,3,5,7,4,6] => [2,1,3,6,4,7,5] => [2,1,3,7,6,4,5] => ? = 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
 => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => [2,1,3,5,4,6,7] => ? = 5
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
 => [2,1,5,3,6,7,4] => [2,1,4,7,3,5,6] => [2,1,7,4,3,5,6] => ? = 4
Description
The number of ascents of distance 2 of a permutation. This is, $\operatorname{asc}_2(\pi) = | \{ i : \pi(i) < \pi(i+2) \} |$.