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Your data matches 58 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000432
Mapping
Mp00035: Dyck paths —to alternating sign matrix⟶ Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St000432: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0]
 => [[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [1,2] => 0
[1,0,1,1,0,0]
 => [[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [1,2] => 0
[1,1,0,0,1,0]
 => [[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [2,1] => 0
[1,1,0,1,0,0]
 => [[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [1,2] => 0
[1,1,1,0,0,0]
 => [[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => [1,2] => 0
[1,0,1,0,1,0,1,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,2,3,4] => [1,2,3] => 0
[1,0,1,0,1,1,0,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,2,4,3] => [1,2,3] => 0
[1,0,1,1,0,0,1,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [1,3,2] => 0
[1,0,1,1,0,1,0,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [1,2,3] => 0
[1,0,1,1,1,0,0,0]
 => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [1,2,3] => 0
[1,1,0,0,1,0,1,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [2,1,3,4] => [2,1,3] => 0
[1,1,0,0,1,1,0,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [2,1,4,3] => [2,1,3] => 0
[1,1,0,1,0,0,1,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [1,3,2] => 0
[1,1,0,1,0,1,0,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [1,2,3] => 0
[1,1,0,1,1,0,0,0]
 => [[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [1,2,3] => 0
[1,1,1,0,0,0,1,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [3,1,2,4] => [3,1,2] => 1
[1,1,1,0,0,1,0,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [2,1,3] => 0
[1,1,1,0,1,0,0,0]
 => [[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [1,2,3] => 0
[1,1,1,1,0,0,0,0]
 => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [4,1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,2,3,4,5] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [1,2,4,3] => 0
[1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [1,3,2,4] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [1,2,4,3] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [1,4,2,3] => 1
[1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,1,3,4,5] => [2,1,3,4] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [2,1,3,4] => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [2,1,4,3] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [2,1,3,4] => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [2,1,5,3,4] => [2,1,3,4] => 0
[1,1,0,1,0,0,1,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [1,3,2,4] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [1,2,4,3] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [1,4,2,3] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [1,2,3,4] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [3,1,2,4,5] => [3,1,2,4] => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [3,1,2,5,4] => [3,1,2,4] => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [2,1,4,3] => 0
Description
The number of occurrences of the pattern 231 or of the pattern 312 in a permutation.
Matching statistic: St000437
Mapping
Mp00035: Dyck paths —to alternating sign matrix⟶ Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St000437: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0]
 => [[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [1,2] => 0
[1,0,1,1,0,0]
 => [[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [1,2] => 0
[1,1,0,0,1,0]
 => [[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [2,1] => 0
[1,1,0,1,0,0]
 => [[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [1,2] => 0
[1,1,1,0,0,0]
 => [[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => [1,2] => 0
[1,0,1,0,1,0,1,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,2,3,4] => [1,2,3] => 0
[1,0,1,0,1,1,0,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,2,4,3] => [1,2,3] => 0
[1,0,1,1,0,0,1,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [1,3,2] => 0
[1,0,1,1,0,1,0,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [1,2,3] => 0
[1,0,1,1,1,0,0,0]
 => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [1,2,3] => 0
[1,1,0,0,1,0,1,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [2,1,3,4] => [2,1,3] => 0
[1,1,0,0,1,1,0,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [2,1,4,3] => [2,1,3] => 0
[1,1,0,1,0,0,1,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [1,3,2] => 0
[1,1,0,1,0,1,0,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [1,2,3] => 0
[1,1,0,1,1,0,0,0]
 => [[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [1,2,3] => 0
[1,1,1,0,0,0,1,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [3,1,2,4] => [3,1,2] => 1
[1,1,1,0,0,1,0,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [2,1,3] => 0
[1,1,1,0,1,0,0,0]
 => [[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [1,2,3] => 0
[1,1,1,1,0,0,0,0]
 => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [4,1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,2,3,4,5] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [1,2,4,3] => 0
[1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [1,3,2,4] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [1,2,4,3] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [1,4,2,3] => 1
[1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,1,3,4,5] => [2,1,3,4] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [2,1,3,4] => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [2,1,4,3] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [2,1,3,4] => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [2,1,5,3,4] => [2,1,3,4] => 0
[1,1,0,1,0,0,1,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [1,3,2,4] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [1,2,4,3] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [1,4,2,3] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [1,2,3,4] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [3,1,2,4,5] => [3,1,2,4] => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [3,1,2,5,4] => [3,1,2,4] => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [2,1,4,3] => 0
Description
The number of occurrences of the pattern 312 or of the pattern 321 in a permutation.
Matching statistic: St000217
(load all 2 compositions to match this statistic)
Mapping
Mp00035: Dyck paths —to alternating sign matrix⟶ Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
St000217: Permutations ⟶ ℤResult quality: 87% ●values known / values provided: 87%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0]
 => [[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [1,2] => 0
[1,0,1,1,0,0]
 => [[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [1,2] => 0
[1,1,0,0,1,0]
 => [[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [2,1] => 0
[1,1,0,1,0,0]
 => [[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [1,2] => 0
[1,1,1,0,0,0]
 => [[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => [1,2] => 0
[1,0,1,0,1,0,1,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,2,3,4] => [1,2,3] => 0
[1,0,1,0,1,1,0,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,2,4,3] => [1,2,3] => 0
[1,0,1,1,0,0,1,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [1,3,2] => 0
[1,0,1,1,0,1,0,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [1,2,3] => 0
[1,0,1,1,1,0,0,0]
 => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [1,2,3] => 0
[1,1,0,0,1,0,1,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [2,1,3,4] => [2,1,3] => 0
[1,1,0,0,1,1,0,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [2,1,4,3] => [2,1,3] => 0
[1,1,0,1,0,0,1,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [1,3,2] => 0
[1,1,0,1,0,1,0,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [1,2,3] => 0
[1,1,0,1,1,0,0,0]
 => [[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [1,2,3] => 0
[1,1,1,0,0,0,1,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [3,1,2,4] => [3,1,2] => 1
[1,1,1,0,0,1,0,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [2,1,3] => 0
[1,1,1,0,1,0,0,0]
 => [[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [1,2,3] => 0
[1,1,1,1,0,0,0,0]
 => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [4,1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,2,3,4,5] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [1,2,4,3] => 0
[1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [1,3,2,4] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [1,2,4,3] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [1,4,2,3] => 1
[1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [1,2,3,4] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,1,3,4,5] => [2,1,3,4] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [2,1,3,4] => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [2,1,4,3] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [2,1,3,4] => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [2,1,5,3,4] => [2,1,3,4] => 0
[1,1,0,1,0,0,1,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [1,3,2,4] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [1,2,4,3] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [1,2,3,4] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [1,4,2,3] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [1,3,2,4] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [1,2,3,4] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [1,2,3,4] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [3,1,2,4,5] => [3,1,2,4] => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [3,1,2,5,4] => [3,1,2,4] => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [2,1,4,3] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]
 => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]
 => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,8,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,4,3,8,5,6,7] => [1,2,4,3,5,6,7] => ? = 0
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,1,0,0,0,-1,1],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,8,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,4,3,8,5,6,7] => [1,2,4,3,5,6,7] => ? = 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]
 => [1,4,2,3,5,6,7,8] => [1,4,2,3,5,6,7] => ? = 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7] => ? = 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,1,0,-1,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,6,7] => ? = 0
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0],[0,1,0,0,-1,1,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,4,2,3,5,8,6,7] => [1,4,2,3,5,6,7] => ? = 1
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,-1,1,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,3,2,4,8,5,6,7] => [1,3,2,4,5,6,7] => ? = 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,-1,1,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,4,3,8,5,6,7] => [1,2,4,3,5,6,7] => ? = 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0],[0,1,0,0,0,-1,1,0],[0,0,1,0,0,0,-1,1],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,8,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,4,2,3,8,5,6,7] => [1,4,2,3,5,6,7] => ? = 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,-1,1],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,3,2,8,4,5,6,7] => [1,3,2,4,5,6,7] => ? = 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,8,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]
 => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7] => ? = 0
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,3,2,4,8,5,6,7] => [1,3,2,4,5,6,7] => ? = 0
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,3,2,4,8,5,6,7] => [1,3,2,4,5,6,7] => ? = 0
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,3,2,8,4,5,6,7] => [1,3,2,4,5,6,7] => ? = 0
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,4,3,8,5,6,7] => [1,2,4,3,5,6,7] => ? = 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7] => ? = 0
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,6,7] => ? = 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]
 => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6] => ? = 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,1,0],[0,0,0,0,0,1,-1,1],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,7] => ? = 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,1,0,0],[0,0,0,0,1,-1,0,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,1,0,0,0],[0,0,0,1,-1,0,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7] => ? = 1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,1,0,-1,1,0],[0,0,0,0,1,0,-1,1],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,1,0,0],[0,0,0,1,0,-1,0,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1]]
 => [1,2,3,7,4,5,6,8] => [1,2,3,7,4,5,6] => ? = 3
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,1,0,0,0,0],[0,0,1,-1,0,0,1,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,1,0,-1,1,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7,8] => [1,2,3,6,4,5,7] => ? = 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
 => [[0,1,0,0,0,0,0,0],[1,-1,1,0,0,0,0,0],[0,1,-1,0,1,0,0,0],[0,0,1,0,-1,0,1,0],[0,0,0,1,0,0,-1,1],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0]]
 => [1,2,3,4,8,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
Description
The number of occurrences of the pattern 312 in a permutation.
Matching statistic: St001193
(load all 31 compositions to match this statistic)
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
St001193: Dyck paths ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 67%
Values
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => 0
[1,0,1,1,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 0
[1,1,0,0,1,0]
 => [2]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 0
[1,1,0,1,0,0]
 => [1]
 => [1,0,1,0]
 => [1,0,1,0]
 => 0
[1,1,1,0,0,0]
 => []
 => []
 => []
 => ? = 0
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 0
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 0
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 0
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0]
 => 0
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => 0
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 0
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0]
 => 0
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => 0
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 0
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => 1
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 0
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0,1,0]
 => [1,0,1,0]
 => 0
[1,1,1,1,0,0,0,0]
 => []
 => []
 => []
 => ? = 0
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => 0
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 0
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => 0
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => 0
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 0
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => 0
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 0
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 0
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 1
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 0
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 0
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 0
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => 0
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => 0
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 0
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => 0
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 0
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0]
 => 0
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => 0
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => 0
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0]
 => 0
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 1
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 0
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 0
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0]
 => 0
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => 1
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 1
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => 0
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => 0
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 0
[1,1,1,1,1,0,0,0,0,0]
 => []
 => []
 => []
 => ? = 0
[1,1,1,1,1,1,0,0,0,0,0,0]
 => []
 => []
 => []
 => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [6,5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [5,5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [6,4,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [5,4,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [4,4,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [6,5,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [5,5,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [6,4,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [5,4,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [4,4,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [6,3,3,3,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [5,3,3,3,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [4,3,3,3,2,1]
 => [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [3,3,3,3,2,1]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [6,5,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [5,5,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [6,4,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [5,4,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [4,4,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [6,5,3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [5,5,3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [6,4,3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [5,4,3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [4,4,3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [6,3,3,2,2,1]
 => [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
 => ? = 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [5,3,3,2,2,1]
 => [1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [4,3,3,2,2,1]
 => [1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [3,3,3,2,2,1]
 => [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [6,5,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [5,5,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]
 => ? = 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [6,4,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [5,4,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [4,4,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [6,3,2,2,2,1]
 => [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0,1,0]
 => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [5,3,2,2,2,1]
 => [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [4,3,2,2,2,1]
 => [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [3,3,2,2,2,1]
 => [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [6,2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [5,2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [4,2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [3,2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
 => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [6,5,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [5,5,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]
 => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [6,4,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [5,4,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,1,0,0,1,0]
 => ? = 0
Description
The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module.
Matching statistic: St000709
(load all 8 compositions to match this statistic)
Mapping
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St000709: Permutations ⟶ ℤResult quality: 42% ●values known / values provided: 42%●distinct values known / distinct values provided: 83%
Values
[1,0,1,0,1,0]
 => [3,2,1] => [1,2,3] => 0
[1,0,1,1,0,0]
 => [2,3,1] => [2,1,3] => 0
[1,1,0,0,1,0]
 => [3,1,2] => [1,3,2] => 0
[1,1,0,1,0,0]
 => [2,1,3] => [2,3,1] => 0
[1,1,1,0,0,0]
 => [1,2,3] => [3,2,1] => 0
[1,0,1,0,1,0,1,0]
 => [4,3,2,1] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0]
 => [3,4,2,1] => [2,1,3,4] => 0
[1,0,1,1,0,0,1,0]
 => [4,2,3,1] => [1,3,2,4] => 0
[1,0,1,1,0,1,0,0]
 => [3,2,4,1] => [2,3,1,4] => 0
[1,0,1,1,1,0,0,0]
 => [2,3,4,1] => [3,2,1,4] => 0
[1,1,0,0,1,0,1,0]
 => [4,3,1,2] => [1,2,4,3] => 0
[1,1,0,0,1,1,0,0]
 => [3,4,1,2] => [2,1,4,3] => 0
[1,1,0,1,0,0,1,0]
 => [4,2,1,3] => [1,3,4,2] => 0
[1,1,0,1,0,1,0,0]
 => [3,2,1,4] => [2,3,4,1] => 0
[1,1,0,1,1,0,0,0]
 => [2,3,1,4] => [3,2,4,1] => 0
[1,1,1,0,0,0,1,0]
 => [4,1,2,3] => [1,4,3,2] => 1
[1,1,1,0,0,1,0,0]
 => [3,1,2,4] => [2,4,3,1] => 0
[1,1,1,0,1,0,0,0]
 => [2,1,3,4] => [3,4,2,1] => 0
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => [4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => [2,1,3,4,5] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => [1,3,2,4,5] => 0
[1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => [2,3,1,4,5] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => [3,2,1,4,5] => 0
[1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => [1,2,4,3,5] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => [2,1,4,3,5] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => [1,3,4,2,5] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => [2,3,4,1,5] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => [3,2,4,1,5] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => [1,4,3,2,5] => 1
[1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => [2,4,3,1,5] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => [3,4,2,1,5] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [4,3,2,1,5] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => [1,2,3,5,4] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => [2,1,3,5,4] => 0
[1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => [1,3,2,5,4] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [4,3,5,1,2] => [2,3,1,5,4] => 0
[1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => [3,2,1,5,4] => 0
[1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,3] => [1,2,4,5,3] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [4,5,2,1,3] => [2,1,4,5,3] => 0
[1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,4] => [1,3,4,5,2] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => [2,3,4,5,1] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => [3,2,4,5,1] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => [1,4,3,5,2] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [4,2,3,1,5] => [2,4,3,5,1] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [3,2,4,1,5] => [3,4,2,5,1] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [2,3,4,1,5] => [4,3,2,5,1] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => [1,2,5,4,3] => 1
[1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => [2,1,5,4,3] => 1
[1,1,1,0,0,1,0,0,1,0]
 => [5,3,1,2,4] => [1,3,5,4,2] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [6,7,5,4,3,2,1] => [2,1,3,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [6,5,7,4,3,2,1] => [2,3,1,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [5,6,7,4,3,2,1] => [3,2,1,4,5,6,7] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [6,7,4,5,3,2,1] => [2,1,4,3,5,6,7] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [6,5,4,7,3,2,1] => [2,3,4,1,5,6,7] => ? = 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [5,6,4,7,3,2,1] => [3,2,4,1,5,6,7] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [6,4,5,7,3,2,1] => [2,4,3,1,5,6,7] => ? = 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [5,4,6,7,3,2,1] => [3,4,2,1,5,6,7] => ? = 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [4,5,6,7,3,2,1] => [4,3,2,1,5,6,7] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [6,7,5,3,4,2,1] => [2,1,3,5,4,6,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [6,5,7,3,4,2,1] => [2,3,1,5,4,6,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [5,6,7,3,4,2,1] => [3,2,1,5,4,6,7] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [6,7,4,3,5,2,1] => [2,1,4,5,3,6,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [6,5,4,3,7,2,1] => [2,3,4,5,1,6,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [5,6,4,3,7,2,1] => [3,2,4,5,1,6,7] => ? = 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [6,4,5,3,7,2,1] => [2,4,3,5,1,6,7] => ? = 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [5,4,6,3,7,2,1] => [3,4,2,5,1,6,7] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [4,5,6,3,7,2,1] => [4,3,2,5,1,6,7] => ? = 0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [6,7,3,4,5,2,1] => [2,1,5,4,3,6,7] => ? = 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [6,5,3,4,7,2,1] => [2,3,5,4,1,6,7] => ? = 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [5,6,3,4,7,2,1] => [3,2,5,4,1,6,7] => ? = 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [6,4,3,5,7,2,1] => [2,4,5,3,1,6,7] => ? = 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [5,4,3,6,7,2,1] => [3,4,5,2,1,6,7] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [4,5,3,6,7,2,1] => [4,3,5,2,1,6,7] => ? = 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [7,3,4,5,6,2,1] => [1,5,4,3,2,6,7] => ? = 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [6,3,4,5,7,2,1] => [2,5,4,3,1,6,7] => ? = 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [5,3,4,6,7,2,1] => [3,5,4,2,1,6,7] => ? = 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [4,3,5,6,7,2,1] => [4,5,3,2,1,6,7] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [3,4,5,6,7,2,1] => [5,4,3,2,1,6,7] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [6,7,5,4,2,3,1] => [2,1,3,4,6,5,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [6,5,7,4,2,3,1] => [2,3,1,4,6,5,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [5,6,7,4,2,3,1] => [3,2,1,4,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [6,7,4,5,2,3,1] => [2,1,4,3,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [6,5,4,7,2,3,1] => [2,3,4,1,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
 => [5,6,4,7,2,3,1] => [3,2,4,1,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
 => [6,4,5,7,2,3,1] => [2,4,3,1,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
 => [5,4,6,7,2,3,1] => [3,4,2,1,6,5,7] => ? = 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [4,5,6,7,2,3,1] => [4,3,2,1,6,5,7] => ? = 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [6,7,5,3,2,4,1] => [2,1,3,5,6,4,7] => ? = 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
 => [6,5,7,3,2,4,1] => [2,3,1,5,6,4,7] => ? = 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
 => [5,6,7,3,2,4,1] => [3,2,1,5,6,4,7] => ? = 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
 => [6,7,4,3,2,5,1] => [2,1,4,5,6,3,7] => ? = 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [6,5,4,3,2,7,1] => [2,3,4,5,6,1,7] => ? = 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
 => [5,6,4,3,2,7,1] => [3,2,4,5,6,1,7] => ? = 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
 => [6,4,5,3,2,7,1] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
 => [5,4,6,3,2,7,1] => [3,4,2,5,6,1,7] => ? = 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
 => [4,5,6,3,2,7,1] => [4,3,2,5,6,1,7] => ? = 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
 => [6,7,3,4,2,5,1] => [2,1,5,4,6,3,7] => ? = 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
 => [6,5,3,4,2,7,1] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
 => [5,6,3,4,2,7,1] => [3,2,5,4,6,1,7] => ? = 0
Description
The number of occurrences of 14-2-3 or 14-3-2. The number of permutations avoiding both of these patterns is the case $k=2$ of the third item in Corollary 34 of [1].
Matching statistic: St000408
(load all 2 compositions to match this statistic)
Mapping
Mp00035: Dyck paths —to alternating sign matrix⟶ Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
St000408: Permutations ⟶ ℤResult quality: 35% ●values known / values provided: 35%●distinct values known / distinct values provided: 67%
Values
[1,0,1,0,1,0]
 => [[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [2,3,1] => 0
[1,0,1,1,0,0]
 => [[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [2,1,3] => 0
[1,1,0,0,1,0]
 => [[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [3,2,1] => 0
[1,1,0,1,0,0]
 => [[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [2,1,3] => 0
[1,1,1,0,0,0]
 => [[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => [1,3,2] => 0
[1,0,1,0,1,0,1,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,2,3,4] => [2,3,4,1] => 0
[1,0,1,0,1,1,0,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,0,1,1,0,0,1,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [2,4,3,1] => 0
[1,0,1,1,0,1,0,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,0,1,1,1,0,0,0]
 => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,0,0,1,0,1,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [2,1,3,4] => [3,2,4,1] => 0
[1,1,0,0,1,1,0,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [2,1,4,3] => [3,2,1,4] => 0
[1,1,0,1,0,0,1,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [2,4,3,1] => 0
[1,1,0,1,0,1,0,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,1,0,1,1,0,0,0]
 => [[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,1,0,0,0,1,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [3,1,2,4] => [4,2,3,1] => 1
[1,1,1,0,0,1,0,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [3,2,1,4] => 0
[1,1,1,0,1,0,0,0]
 => [[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,1,1,0,0,0,0]
 => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [4,1,2,3] => [1,3,4,2] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,2,3,4,5] => [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [2,4,3,5,1] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [2,5,3,4,1] => 1
[1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [2,1,4,5,3] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,1,3,4,5] => [3,2,4,5,1] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [3,2,4,1,5] => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [3,2,5,4,1] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [3,2,4,1,5] => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [2,1,5,3,4] => [3,2,1,5,4] => 0
[1,1,0,1,0,0,1,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [2,4,3,5,1] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [2,5,3,4,1] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [2,1,4,5,3] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [3,1,2,4,5] => [4,2,3,5,1] => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [3,1,2,5,4] => [4,2,3,1,5] => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [3,2,5,4,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,5,3,4,6,7] => [2,3,6,4,5,7,1] => ? = 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,5,3,4,7,6] => [2,3,6,4,5,1,7] => ? = 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,6,3,4,5,7] => [2,3,7,4,5,6,1] => ? = 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,5,3,4,7,6] => [2,3,6,4,5,1,7] => ? = 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,7,3,4,5,6] => [2,3,1,5,6,7,4] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,5,6,7] => [2,4,3,5,6,7,1] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,4,7,5,6] => [2,4,3,5,1,7,6] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,5,4,6,7] => [2,4,3,6,5,7,1] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,5,4,7,6] => [2,4,3,6,5,1,7] => ? = 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => ? = 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,4,7,5,6] => [2,4,3,5,1,7,6] => ? = 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,6,4,5,7] => [2,4,3,7,5,6,1] => ? = 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,3,2,5,4,7,6] => [2,4,3,6,5,1,7] => ? = 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,4,7,5,6] => [2,4,3,5,1,7,6] => ? = 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,7,4,5,6] => [2,4,3,1,6,7,5] => ? = 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => ? = 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
Description
The number of occurrences of the pattern 4231 in a permutation. It is a necessary condition that a permutation $\pi$ avoids this pattern for the Schubert variety associated to $\pi$ to be smooth [2].
Matching statistic: St000440
(load all 2 compositions to match this statistic)
Mapping
Mp00035: Dyck paths —to alternating sign matrix⟶ Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
St000440: Permutations ⟶ ℤResult quality: 35% ●values known / values provided: 35%●distinct values known / distinct values provided: 67%
Values
[1,0,1,0,1,0]
 => [[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [2,3,1] => 0
[1,0,1,1,0,0]
 => [[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [2,1,3] => 0
[1,1,0,0,1,0]
 => [[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [3,2,1] => 0
[1,1,0,1,0,0]
 => [[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [2,1,3] => 0
[1,1,1,0,0,0]
 => [[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => [1,3,2] => 0
[1,0,1,0,1,0,1,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,2,3,4] => [2,3,4,1] => 0
[1,0,1,0,1,1,0,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,0,1,1,0,0,1,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [2,4,3,1] => 0
[1,0,1,1,0,1,0,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,0,1,1,1,0,0,0]
 => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,0,0,1,0,1,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [2,1,3,4] => [3,2,4,1] => 0
[1,1,0,0,1,1,0,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [2,1,4,3] => [3,2,1,4] => 0
[1,1,0,1,0,0,1,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [2,4,3,1] => 0
[1,1,0,1,0,1,0,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,1,0,1,1,0,0,0]
 => [[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,1,0,0,0,1,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [3,1,2,4] => [4,2,3,1] => 1
[1,1,1,0,0,1,0,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [3,2,1,4] => 0
[1,1,1,0,1,0,0,0]
 => [[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,1,1,0,0,0,0]
 => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [4,1,2,3] => [1,3,4,2] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,2,3,4,5] => [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [2,4,3,5,1] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [2,5,3,4,1] => 1
[1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [2,1,4,5,3] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,1,3,4,5] => [3,2,4,5,1] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [3,2,4,1,5] => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [3,2,5,4,1] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [3,2,4,1,5] => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [2,1,5,3,4] => [3,2,1,5,4] => 0
[1,1,0,1,0,0,1,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [2,4,3,5,1] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [2,5,3,4,1] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [2,1,4,5,3] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [3,1,2,4,5] => [4,2,3,5,1] => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [3,1,2,5,4] => [4,2,3,1,5] => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [3,2,5,4,1] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,5,3,4,6,7] => [2,3,6,4,5,7,1] => ? = 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,5,3,4,7,6] => [2,3,6,4,5,1,7] => ? = 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,6,3,4,5,7] => [2,3,7,4,5,6,1] => ? = 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,5,3,4,7,6] => [2,3,6,4,5,1,7] => ? = 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,7,3,4,5,6] => [2,3,1,5,6,7,4] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,5,6,7] => [2,4,3,5,6,7,1] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,4,7,5,6] => [2,4,3,5,1,7,6] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,5,4,6,7] => [2,4,3,6,5,7,1] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,5,4,7,6] => [2,4,3,6,5,1,7] => ? = 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => ? = 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,4,7,5,6] => [2,4,3,5,1,7,6] => ? = 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,6,4,5,7] => [2,4,3,7,5,6,1] => ? = 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,3,2,5,4,7,6] => [2,4,3,6,5,1,7] => ? = 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,4,7,5,6] => [2,4,3,5,1,7,6] => ? = 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,7,4,5,6] => [2,4,3,1,6,7,5] => ? = 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => ? = 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
Description
The number of occurrences of the pattern 4132 or of the pattern 4231 in a permutation. There is a bijection between permutations avoiding these two pattern and Schröder paths [1,2].
Matching statistic: St000622
Mapping
Mp00035: Dyck paths —to alternating sign matrix⟶ Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
St000622: Permutations ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 67%
Values
[1,0,1,0,1,0]
 => [[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [2,3,1] => 0
[1,0,1,1,0,0]
 => [[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [2,1,3] => 0
[1,1,0,0,1,0]
 => [[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [3,2,1] => 0
[1,1,0,1,0,0]
 => [[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [2,1,3] => 0
[1,1,1,0,0,0]
 => [[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => [1,3,2] => 0
[1,0,1,0,1,0,1,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,2,3,4] => [2,3,4,1] => 0
[1,0,1,0,1,1,0,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,0,1,1,0,0,1,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [2,4,3,1] => 0
[1,0,1,1,0,1,0,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,0,1,1,1,0,0,0]
 => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,0,0,1,0,1,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [2,1,3,4] => [3,2,4,1] => 0
[1,1,0,0,1,1,0,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [2,1,4,3] => [3,2,1,4] => 0
[1,1,0,1,0,0,1,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [2,4,3,1] => 0
[1,1,0,1,0,1,0,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,1,0,1,1,0,0,0]
 => [[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,1,0,0,0,1,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [3,1,2,4] => [4,2,3,1] => 1
[1,1,1,0,0,1,0,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [3,2,1,4] => 0
[1,1,1,0,1,0,0,0]
 => [[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,1,1,0,0,0,0]
 => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [4,1,2,3] => [1,3,4,2] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,2,3,4,5] => [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [2,4,3,5,1] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [2,5,3,4,1] => 1
[1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [2,1,4,5,3] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,1,3,4,5] => [3,2,4,5,1] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [3,2,4,1,5] => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [3,2,5,4,1] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [3,2,4,1,5] => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [2,1,5,3,4] => [3,2,1,5,4] => 0
[1,1,0,1,0,0,1,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [2,4,3,5,1] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [2,5,3,4,1] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [2,1,4,5,3] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [3,1,2,4,5] => [4,2,3,5,1] => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [3,1,2,5,4] => [4,2,3,1,5] => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [3,2,5,4,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => ? = 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,5,3,4,6,7] => [2,3,6,4,5,7,1] => ? = 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,5,3,4,7,6] => [2,3,6,4,5,1,7] => ? = 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,6,3,4,5,7] => [2,3,7,4,5,6,1] => ? = 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,5,3,4,7,6] => [2,3,6,4,5,1,7] => ? = 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,7,3,4,5,6] => [2,3,1,5,6,7,4] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,5,6,7] => [2,4,3,5,6,7,1] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,4,7,5,6] => [2,4,3,5,1,7,6] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,5,4,6,7] => [2,4,3,6,5,7,1] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,5,4,7,6] => [2,4,3,6,5,1,7] => ? = 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => ? = 0
Description
The number of occurrences of the patterns 2143 or 4231 in a permutation. It is a necessary and sufficient condition that a permutation $\pi$ avoids these two patterns for the Schubert variety associated to $\pi$ to be smooth [1].
Matching statistic: St001559
Mapping
Mp00035: Dyck paths —to alternating sign matrix⟶ Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
St001559: Permutations ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 67%
Values
[1,0,1,0,1,0]
 => [[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [2,3,1] => 0
[1,0,1,1,0,0]
 => [[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [2,1,3] => 0
[1,1,0,0,1,0]
 => [[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [3,2,1] => 0
[1,1,0,1,0,0]
 => [[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [2,1,3] => 0
[1,1,1,0,0,0]
 => [[0,0,1],[1,0,0],[0,1,0]]
 => [3,1,2] => [1,3,2] => 0
[1,0,1,0,1,0,1,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,2,3,4] => [2,3,4,1] => 0
[1,0,1,0,1,1,0,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,0,1,1,0,0,1,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [2,4,3,1] => 0
[1,0,1,1,0,1,0,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,0,1,1,1,0,0,0]
 => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,0,0,1,0,1,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [2,1,3,4] => [3,2,4,1] => 0
[1,1,0,0,1,1,0,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [2,1,4,3] => [3,2,1,4] => 0
[1,1,0,1,0,0,1,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [2,4,3,1] => 0
[1,1,0,1,0,1,0,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,3,1,4] => 0
[1,1,0,1,1,0,0,0]
 => [[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,1,0,0,0,1,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [3,1,2,4] => [4,2,3,1] => 1
[1,1,1,0,0,1,0,0]
 => [[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [3,2,1,4] => 0
[1,1,1,0,1,0,0,0]
 => [[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [2,1,4,3] => 0
[1,1,1,1,0,0,0,0]
 => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [4,1,2,3] => [1,3,4,2] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,2,3,4,5] => [2,3,4,5,1] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [2,4,3,5,1] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [2,5,3,4,1] => 1
[1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [2,1,4,5,3] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,1,3,4,5] => [3,2,4,5,1] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [3,2,4,1,5] => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [3,2,5,4,1] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [3,2,4,1,5] => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [2,1,5,3,4] => [3,2,1,5,4] => 0
[1,1,0,1,0,0,1,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [2,4,3,5,1] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,3,5,4,1] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [2,3,4,1,5] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [2,5,3,4,1] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [2,4,3,1,5] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,2,5,3,4] => [2,3,1,5,4] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [1,5,2,3,4] => [2,1,4,5,3] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [3,1,2,4,5] => [4,2,3,5,1] => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [3,1,2,5,4] => [4,2,3,1,5] => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [3,2,5,4,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,5,6,7] => [2,3,4,5,6,7,1] => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => ? = 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => ? = 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => ? = 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,5,3,4,6,7] => [2,3,6,4,5,7,1] => ? = 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,5,3,4,7,6] => [2,3,6,4,5,1,7] => ? = 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => ? = 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => ? = 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,0,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,4,5,7] => [2,3,4,7,5,6,1] => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => ? = 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,1,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,4,7,5,6] => [2,3,4,5,1,7,6] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,1,0,-1,0,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,6,3,4,5,7] => [2,3,7,4,5,6,1] => ? = 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,5,3,4,7,6] => [2,3,6,4,5,1,7] => ? = 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,4,3,7,5,6] => [2,3,5,4,1,7,6] => ? = 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,1,0,0,-1,1],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,3,7,4,5,6] => [2,3,4,1,6,7,5] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,2,7,3,4,5,6] => [2,3,1,5,6,7,4] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,5,6,7] => [2,4,3,5,6,7,1] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [2,4,3,5,6,1,7] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0]]
 => [1,3,2,4,7,5,6] => [2,4,3,5,1,7,6] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,5,4,6,7] => [2,4,3,6,5,7,1] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,5,4,7,6] => [2,4,3,6,5,1,7] => ? = 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [2,4,3,5,7,6,1] => ? = 0
Description
The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. This statistic is the difference between [[St001558]] and [[St000018]]. A permutation is '''smooth''' if and only if this number is zero. Equivalently, this number is zero if and only if the permutation avoids the two patterns $4231$ and $3412$.
Matching statistic: St001745
Mapping
Mp00137: Dyck paths —to symmetric ASM⟶ Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
St001745: Permutations ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 67%
Values
[1,0,1,0,1,0]
 => [[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [3,2,1] => 0
[1,0,1,1,0,0]
 => [[1,0,0],[0,0,1],[0,1,0]]
 => [1,3,2] => [2,3,1] => 0
[1,1,0,0,1,0]
 => [[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [3,1,2] => 0
[1,1,0,1,0,0]
 => [[0,1,0],[1,-1,1],[0,1,0]]
 => [1,3,2] => [2,3,1] => 0
[1,1,1,0,0,0]
 => [[0,0,1],[0,1,0],[1,0,0]]
 => [3,2,1] => [1,2,3] => 0
[1,0,1,0,1,0,1,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,2,3,4] => [4,3,2,1] => 0
[1,0,1,0,1,1,0,0]
 => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,2,4,3] => [3,4,2,1] => 0
[1,0,1,1,0,0,1,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [4,2,3,1] => 0
[1,0,1,1,0,1,0,0]
 => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [3,4,2,1] => 0
[1,0,1,1,1,0,0,0]
 => [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => [1,4,3,2] => [2,3,4,1] => 0
[1,1,0,0,1,0,1,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [2,1,3,4] => [4,3,1,2] => 0
[1,1,0,0,1,1,0,0]
 => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [2,1,4,3] => [3,4,1,2] => 0
[1,1,0,1,0,0,1,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [4,2,3,1] => 0
[1,1,0,1,0,1,0,0]
 => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [3,4,2,1] => 0
[1,1,0,1,1,0,0,0]
 => [[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => [1,4,3,2] => [2,3,4,1] => 0
[1,1,1,0,0,0,1,0]
 => [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => [3,2,1,4] => [4,1,2,3] => 1
[1,1,1,0,0,1,0,0]
 => [[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [3,4,1,2] => 0
[1,1,1,0,1,0,0,0]
 => [[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
 => [1,4,3,2] => [2,3,4,1] => 0
[1,1,1,1,0,0,0,0]
 => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
 => [4,3,2,1] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,2,3,4,5] => [5,4,3,2,1] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [4,5,3,2,1] => 0
[1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [5,3,4,2,1] => 0
[1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [4,5,3,2,1] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
 => [1,2,5,4,3] => [3,4,5,2,1] => 0
[1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [5,4,2,3,1] => 0
[1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [4,5,2,3,1] => 0
[1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [5,3,4,2,1] => 0
[1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [4,5,3,2,1] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
 => [1,2,5,4,3] => [3,4,5,2,1] => 0
[1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,4,3,2,5] => [5,2,3,4,1] => 1
[1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [4,5,2,3,1] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
 => [1,2,5,4,3] => [3,4,5,2,1] => 0
[1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
 => [1,5,4,3,2] => [2,3,4,5,1] => 0
[1,1,0,0,1,0,1,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,1,3,4,5] => [5,4,3,1,2] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [4,5,3,1,2] => 0
[1,1,0,0,1,1,0,0,1,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [5,3,4,1,2] => 0
[1,1,0,0,1,1,0,1,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [2,1,3,5,4] => [4,5,3,1,2] => 0
[1,1,0,0,1,1,1,0,0,0]
 => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
 => [2,1,5,4,3] => [3,4,5,1,2] => 0
[1,1,0,1,0,0,1,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [5,4,2,3,1] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [4,5,2,3,1] => 0
[1,1,0,1,0,1,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [5,3,4,2,1] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]]
 => [1,2,3,5,4] => [4,5,3,2,1] => 0
[1,1,0,1,0,1,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
 => [1,2,5,4,3] => [3,4,5,2,1] => 0
[1,1,0,1,1,0,0,0,1,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [1,4,3,2,5] => [5,2,3,4,1] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]]
 => [1,3,2,5,4] => [4,5,2,3,1] => 0
[1,1,0,1,1,0,1,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]]
 => [1,2,5,4,3] => [3,4,5,2,1] => 0
[1,1,0,1,1,1,0,0,0,0]
 => [[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
 => [1,5,4,3,2] => [2,3,4,5,1] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [3,2,1,4,5] => [5,4,1,2,3] => 1
[1,1,1,0,0,0,1,1,0,0]
 => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [3,2,1,5,4] => [4,5,1,2,3] => 1
[1,1,1,0,0,1,0,0,1,0]
 => [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [5,3,4,1,2] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => ? = 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [7,5,6,4,3,2,1] => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => ? = 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
 => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [7,6,4,5,3,2,1] => ? = 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [7,5,6,4,3,2,1] => ? = 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => ? = 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
 => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => ? = 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,5,4,7] => [7,4,5,6,3,2,1] => ? = 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => ? = 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
 => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => ? = 0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]
 => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,5,6,7] => [7,6,5,3,4,2,1] => ? = 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [7,5,6,3,4,2,1] => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => ? = 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
 => [1,2,4,3,7,6,5] => [5,6,7,3,4,2,1] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,3,5,4,6,7] => [7,6,4,5,3,2,1] => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,4,6,5,7] => [7,5,6,4,3,2,1] => ? = 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => ? = 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
 => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => ? = 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,5,4,7] => [7,4,5,6,3,2,1] => ? = 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => ? = 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
 => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => ? = 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]
 => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => ? = 0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,2,5,4,3,6,7] => [7,6,3,4,5,2,1] => ? = 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,2,5,4,3,7,6] => [6,7,3,4,5,2,1] => ? = 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,2,4,3,6,5,7] => [7,5,6,3,4,2,1] => ? = 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => ? = 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
 => [1,2,4,3,7,6,5] => [5,6,7,3,4,2,1] => ? = 0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
 => [1,2,3,6,5,4,7] => [7,4,5,6,3,2,1] => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => ? = 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
 => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => ? = 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0]]
 => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => ? = 0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,0,1]]
 => [1,2,6,5,4,3,7] => [7,3,4,5,6,2,1] => ? = 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,-1,1],[0,0,0,0,0,1,0]]
 => [1,2,5,4,3,7,6] => [6,7,3,4,5,2,1] => ? = 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,-1,1],[0,0,1,0,-1,1,0],[0,0,0,0,1,0,0]]
 => [1,2,4,3,7,6,5] => [5,6,7,3,4,2,1] => ? = 0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0]]
 => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => ? = 0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
 => [[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]
 => [1,2,7,6,5,4,3] => [3,4,5,6,7,2,1] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,5,6,7] => [7,6,5,4,2,3,1] => ? = 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [6,7,5,4,2,3,1] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [7,5,6,4,2,3,1] => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,0,0,1,0]]
 => [1,3,2,4,5,7,6] => [6,7,5,4,2,3,1] => ? = 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
 => [1,3,2,4,7,6,5] => [5,6,7,4,2,3,1] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
 => [1,3,2,5,4,6,7] => [7,6,4,5,2,3,1] => ? = 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0]]
 => [1,3,2,5,4,7,6] => [6,7,4,5,2,3,1] => ? = 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0],[0,0,0,0,0,0,1]]
 => [1,3,2,4,6,5,7] => [7,5,6,4,2,3,1] => ? = 0
Description
The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. Let $\nu$ be a (partial) permutation of $[k]$ with $m$ letters together with dashes between some of its letters. An occurrence of $\nu$ in a permutation $\tau$ is a subsequence $\tau_{a_1},\dots,\tau_{a_m}$ such that $a_i + 1 = a_{i+1}$ whenever there is a dash between the $i$-th and the $(i+1)$-st letter of $\nu$, which is order isomorphic to $\nu$. Thus, $\nu$ is a vincular pattern, except that it is not required to be a permutation. An arrow pattern of size $k$ consists of such a generalized vincular pattern $\nu$ and arrows $b_1\to c_1, b_2\to c_2,\dots$, such that precisely the numbers $1,\dots,k$ appear in the vincular pattern and the arrows. Let $\Phi$ be the map [[Mp00087]]. Let $\tau$ be a permutation and $\sigma = \Phi(\tau)$. Then a subsequence $w = (x_{a_1},\dots,x_{a_m})$ of $\tau$ is an occurrence of the arrow pattern if $w$ is an occurrence of $\nu$, for each arrow $b\to c$ we have $\sigma(x_b) = x_c$ and $x_1 < x_2 < \dots < x_k$.
The following 48 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001330The hat guessing number of a graph. St001964The interval resolution global dimension of a poset. St001613The binary logarithm of the size of the center of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St000741The Colin de Verdière graph invariant. St000022The number of fixed points of a permutation. St000119The number of occurrences of the pattern 321 in a permutation. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000153The number of adjacent cycles of a permutation. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000223The number of nestings in the permutation. St000366The number of double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000546The number of global descents of a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St000035The number of left outer peaks of a permutation. St000884The number of isolated descents of a permutation. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St000007The number of saliances of the permutation. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000834The number of right outer peaks of a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000404The number of occurrences of the pattern 3241 or of the pattern 4231 in a permutation. St000647The number of big descents of a permutation. St000862The number of parts of the shifted shape of a permutation. St001301The first Betti number of the order complex associated with the poset. St001396Number of triples of incomparable elements in a finite poset. St000908The length of the shortest maximal antichain in a poset. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St000914The sum of the values of the Möbius function of a poset. St001845The number of join irreducibles minus the rank of a lattice. St000181The number of connected components of the Hasse diagram for the poset. St001890The maximum magnitude of the Möbius function of a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St001490The number of connected components of a skew partition. St001533The largest coefficient of the Poincare polynomial of the poset cone. St000068The number of minimal elements in a poset. St000629The defect of a binary word. St001722The number of minimal chains with small intervals between a binary word and the top element. St001850The number of Hecke atoms of a permutation. St001867The number of alignments of type EN of a signed permutation.