Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000227
Mapping
St000227: Alternating sign matrices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,0],[0,1]]
 => 2
[[0,1],[1,0]]
 => 0
[[1,0,0],[0,1,0],[0,0,1]]
 => 8
[[0,1,0],[1,0,0],[0,0,1]]
 => 6
[[1,0,0],[0,0,1],[0,1,0]]
 => 4
[[0,1,0],[1,-1,1],[0,1,0]]
 => 5
[[0,0,1],[1,0,0],[0,1,0]]
 => 2
[[0,1,0],[0,0,1],[1,0,0]]
 => 3
[[0,0,1],[0,1,0],[1,0,0]]
 => 0
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => 20
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => 18
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => 16
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => 17
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => 14
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => 15
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => 12
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => 14
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => 12
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => 15
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => 16
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => 13
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => 14
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => 11
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => 10
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => 11
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => 12
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => 8
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => 9
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => 10
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => 6
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => 11
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => 12
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => 9
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => 13
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
 => 10
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => 6
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => 7
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]
 => 8
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => 4
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => 8
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
 => 9
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
 => 5
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => 6
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => 2
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => 11
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => 8
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => 6
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => 7
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => 3
[[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
 => 4
Description
The osculating paths major index of an alternating sign matrix. This is the sum of the major indices of the Dyck paths in the tuple of osculating paths in bijection with the alternating sign matrix.