Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000889
(load all 4 compositions to match this statistic)
Mapping
St000889: Alternating sign matrices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => 1
[[1,0],[0,1]]
 => 1
[[0,1],[1,0]]
 => 1
[[1,0,0],[0,1,0],[0,0,1]]
 => 1
[[0,1,0],[1,0,0],[0,0,1]]
 => 1
[[1,0,0],[0,0,1],[0,1,0]]
 => 1
[[0,1,0],[1,-1,1],[0,1,0]]
 => 1
[[0,0,1],[1,0,0],[0,1,0]]
 => 2
[[0,1,0],[0,0,1],[1,0,0]]
 => 2
[[0,0,1],[0,1,0],[1,0,0]]
 => 1
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => 1
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => 1
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => 1
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => 1
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => 2
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => 2
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => 1
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => 1
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => 1
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => 1
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => 1
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => 2
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => 2
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => 1
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => 2
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => 2
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => 4
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => 2
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => 4
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => 2
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => 2
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => 2
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => 2
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => 4
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => 4
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
 => 2
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => 1
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => 1
[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]]
 => 2
[[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => 2
[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]]
 => 2
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]]
 => 1
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
 => 3
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => 3
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => 3
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => 2
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => 2
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => 2
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => 3
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => 3
Description
The number of alternating sign matrices with the same antidiagonal sums. The X-ray of an alternating sign matrix $A$ is the vector of the sums of the antidiagonals of $A$, read from top to bottom. This statistic records the number of alternating sign matrices having the same X-ray as the given matrix. The analogous concept for permutations is called the degeneracy of the X-ray of the permutation in [1], see [[St000886]]. The number of alternating sign matrices determined by their X-ray is the Catalan number, see [2].