Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000134
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Mapping
St000134: 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]]
 => 2
[[0,1],[1,0]]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => 3
[[0,1,0],[1,0,0],[0,0,1]]
 => 2
[[1,0,0],[0,0,1],[0,1,0]]
 => 2
[[0,1,0],[1,-1,1],[0,1,0]]
 => 3
[[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]]
 => 3
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => 4
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => 8
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => 2
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => 8
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => 8
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => 8
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => 8
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => 8
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => 2
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => 8
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => 4
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => 8
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => 8
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => 8
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => 8
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => 8
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => 8
[[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]]
 => 2
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => 8
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => 8
[[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => 8
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]]
 => 8
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => 2
[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]]
 => 8
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
 => 8
[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => 8
[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]]
 => 8
[[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]]
 => 8
[[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]]
 => 4
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
 => 8
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => 2
[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => 8
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => 8
[[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]]
 => 8
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => 8
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => 2
Description
The size of the orbit of an alternating sign matrix under gyration. Wieland defined gyration in [2] and proved that the action rotates the link pattern of the associated fully-packed loop. It was also proved in [1] that gyration is in equivariant bijection with rowmotion on the alternating sign matrix poset.