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Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001965
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St001965: Alternating sign matrices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> 0
[[1,0],[0,1]]
=> 1
[[0,1],[1,0]]
=> 0
[[1,0,0],[0,1,0],[0,0,1]]
=> 2
[[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]]
=> 2
[[0,0,1],[1,0,0],[0,1,0]]
=> 1
[[0,1,0],[0,0,1],[1,0,0]]
=> 1
[[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]]
=> 3
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
=> 2
[[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]]
=> 3
[[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]]
=> 2
[[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]]
=> 3
[[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]]
=> 3
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
=> 3
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
=> 2
[[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]]
=> 3
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
=> 3
[[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]]
=> 2
[[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]]
=> 1
[[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]]
=> 3
[[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]]
=> 3
[[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]]
=> 2
[[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]]
=> 1
[[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]]
=> 3
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]]
=> 2
[[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]]
=> 1
[[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]]
=> 1
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
=> 1
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
=> 2
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
=> 1
Description
The number of decreasable positions in the corner sum matrix of an alternating sign matrix.
A decreasable position in a corner sum matrix is an entry such that the matrix obtained by decreasing it by one yields the corner sum matrix of some alternating sign matrix.
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