- FindStat

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Identifier

St001260: Alternating sign matrices ⟶ ℤ

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]] => 0

[[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]] => 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]] => 0

[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]] => 1

[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]] => 1

[[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]] => 0

[[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]] => 0

[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]] => 0

[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]] => 0

[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]] => 1

[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]] => 0

[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]] => 0

[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]] => 1

[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]] => 1

[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]] => 0

[[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]] => 1

[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]] => 0

[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]] => 1

[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]] => 0

[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]] => 0

[[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]] => 0

[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]] => 0

[[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]] => 0

[[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]] => 0

[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]] => 1

[[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]] => 1

[[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]] => 0

[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]] => 1

[[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]] => 1

[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]] => 1

[[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

[[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]] => 1

[[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

[[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]] => 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]] => 1

[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => 1

[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]] => 1

[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]] => 1

[[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]] => 1

[[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]] => 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

[[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]] => 0

[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]] => 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]] => 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

[[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]] => 0

[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => 0

[[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => 1

[[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => 1

[[0,0,1,0,0],[0,1,-1,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => 0

[[0,0,0,1,0],[0,1,0,0,0],[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],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]] => 1

[[0,1,0,0,0],[1,-1,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]] => 0

[[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]] => 1

[[0,1,0,0,0],[0,0,1,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]] => 0

[[0,0,1,0,0],[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,0,0,1]] => 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

[[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]] => 0

[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 0

[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 1

[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 0

[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 1

[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 0

[[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 1

[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]] => 1

[[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]] => 1

[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]] => 1

[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]] => 1

[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]] => 0

[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]] => 1

[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]] => 1

[[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]] => 1

[[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

[[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]] => 1

[[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

[[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]] => 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]] => 1

[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => 1

[[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]] => 1

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Description

The permanent of an alternating sign matrix.

Code

def statistic(A):
    return A.to_matrix().permanent()

Created

Sep 23, 2018 at 14:20 by Martin Rubey

Updated

Sep 23, 2018 at 14:20 by Martin Rubey