- FindStat

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Identifier

St000894: Alternating sign matrices ⟶ ℤ

Values

[[1,0],[0,1]] => 2

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

[[1,0,0],[0,1,0],[0,0,1]] => 3

[[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]] => 0

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

[[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]] => 4

[[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]] => 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]] => 2

[[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]] => 0

[[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]] => -2

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

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

[[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]] => -1

[[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]] => 0

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

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

[[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]] => -1

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

[[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]] => 1

[[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]] => 2

[[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]] => 1

[[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]] => 1

[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]] => 2

[[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]] => 0

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

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

[[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]] => 2

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

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

[[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]] => 5

[[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]] => 3

[[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]] => 3

[[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]] => 1

[[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]] => 2

[[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]] => 2

[[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]] => 3

[[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]] => 3

[[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]] => 1

[[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]] => 1

[[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]] => 2

[[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]] => 1

[[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]] => 2

[[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]] => 2

[[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]] => 2

[[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]] => 1

[[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]] => 2

[[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]] => 3

[[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]] => 1

[[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]] => 2

[[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]] => 2

[[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]] => 2

[[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]] => 3

[[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]] => 3

[[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]] => 2

[[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]] => 2

[[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]] => 3

[[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]] => 3

[[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]] => 3

[[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]] => -1

[[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]] => 0

[[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]] => 0

[[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

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

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Description

The trace of an alternating sign matrix.

Code

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

Created

Jul 15, 2017 at 08:06 by Martin Rubey

Updated

Jul 15, 2017 at 08:06 by Martin Rubey