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Identifier

St001925: Alternating sign matrices ⟶ ℤ

Values

[[1]] => 0

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

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

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

[[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]] => 0

[[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]] => 2

[[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]] => 3

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

[[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]] => 3

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

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

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

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

[[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]] => 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]] => 1

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

[[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]] => 1

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

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

[[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]] => 3

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

[[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]] => 3

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

[[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]] => 3

[[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]] => 1

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

[[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]] => 1

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

[[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]] => 3

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

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

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

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

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

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

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 2

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 2

[[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]] => 2

[[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]] => 2

[[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]] => 2

[[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]] => 2

[[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]] => 4

[[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]] => 2

[[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]] => 2

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 2

[[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]] => 4

[[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]] => 2

[[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]] => 4

[[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]] => 2

[[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]] => 4

[[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]] => 2

[[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]] => 2

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 2

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 2

[[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]] => 4

[[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]] => 4

[[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]] => 4

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Description

The minimal number of zeros in a row of an alternating sign matrix.

Code

def statistic(m):
    return min(list(r).count(Integer(0)) for r in m.to_matrix())

Created

Sep 06, 2023 at 11:42 by Martin Rubey

Updated

Sep 06, 2023 at 11:42 by Martin Rubey