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Identifier

St000896: Alternating sign matrices ⟶ ℤ

Values

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

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

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

[[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]] => 2

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

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

[[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]] => 0

[[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]] => 2

[[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]] => 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]] => 4

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

[[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]] => 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]] => 3

[[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]] => 4

[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]] => 4

[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]] => 4

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

[[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]] => 3

[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]] => 4

[[0,1,0,0],[0,0,1,0],[1,-1,0,1],[0,1,0,0]] => 4

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

[[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]] => 2

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

[[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]] => 3

[[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]] => 4

[[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]] => 4

[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]] => 4

[[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]] => 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]] => 4

[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]] => 4

[[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]] => 0

[[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]] => 2

[[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]] => 2

[[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]] => 3

[[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]] => 3

[[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]] => 2

[[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]] => 2

[[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]] => 3

[[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]] => 3

[[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]] => 3

[[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]] => 3

[[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]] => 4

[[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]] => 3

[[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]] => 3

[[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]] => 3

[[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]] => 3

[[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]] => 4

[[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]] => 3

[[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]] => 2

[[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]] => 3

[[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]] => 3

[[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]] => 3

[[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]] => 3

[[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]] => 3

[[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]] => 2

[[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]] => 2

[[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]] => 4

[[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]] => 5

[[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]] => 5

[[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

[[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]] => 2

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Description

The number of zeros on the main diagonal of an alternating sign matrix.

Code

def statistic(A):
    M = A.to_matrix()
    return [M[i][i] for i in range(M.nrows())].count(0)

Created

Jul 15, 2017 at 07:59 by Martin Rubey

Updated

Jul 15, 2017 at 07:59 by Martin Rubey