- FindStat

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Identifier

St000890: Alternating sign matrices ⟶ ℤ

Values

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

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

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

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

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

[[0,1,0],[1,-1,1],[0,1,0]] => 5

[[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]] => 3

[[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]] => 4

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

[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]] => 6

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

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

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

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

[[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]] => 6

[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]] => 8

[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]] => 6

[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]] => 6

[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]] => 6

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

[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]] => 6

[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]] => 6

[[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]] => 6

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

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

[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]] => 6

[[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]] => 6

[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]] => 6

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

[[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]] => 6

[[0,0,1,0],[1,0,-1,1],[0,0,1,0],[0,1,0,0]] => 6

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

[[0,1,0,0],[0,0,0,1],[1,-1,1,0],[0,1,0,0]] => 6

[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]] => 8

[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]] => 6

[[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]] => 4

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

[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]] => 6

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

[[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]] => 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]] => 5

[[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]] => 5

[[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]] => 7

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 7

[[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]] => 9

[[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]] => 7

[[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]] => 7

[[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]] => 7

[[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]] => 5

[[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]] => 7

[[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]] => 7

[[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]] => 5

[[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]] => 5

[[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]] => 7

[[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]] => 5

[[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]] => 5

[[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]] => 7

[[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]] => 5

[[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]] => 7

[[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]] => 7

[[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]] => 5

[[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]] => 7

[[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]] => 7

[[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]] => 5

[[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]] => 7

[[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]] => 9

[[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]] => 7

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 7

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 7

[[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]] => 5

[[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]] => 7

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$F_{2} = 2\ q^{2}$

$F_{3} = 6\ q^{3} + q^{5}$

$F_{4} = 24\ q^{4} + 16\ q^{6} + 2\ q^{8}$

$F_{5} = 120\ q^{5} + 200\ q^{7} + 94\ q^{9} + 14\ q^{11} + q^{13}$

Description

The number of nonzero entries in an alternating sign matrix.

Code

def statistic(A):
    return len([i for i in A.to_matrix().list() if i != 0])

Created

Jul 14, 2017 at 14:22 by Martin Rubey

Updated

Jul 14, 2017 at 14:22 by Martin Rubey