- FindStat

edit this statistic or download as text // json

Identifier

St001030: Alternating sign matrices ⟶ ℤ

Values

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

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

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

[[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]] => 3

[[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]] => 1

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

[[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]] => 4

[[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]] => 3

[[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]] => 4

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

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

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

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

[[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]] => 4

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

[[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]] => 3

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

[[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]] => 4

[[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]] => 3

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

[[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]] => 3

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

[[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]] => 2

[[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]] => 2

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

[[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]] => 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]] => 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]] => 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]] => 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]] => 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]] => 6

[[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]] => 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]] => 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]] => 6

[[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]] => 6

[[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]] => 7

[[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]] => 6

[[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]] => 6

[[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]] => 5

[[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]] => 6

[[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]] => 5

[[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]] => 6

[[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]] => 4

[[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]] => 6

[[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]] => 5

[[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]] => 4

[[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]] => 5

[[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]] => 4

[[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]] => 4

[[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]] => 4

[[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]] => 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]] => 6

[[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]] => 4

[[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]] => 6

[[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]] => 6

[[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]] => 6

[[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]] => 6

[[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]] => 6

[[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]] => 6

>>> Load all 1200 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign matrix.

Code

def statistic(A):
    odd = {0: 0, 1: 1, 2: 1, 3: 1, 4: 0, 5: 0}
    even = {0: 1, 1: 0, 2: 0, 3: 0, 4: 1, 5: 1}
    h = sum(even[entry] if is_even(i+j) else odd[entry]
            for j, row in enumerate(A.to_six_vertex_model())
            for i, entry in enumerate(row))
    return (h - (A.to_matrix().nrows()//2)) / 2

Created

Nov 05, 2017 at 19:10 by Martin Rubey

Updated

Nov 05, 2017 at 19:10 by Martin Rubey