- FindStat

edit this statistic or download as text // json

Identifier

St000199: Alternating sign matrices ⟶ ℤ

Values

[[1]] => 1

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

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

[[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]] => 2

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

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

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

[[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]] => 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]] => 4

[[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]] => 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]] => 3

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

[[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]] => 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]] => 3

[[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]] => 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]] => 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]] => 2

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

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

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

[[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]] => 2

[[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]] => 2

[[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]] => 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]] => 2

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

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

[[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]] => 1

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

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

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

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

[[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]] => 5

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

>>> Load all 481 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

$F_{1} = q$

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

$F_{3} = 2\ q + 3\ q^{2} + 2\ q^{3}$

$F_{4} = 7\ q + 14\ q^{2} + 14\ q^{3} + 7\ q^{4}$

$F_{5} = 42\ q + 105\ q^{2} + 135\ q^{3} + 105\ q^{4} + 42\ q^{5}$

Description

The column of the unique '1' in the last row of the alternating sign matrix.

Code

def statistic(a):
    return a.to_matrix().nrows()+1-(a.rotate_cw().rotate_cw().to_monotone_triangle()[-1][0])

Created

May 16, 2014 at 08:15 by Dakota Ihli

Updated

Feb 17, 2015 at 17:16 by Martin Rubey