- FindStat

edit this statistic or download as text // json

Identifier

St001805: Semistandard tableaux ⟶ ℤ

Values

[[1,2]] => 0

[[2,2]] => 1

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

[[1,3]] => 0

[[2,3]] => 0

[[3,3]] => 1

[[1],[3]] => 2

[[2],[3]] => 2

[[1,4]] => 0

[[2,4]] => 0

[[3,4]] => 0

[[4,4]] => 1

[[1],[4]] => 2

[[2],[4]] => 2

[[3],[4]] => 2

[[1,5]] => 0

[[2,5]] => 0

[[3,5]] => 0

[[4,5]] => 0

[[5,5]] => 1

[[1],[5]] => 2

[[2],[5]] => 2

[[3],[5]] => 2

[[4],[5]] => 2

[[1,6]] => 0

[[2,6]] => 0

[[3,6]] => 0

[[4,6]] => 0

[[5,6]] => 0

[[6,6]] => 1

[[1],[6]] => 2

[[2],[6]] => 2

[[3],[6]] => 2

[[4],[6]] => 2

[[5],[6]] => 2

[[1,7]] => 0

[[2,7]] => 0

[[3,7]] => 0

[[4,7]] => 0

[[5,7]] => 0

[[6,7]] => 0

[[7,7]] => 1

[[1],[7]] => 2

[[2],[7]] => 2

[[3],[7]] => 2

[[4],[7]] => 2

[[5],[7]] => 2

[[6],[7]] => 2

[[1,8]] => 0

[[2,8]] => 0

[[3,8]] => 0

[[4,8]] => 0

[[5,8]] => 0

[[6,8]] => 0

[[7,8]] => 0

[[8,8]] => 1

[[1],[8]] => 2

[[2],[8]] => 2

[[3],[8]] => 2

[[4],[8]] => 2

[[5],[8]] => 2

[[6],[8]] => 2

[[7],[8]] => 2

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

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

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

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

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

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

[[1,2,3]] => 0

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

[[2,2,3]] => 0

[[2,3,3]] => 0

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

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

[[1,2],[3]] => 1

[[1,3],[2]] => 0

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

[[2,2],[3]] => 1

[[2,3],[3]] => 1

[[1],[2],[3]] => 3

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

[[1,2,4]] => 0

[[1,3,4]] => 0

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

[[2,2,4]] => 0

[[2,3,4]] => 0

[[2,4,4]] => 0

[[3,3,4]] => 0

[[3,4,4]] => 0

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

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

[[1,2],[4]] => 1

[[1,4],[2]] => 0

[[1,3],[4]] => 1

[[1,4],[3]] => 0

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

[[2,2],[4]] => 1

[[2,3],[4]] => 1

[[2,4],[3]] => 0

[[2,4],[4]] => 1

>>> 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

The maximal overlap of a cylindrical tableau associated with a semistandard tableau.
A cylindrical tableau associated with a semistandard Young tableau $T$ is the skew semistandard tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle.
The overlap, recorded in this statistic, equals $\max_C\big(2\ell(T) - \ell(C)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux.

Code

def statistic(T):
    if not T:
        return 0
    w = len(T[0])
    l = len(T)
    d = 0
    while d < l and len(T[d]) == w and T[0][w-1] <= T[l-1-d][0]:
        d += 1
    return d

Created

Jun 06, 2022 at 20:05 by Martin Rubey

Updated

Jun 06, 2022 at 20:05 by Martin Rubey