- FindStat

Identifier

St001407: Semistandard tableaux ⟶ ℤ

Values

[[1,2]] => 1

[[2,2]] => 1

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

[[1,3]] => 1

[[2,3]] => 0

[[3,3]] => 1

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

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

[[1,4]] => 1

[[2,4]] => 0

[[3,4]] => 0

[[4,4]] => 1

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

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

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

[[1,5]] => 1

[[2,5]] => 0

[[3,5]] => 0

[[4,5]] => 0

[[5,5]] => 1

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

[[2],[5]] => 0

[[3],[5]] => 0

[[4],[5]] => 1

[[1,6]] => 1

[[2,6]] => 0

[[3,6]] => 0

[[4,6]] => 0

[[5,6]] => 0

[[6,6]] => 1

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

[[2],[6]] => 0

[[3],[6]] => 0

[[4],[6]] => 0

[[5],[6]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,3,5]] => 1

[[1,4,5]] => 1

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

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

[[2,3,5]] => 0

[[2,4,5]] => 0

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

[[3,3,5]] => 1

[[3,4,5]] => 0

[[3,5,5]] => 1

[[4,4,5]] => 1

[[4,5,5]] => 1

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

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

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

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

[[1,3],[5]] => 1

[[1,5],[3]] => 1

[[1,4],[5]] => 1

[[1,5],[4]] => 1

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

>>> Load all 317 entries. <<<

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Description

The number of minimal entries in a semistandard tableau.
An entry is minimal if replacing it with a smaller entry does not yield a semistandard tableau.

Code

def statistic(T):
    S = [[e for e in row] for row in T]
    count = 0
    for i, row in enumerate(S):
        for j, e in enumerate(row):
            S[i][j] = e-1
            try:
                _ = SemistandardTableau(S)
            except StandardError:
                count += 1
            S[i][j] = e
    return count

Created

Jun 02, 2019 at 23:09 by Martin Rubey

Updated

Jun 02, 2019 at 23:09 by Martin Rubey