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Identifier

St001401: Semistandard tableaux ⟶ ℤ

Values

[[1]] => 1

[[1,1]] => 1

[[1,2]] => 2

[[2,2]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1200 entries. <<<

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$F_{(2, 2)} = q + 2\ q^{2}$

$F_{(3, 2)} = q + 4\ q^{2}$

$F_{(3, 3)} = q + 8\ q^{2} + 4\ q^{3}$

$F_{(4, 2)} = q + 7\ q^{2}$

$F_{(4, 3)} = q + 14\ q^{2} + 15\ q^{3}$

$F_{(5, 2)} = q + 10\ q^{2}$

$F_{(4, 4)} = q + 21\ q^{2} + 45\ q^{3} + 10\ q^{4}$

$F_{(5, 3)} = q + 20\ q^{2} + 36\ q^{3}$

$F_{(5, 4)} = q + 30\ q^{2} + 108\ q^{3} + 52\ q^{4}$

$F_{(5, 5)} = q + 40\ q^{2} + 216\ q^{3} + 208\ q^{4} + 26\ q^{5}$

Description

The number of distinct entries in a semistandard tableau.

Code

def statistic(T):
    return len(set(T.entries()))

Created

May 29, 2019 at 12:16 by Martin Rubey

Updated

May 29, 2019 at 12:16 by Martin Rubey