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Identifier

St000737: Semistandard tableaux ⟶ ℤ

Values

[[1]] => 1

[[2]] => 2

[[3]] => 3

[[4]] => 4

[[5]] => 5

[[6]] => 6

[[1,1]] => 1

[[1,2]] => 1

[[2,2]] => 2

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

[[1,3]] => 1

[[2,3]] => 2

[[3,3]] => 3

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

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

[[1,4]] => 1

[[2,4]] => 2

[[3,4]] => 3

[[4,4]] => 4

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

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

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

[[1,5]] => 1

[[2,5]] => 2

[[3,5]] => 3

[[4,5]] => 4

[[5,5]] => 5

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

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

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

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

[[1,6]] => 1

[[2,6]] => 2

[[3,6]] => 3

[[4,6]] => 4

[[5,6]] => 5

[[6,6]] => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1881 entries. <<<

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

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

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

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

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

$F_{(4, 2)} = 6\ q + 2\ q^{2}$

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

$F_{(3, 4)} = 12\ q + 8\ q^{2} + 4\ q^{3} + q^{4}$

$F_{(4, 3)} = 18\ q + 6\ q^{2} + 6\ q^{3}$

$F_{(5, 2)} = 8\ q + 3\ q^{2}$

$F_{(2, 6)} = 2\ q + 2\ q^{2} + 2\ q^{3} + 2\ q^{4} + 2\ q^{5} + q^{6}$

$F_{(3, 5)} = 16\ q + 12\ q^{2} + 8\ q^{3} + 4\ q^{4} + q^{5}$

$F_{(4, 4)} = 38\ q + 18\ q^{2} + 6\ q^{3} + 15\ q^{4}$

$F_{(5, 3)} = 32\ q + 10\ q^{2} + 15\ q^{3}$

$F_{(6, 2)} = 10\ q + 5\ q^{2}$

$F_{(5, 4)} = 88\ q + 34\ q^{2} + 18\ q^{3} + 51\ q^{4}$

$F_{(5, 5)} = 192\ q + 90\ q^{2} + 42\ q^{3} + 36\ q^{4} + 131\ q^{5}$

Description

The last entry on the main diagonal of a semistandard tableau.

Code

def statistic(T):
    m = None
    for i, row in enumerate(T):
        try:
            m = row[i]
        except IndexError:
            break
    return m

Created

Mar 29, 2017 at 11:10 by Christian Stump

Updated

Aug 09, 2019 at 12:40 by Martin Rubey