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Identifier

St001450: Plane partitions ⟶ ℤ

Values

[[1]] => 1

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

[[2]] => 2

[[1,1]] => 1

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

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

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

[[3]] => 3

[[2,1]] => 1

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

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

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

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

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

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

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

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

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

[[4]] => 4

[[3,1]] => 1

[[2,2]] => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5]] => 5

[[4,1]] => 1

[[3,2]] => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[6]] => 6

[[5,1]] => 1

[[4,2]] => 2

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

[[3,3]] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = q$

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

$F_{3} = 5\ q + q^{3}$

$F_{4} = 10\ q + 2\ q^{2} + q^{4}$

$F_{5} = 20\ q + 3\ q^{2} + q^{5}$

$F_{6} = 38\ q + 7\ q^{2} + 2\ q^{3} + q^{6}$

$F_{7} = 72\ q + 10\ q^{2} + 3\ q^{3} + q^{7}$

$F_{8} = 130\ q + 22\ q^{2} + 5\ q^{3} + 2\ q^{4} + q^{8}$

$F_{9} = 235\ q + 33\ q^{2} + 10\ q^{3} + 3\ q^{4} + q^{9}$

$F_{10} = 413\ q + 64\ q^{2} + 15\ q^{3} + 5\ q^{4} + 2\ q^{5} + q^{10}$

Description

The minimum height of a plane partition.

Code

def statistic(P):
    return P[-1][-1]

Created

Jul 26, 2019 at 17:42 by Joseph Bernstein

Updated

Jul 27, 2019 at 16:34 by Christian Stump