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Identifier

St001920: Plane partitions ⟶ ℤ

Values

[[1]] => 1

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

[[2]] => 2

[[1,1]] => 2

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

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

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

[[3]] => 3

[[2,1]] => 2

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

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

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

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

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

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

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

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

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

[[4]] => 4

[[3,1]] => 3

[[2,2]] => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5]] => 5

[[4,1]] => 4

[[3,2]] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[6]] => 6

[[5,1]] => 5

[[4,2]] => 4

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

[[3,3]] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The minimal size of an ambient cube that contains the plane partition.
This is the maximum of the number of partitions, the length of the first partition and the maximal part of the first partition of a plane partition.

References

[1] Stanley, R. P. The conjugate trace and trace of a plane partition MathSciNet:0309748

Code

def statistic(p):
    return max(len(p), len(p[0]), p[0][0])

Created

Aug 28, 2023 at 09:47 by Martin Rubey

Updated

Aug 28, 2023 at 09:47 by Martin Rubey