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Identifier

St001449: Plane partitions ⟶ ℤ

Values

[[1]] => 2

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

[[2]] => 1

[[1,1]] => 2

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

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

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

[[3]] => 1

[[2,1]] => 3

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

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

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

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

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

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

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

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

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

[[4]] => 1

[[3,1]] => 2

[[2,2]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5]] => 1

[[4,1]] => 2

[[3,2]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[6]] => 1

[[5,1]] => 2

[[4,2]] => 1

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

[[3,3]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The smallest missing nonzero part in the plane partition.

Code

def statistic(P):
    P = set(sum([list(row) for row in P],[]))
    i = 1
    while i in P:
        i += 1
    return i

Created

Jul 26, 2019 at 20:30 by Erika Pirnes

Updated

Jul 27, 2019 at 16:36 by Christian Stump