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Identifier

St001921: Plane partitions ⟶ ℤ

Values

[[1]] => 3

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

[[2]] => 3

[[1,1]] => 3

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

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

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

[[3]] => 3

[[2,1]] => 4

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

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

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

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

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

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

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

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

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

[[4]] => 3

[[3,1]] => 4

[[2,2]] => 3

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

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

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

[[2],[1],[1],[1]] => 7

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

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

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

[[3],[1],[1]] => 6

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

[[2,1],[1],[1]] => 7

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

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

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

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

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

[[3,1],[1]] => 6

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

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

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

[[5]] => 3

[[4,1]] => 4

[[3,2]] => 4

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

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

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

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

[[1],[1],[1],[1],[1],[1]] => 8

[[2],[1],[1],[1],[1]] => 8

[[2],[2],[1],[1]] => 7

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

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

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

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

[[3],[1],[1],[1]] => 7

[[3],[2],[1]] => 7

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

[[2,1],[1],[1],[1]] => 8

[[2,1],[2],[1]] => 7

[[2,1],[1,1],[1]] => 7

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

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

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

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

[[4],[1],[1]] => 6

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

[[3,1],[1],[1]] => 7

[[3,1],[2]] => 6

[[3,1],[1,1]] => 6

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

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

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

[[2,1,1],[1],[1]] => 7

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

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

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

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

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

[[4,1],[1]] => 6

[[3,2],[1]] => 6

[[3,1,1],[1]] => 6

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

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

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

[[6]] => 3

[[5,1]] => 4

[[4,2]] => 4

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

[[3,3]] => 3

[[3,2,1]] => 5

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

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

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

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

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

[[1],[1],[1],[1],[1],[1],[1]] => 9

[[2],[1],[1],[1],[1],[1]] => 9

[[2],[2],[1],[1],[1]] => 8

[[2],[2],[2],[1]] => 7

[[1,1],[1],[1],[1],[1],[1]] => 8

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

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Description

The number of boxes that can be added such that the result is a plane partition.

Code

def statistic(p):
    c = 0
    for i, row in enumerate(list(p) + [(0,)]):
        for j, entry in enumerate(row + (0,)):
            h = None if not j else row[j-1]
            v = None if not i or len(p[i-1]) == j else p[i-1][j]
            if (h is None or entry < h) and (v is None or entry < v):
                c += 1
    return c

Created

Aug 28, 2023 at 09:50 by Martin Rubey

Updated

Aug 28, 2023 at 09:50 by Martin Rubey