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Identifier

St001596: Skew partitions ⟶ ℤ

Values

[[1],[]] => 0

[[2],[]] => 0

[[1,1],[]] => 0

[[2,1],[1]] => 0

[[3],[]] => 0

[[2,1],[]] => 0

[[3,1],[1]] => 0

[[2,2],[1]] => 0

[[3,2],[2]] => 0

[[1,1,1],[]] => 0

[[2,2,1],[1,1]] => 0

[[2,1,1],[1]] => 0

[[3,2,1],[2,1]] => 0

[[4],[]] => 0

[[3,1],[]] => 0

[[4,1],[1]] => 0

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

[[3,2],[1]] => 0

[[4,2],[2]] => 0

[[2,1,1],[]] => 0

[[3,2,1],[1,1]] => 0

[[3,1,1],[1]] => 0

[[4,2,1],[2,1]] => 0

[[3,3],[2]] => 0

[[4,3],[3]] => 0

[[2,2,1],[1]] => 0

[[3,3,1],[2,1]] => 0

[[3,2,1],[2]] => 0

[[4,3,1],[3,1]] => 0

[[2,2,2],[1,1]] => 0

[[3,3,2],[2,2]] => 0

[[3,2,2],[2,1]] => 0

[[4,3,2],[3,2]] => 0

[[1,1,1,1],[]] => 0

[[2,2,2,1],[1,1,1]] => 0

[[2,2,1,1],[1,1]] => 0

[[3,3,2,1],[2,2,1]] => 0

[[2,1,1,1],[1]] => 0

[[3,2,2,1],[2,1,1]] => 0

[[3,2,1,1],[2,1]] => 0

[[4,3,2,1],[3,2,1]] => 0

[[5],[]] => 0

[[4,1],[]] => 0

[[5,1],[1]] => 0

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

[[4,2],[1]] => 0

[[5,2],[2]] => 0

[[3,1,1],[]] => 0

[[4,2,1],[1,1]] => 0

[[4,1,1],[1]] => 0

[[5,2,1],[2,1]] => 0

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

[[4,3],[2]] => 0

[[5,3],[3]] => 0

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

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

[[3,2,1],[1]] => 0

[[4,3,1],[2,1]] => 0

[[4,2,1],[2]] => 0

[[5,3,1],[3,1]] => 0

[[3,2,2],[1,1]] => 0

[[4,3,2],[2,2]] => 0

[[4,2,2],[2,1]] => 0

[[5,3,2],[3,2]] => 0

[[2,1,1,1],[]] => 0

[[3,2,2,1],[1,1,1]] => 0

[[3,2,1,1],[1,1]] => 0

[[4,3,2,1],[2,2,1]] => 0

[[3,1,1,1],[1]] => 0

[[4,2,2,1],[2,1,1]] => 0

[[4,2,1,1],[2,1]] => 0

[[5,3,2,1],[3,2,1]] => 0

[[4,4],[3]] => 0

[[5,4],[4]] => 0

[[3,3,1],[2]] => 0

[[4,4,1],[3,1]] => 0

[[4,3,1],[3]] => 0

[[5,4,1],[4,1]] => 0

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

[[3,3,2],[2,1]] => 0

[[4,4,2],[3,2]] => 0

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

[[4,3,2],[3,1]] => 0

[[5,4,2],[4,2]] => 0

[[2,2,1,1],[1]] => 0

[[3,3,2,1],[2,1,1]] => 0

[[3,3,1,1],[2,1]] => 0

[[4,4,2,1],[3,2,1]] => 0

[[3,2,1,1],[2]] => 0

[[4,3,2,1],[3,1,1]] => 0

[[4,3,1,1],[3,1]] => 0

[[5,4,2,1],[4,2,1]] => 0

[[3,3,3],[2,2]] => 0

[[4,4,3],[3,3]] => 0

[[4,3,3],[3,2]] => 0

[[5,4,3],[4,3]] => 0

[[2,2,2,1],[1,1]] => 0

[[3,3,3,1],[2,2,1]] => 0

[[3,3,2,1],[2,2]] => 0

[[4,4,3,1],[3,3,1]] => 0

[[3,2,2,1],[2,1]] => 0

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Description

The number of two-by-two squares inside a skew partition.
This is, the number of cells $(i,j)$ in a skew partition for which the box $(i+1,j+1)$ is also a cell inside the skew partition.

Code

def statistic(L):
    cs = L.cells()
    return sum(1 for a,b in cs if (a+1,b+1) in cs)

Created

Sep 23, 2020 at 20:42 by Christian Stump

Updated

Sep 23, 2020 at 20:42 by Christian Stump