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Identifier

St001660: Skew partitions ⟶ ℤ

Values

[[1],[]] => 1

[[2],[]] => 2

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

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

[[3],[]] => 3

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

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

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

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

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

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

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

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

[[4],[]] => 4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5],[]] => 5

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

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

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

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

[[5,2],[2]] => 6

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

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

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

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

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

[[4,3],[2]] => 5

[[5,3],[3]] => 6

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

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

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

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

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

[[5,3,1],[3,1]] => 4

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

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

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

[[5,3,2],[3,2]] => 4

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5,4,1],[4,1]] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[4,4,3],[3,3]] => 6

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

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

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

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

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

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

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

>>> Load all 1200 entries. <<<

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Description

The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board.

References

[1] wikipedia:Rook_polynomial

Code

def statistic(nu):
    import itertools
    rook_matrix = matrix([[0]*q + [1]*(p-q) + [0]*(nu[0][0]-p)
                         for p, q in itertools.zip_longest(*nu, fillvalue=0)])
    return next(v for v in reversed(rook_matrix.rook_vector()) if v)

Created

Dec 22, 2020 at 14:22 by Martin Rubey

Updated

Dec 22, 2020 at 14:22 by Martin Rubey