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Identifier

St001658: Skew partitions ⟶ ℤ

Values

[[1],[]] => 2

[[2],[]] => 3

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

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

[[3],[]] => 4

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

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

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

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

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

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

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

[[3,2,1],[2,1]] => 8

[[4],[]] => 5

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

[[4,1],[1]] => 8

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

[[3,2],[1]] => 8

[[4,2],[2]] => 9

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

[[3,2,1],[1,1]] => 10

[[3,1,1],[1]] => 9

[[4,2,1],[2,1]] => 12

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

[[4,3],[3]] => 8

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

[[3,3,1],[2,1]] => 10

[[3,2,1],[2]] => 10

[[4,3,1],[3,1]] => 12

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

[[3,3,2],[2,2]] => 9

[[3,2,2],[2,1]] => 10

[[4,3,2],[3,2]] => 12

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

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

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

[[3,3,2,1],[2,2,1]] => 12

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

[[3,2,2,1],[2,1,1]] => 12

[[3,2,1,1],[2,1]] => 12

[[4,3,2,1],[3,2,1]] => 16

[[5],[]] => 6

[[4,1],[]] => 9

[[5,1],[1]] => 10

[[3,2],[]] => 10

[[4,2],[1]] => 11

[[5,2],[2]] => 12

[[3,1,1],[]] => 10

[[4,2,1],[1,1]] => 14

[[4,1,1],[1]] => 12

[[5,2,1],[2,1]] => 16

[[3,3],[1]] => 10

[[4,3],[2]] => 11

[[5,3],[3]] => 12

[[2,2,1],[]] => 10

[[3,3,1],[1,1]] => 14

[[3,2,1],[1]] => 13

[[4,3,1],[2,1]] => 16

[[4,2,1],[2]] => 15

[[5,3,1],[3,1]] => 18

[[3,2,2],[1,1]] => 12

[[4,3,2],[2,2]] => 15

[[4,2,2],[2,1]] => 15

[[5,3,2],[3,2]] => 18

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

[[3,2,2,1],[1,1,1]] => 14

[[3,2,1,1],[1,1]] => 15

[[4,3,2,1],[2,2,1]] => 20

[[3,1,1,1],[1]] => 12

[[4,2,2,1],[2,1,1]] => 18

[[4,2,1,1],[2,1]] => 18

[[5,3,2,1],[3,2,1]] => 24

[[4,4],[3]] => 9

[[5,4],[4]] => 10

[[3,3,1],[2]] => 12

[[4,4,1],[3,1]] => 14

[[4,3,1],[3]] => 14

[[5,4,1],[4,1]] => 16

[[2,2,2],[1]] => 10

[[3,3,2],[2,1]] => 13

[[4,4,2],[3,2]] => 15

[[3,2,2],[2]] => 14

[[4,3,2],[3,1]] => 16

[[5,4,2],[4,2]] => 18

[[2,2,1,1],[1]] => 11

[[3,3,2,1],[2,1,1]] => 16

[[3,3,1,1],[2,1]] => 15

[[4,4,2,1],[3,2,1]] => 20

[[3,2,1,1],[2]] => 14

[[4,3,2,1],[3,1,1]] => 20

[[4,3,1,1],[3,1]] => 18

[[5,4,2,1],[4,2,1]] => 24

[[3,3,3],[2,2]] => 10

[[4,4,3],[3,3]] => 12

[[4,3,3],[3,2]] => 14

[[5,4,3],[4,3]] => 16

[[2,2,2,1],[1,1]] => 11

[[3,3,3,1],[2,2,1]] => 14

[[3,3,2,1],[2,2]] => 15

[[4,4,3,1],[3,3,1]] => 18

[[3,2,2,1],[2,1]] => 16

>>> Load all 1200 entries. <<<

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Description

The total number of rook placements on a 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 sum(rook_matrix.rook_vector())

Created

Dec 22, 2020 at 14:13 by Martin Rubey

Updated

Dec 22, 2020 at 14:13 by Martin Rubey