- FindStat

Identifier

St000532: Integer partitions ⟶ ℤ

Values

[] => 1

[1] => 2

[2] => 3

[1,1] => 3

[3] => 4

[2,1] => 5

[1,1,1] => 4

[4] => 5

[3,1] => 7

[2,2] => 7

[2,1,1] => 7

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

[5] => 6

[4,1] => 9

[3,2] => 10

[3,1,1] => 10

[2,2,1] => 10

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

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

[6] => 7

[5,1] => 11

[4,2] => 13

[4,1,1] => 13

[3,3] => 13

[3,2,1] => 15

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

[2,2,2] => 13

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

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

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

[7] => 8

[6,1] => 13

[5,2] => 16

[5,1,1] => 16

[4,3] => 17

[4,2,1] => 20

[4,1,1,1] => 17

[3,3,1] => 20

[3,2,2] => 20

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

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

[2,2,2,1] => 17

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

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

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

[8] => 9

[7,1] => 15

[6,2] => 19

[6,1,1] => 19

[5,3] => 21

[5,2,1] => 25

[5,1,1,1] => 21

[4,4] => 21

[4,3,1] => 27

[4,2,2] => 27

[4,2,1,1] => 27

[4,1,1,1,1] => 21

[3,3,2] => 27

[3,3,1,1] => 27

[3,2,2,1] => 27

[3,2,1,1,1] => 25

[3,1,1,1,1,1] => 19

[2,2,2,2] => 21

[2,2,2,1,1] => 21

[2,2,1,1,1,1] => 19

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

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

[9] => 10

[8,1] => 17

[7,2] => 22

[7,1,1] => 22

[6,3] => 25

[6,2,1] => 30

[6,1,1,1] => 25

[5,4] => 26

[5,3,1] => 34

[5,2,2] => 34

[5,2,1,1] => 34

[5,1,1,1,1] => 26

[4,4,1] => 34

[4,3,2] => 37

[4,3,1,1] => 37

[4,2,2,1] => 37

[4,2,1,1,1] => 34

[4,1,1,1,1,1] => 25

[3,3,3] => 34

[3,3,2,1] => 37

[3,3,1,1,1] => 34

[3,2,2,2] => 34

[3,2,2,1,1] => 34

[3,2,1,1,1,1] => 30

[3,1,1,1,1,1,1] => 22

[2,2,2,2,1] => 26

[2,2,2,1,1,1] => 25

[2,2,1,1,1,1,1] => 22

[2,1,1,1,1,1,1,1] => 17

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

[10] => 11

[9,1] => 19

[8,2] => 25

[8,1,1] => 25

>>> Load all 288 entries. <<<

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Description

The total number of rook placements on a Ferrers board.

References

[1] wikipedia:Rook_polynomial

Code

def statistic(la):
    return sum(matrix([[1]*p + [0]*(la[0]-p) for p in la]).rook_vector())

Created

Jun 10, 2016 at 23:59 by Martin Rubey

Updated

Apr 26, 2018 at 07:39 by Martin Rubey