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Identifier

St001382: Integer partitions ⟶ ℤ

Values

[] => 0

[1] => 0

[2] => 1

[1,1] => 1

[3] => 2

[2,1] => 2

[1,1,1] => 2

[4] => 3

[3,1] => 3

[2,2] => 0

[2,1,1] => 3

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

[5] => 4

[4,1] => 4

[3,2] => 1

[3,1,1] => 4

[2,2,1] => 1

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

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

[6] => 5

[5,1] => 5

[4,2] => 2

[4,1,1] => 5

[3,3] => 2

[3,2,1] => 2

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

[2,2,2] => 2

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

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

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

[7] => 6

[6,1] => 6

[5,2] => 3

[5,1,1] => 6

[4,3] => 3

[4,2,1] => 3

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

[3,3,1] => 3

[3,2,2] => 3

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

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

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

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

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

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

[8] => 7

[7,1] => 7

[6,2] => 4

[6,1,1] => 7

[5,3] => 4

[5,2,1] => 4

[5,1,1,1] => 7

[4,4] => 4

[4,3,1] => 4

[4,2,2] => 4

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

[4,1,1,1,1] => 7

[3,3,2] => 4

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

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

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

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

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

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

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

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

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

[9] => 8

[8,1] => 8

[7,2] => 5

[7,1,1] => 8

[6,3] => 5

[6,2,1] => 5

[6,1,1,1] => 8

[5,4] => 5

[5,3,1] => 5

[5,2,2] => 5

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

[5,1,1,1,1] => 8

[4,4,1] => 5

[4,3,2] => 5

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

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

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

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

[3,3,3] => 0

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

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

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

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

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

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

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

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

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

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

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

[10] => 9

[9,1] => 9

[8,2] => 6

[8,1,1] => 9

>>> Load all 1329 entries. <<<

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Description

The number of boxes in the diagram of a partition that do not lie in its Durfee square.

References

[1] The side length of the Durfee square of an integer partition. St000183

Code

def statistic(L):

    def St000183(p):

        s = 0

        while len(p) > s and p[s] >= s+1:

            s += 1

        return s

    return sum(L) - St000183(L)^2

Created

Apr 16, 2019 at 19:45 by Christian Stump

Updated

Dec 10, 2022 at 14:45 by Martin Rubey