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Identifier

St001175: Integer partitions ⟶ ℤ

Values

[1] => 0

[2] => 0

[1,1] => 0

[3] => 0

[2,1] => 0

[1,1,1] => 0

[4] => 0

[3,1] => 0

[2,2] => 1

[2,1,1] => 0

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

[5] => 0

[4,1] => 0

[3,2] => 1

[3,1,1] => 0

[2,2,1] => 1

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

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

[6] => 0

[5,1] => 0

[4,2] => 1

[4,1,1] => 0

[3,3] => 2

[3,2,1] => 1

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

[2,2,2] => 2

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

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

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

[7] => 0

[6,1] => 0

[5,2] => 1

[5,1,1] => 0

[4,3] => 2

[4,2,1] => 1

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

[3,3,1] => 2

[3,2,2] => 2

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

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

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

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

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

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

[8] => 0

[7,1] => 0

[6,2] => 1

[6,1,1] => 0

[5,3] => 2

[5,2,1] => 1

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

[4,4] => 3

[4,3,1] => 2

[4,2,2] => 2

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

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

[3,3,2] => 3

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

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

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

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

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

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

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

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

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

[9] => 0

[8,1] => 0

[7,2] => 1

[7,1,1] => 0

[6,3] => 2

[6,2,1] => 1

[6,1,1,1] => 0

[5,4] => 3

[5,3,1] => 2

[5,2,2] => 2

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

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

[4,4,1] => 3

[4,3,2] => 3

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

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

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

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

[3,3,3] => 4

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

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

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

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

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

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

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

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

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

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

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

[10] => 0

[9,1] => 0

[8,2] => 1

[8,1,1] => 0

[7,3] => 2

>>> Load all 1200 entries. <<<

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Description

The size of a partition minus the hook length of the base cell.
This is, the number of boxes in the diagram of a partition that are neither in the first row nor in the first column.

Code

def statistic(L):
    return L.size() - L.hook_length(0,0)

Created

May 05, 2018 at 10:32 by Christian Stump

Updated

May 05, 2018 at 10:32 by Christian Stump