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Identifier

St001924: Integer partitions ⟶ ℤ

Values

[1] => 1

[2] => 1

[1,1] => 1

[3] => 1

[2,1] => 3

[1,1,1] => 1

[4] => 1

[3,1] => 2

[2,2] => 2

[2,1,1] => 2

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

[5] => 1

[4,1] => 2

[3,2] => 3

[3,1,1] => 3

[2,2,1] => 3

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

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

[6] => 1

[5,1] => 2

[4,2] => 2

[4,1,1] => 2

[3,3] => 2

[3,2,1] => 6

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

[2,2,2] => 2

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

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

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

[7] => 1

[6,1] => 2

[5,2] => 2

[5,1,1] => 2

[4,3] => 3

[4,2,1] => 4

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

[3,3,1] => 4

[3,2,2] => 4

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

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

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

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

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

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

[8] => 1

[7,1] => 2

[6,2] => 2

[6,1,1] => 2

[5,3] => 2

[5,2,1] => 4

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

[4,4] => 2

[4,3,1] => 4

[4,2,2] => 4

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

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

[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] => 2

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

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

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

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

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

[9] => 1

[8,1] => 2

[7,2] => 2

[7,1,1] => 2

[6,3] => 2

[6,2,1] => 4

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

[5,4] => 3

[5,3,1] => 3

[5,2,2] => 3

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

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

[4,4,1] => 3

[4,3,2] => 6

[4,3,1,1] => 6

[4,2,2,1] => 6

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

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

[3,3,3] => 3

[3,3,2,1] => 6

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

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

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

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

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

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

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

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

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

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

[10] => 1

[9,1] => 2

[8,2] => 2

[8,1,1] => 2

[7,3] => 2

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Description

The number of cells in an integer partition whose arm and leg length coincide.

Code

def statistic(la):
    return sum(1 for c in la.cells() if la.arm_length(*c) == la.leg_length(*c))

Created

Sep 06, 2023 at 08:05 by Martin Rubey

Updated

Sep 06, 2023 at 08:05 by Martin Rubey