- FindStat

Identifier

St000511: Integer partitions ⟶ ℤ

Values

[] => 1

[1] => 2

[2] => 2

[1,1] => 4

[3] => 2

[2,1] => 4

[1,1,1] => 8

[4] => 2

[3,1] => 4

[2,2] => 4

[2,1,1] => 8

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

[5] => 2

[4,1] => 4

[3,2] => 4

[3,1,1] => 8

[2,2,1] => 8

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

[1,1,1,1,1] => 32

[6] => 2

[5,1] => 4

[4,2] => 4

[4,1,1] => 8

[3,3] => 4

[3,2,1] => 8

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

[2,2,2] => 8

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

[2,1,1,1,1] => 32

[1,1,1,1,1,1] => 64

[7] => 2

[6,1] => 4

[5,2] => 4

[5,1,1] => 8

[4,3] => 4

[4,2,1] => 8

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

[3,3,1] => 8

[3,2,2] => 8

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

[3,1,1,1,1] => 32

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

[2,2,1,1,1] => 32

[2,1,1,1,1,1] => 64

[1,1,1,1,1,1,1] => 128

[8] => 2

[7,1] => 4

[6,2] => 4

[6,1,1] => 8

[5,3] => 4

[5,2,1] => 8

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

[4,4] => 4

[4,3,1] => 8

[4,2,2] => 8

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

[4,1,1,1,1] => 32

[3,3,2] => 8

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

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

[3,2,1,1,1] => 32

[3,1,1,1,1,1] => 64

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

[2,2,2,1,1] => 32

[2,2,1,1,1,1] => 64

[2,1,1,1,1,1,1] => 128

[1,1,1,1,1,1,1,1] => 256

[9] => 2

[8,1] => 4

[7,2] => 4

[7,1,1] => 8

[6,3] => 4

[6,2,1] => 8

[6,1,1,1] => 16

[5,4] => 4

[5,3,1] => 8

[5,2,2] => 8

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

[5,1,1,1,1] => 32

[4,4,1] => 8

[4,3,2] => 8

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

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

[4,2,1,1,1] => 32

[4,1,1,1,1,1] => 64

[3,3,3] => 8

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

[3,3,1,1,1] => 32

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

[3,2,2,1,1] => 32

[3,2,1,1,1,1] => 64

[3,1,1,1,1,1,1] => 128

[2,2,2,2,1] => 32

[2,2,2,1,1,1] => 64

[2,2,1,1,1,1,1] => 128

[2,1,1,1,1,1,1,1] => 256

[1,1,1,1,1,1,1,1,1] => 512

[10] => 2

[9,1] => 4

[8,2] => 4

[8,1,1] => 8

>>> Load all 272 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The number of invariant subsets when acting with a permutation of given cycle type.

References

[1] Bergeron, F., Labelle, G., Leroux, P. Combinatorial species and tree-like structures MathSciNet:1629341

Code

def statistic(la):
    c = species.SubsetSpecies().cycle_index_series()
    return c.count(la)

Created

May 26, 2016 at 21:00 by Martin Rubey

Updated

Oct 29, 2017 at 21:35 by Martin Rubey