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-----------------------------------------------------------------------------
Statistic identifier: St000511
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
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)
-----------------------------------------------------------------------------
Statistic 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
[7,3] => 4
[7,2,1] => 8
[7,1,1,1] => 16
[6,4] => 4
[6,3,1] => 8
[6,2,2] => 8
[6,2,1,1] => 16
[6,1,1,1,1] => 32
[5,5] => 4
[5,4,1] => 8
[5,3,2] => 8
[5,3,1,1] => 16
[5,2,2,1] => 16
[5,2,1,1,1] => 32
[5,1,1,1,1,1] => 64
[4,4,2] => 8
[4,4,1,1] => 16
[4,3,3] => 8
[4,3,2,1] => 16
[4,3,1,1,1] => 32
[4,2,2,2] => 16
[4,2,2,1,1] => 32
[4,2,1,1,1,1] => 64
[4,1,1,1,1,1,1] => 128
[3,3,3,1] => 16
[3,3,2,2] => 16
[3,3,2,1,1] => 32
[3,3,1,1,1,1] => 64
[3,2,2,2,1] => 32
[3,2,2,1,1,1] => 64
[3,2,1,1,1,1,1] => 128
[3,1,1,1,1,1,1,1] => 256
[2,2,2,2,2] => 32
[2,2,2,2,1,1] => 64
[2,2,2,1,1,1,1] => 128
[2,2,1,1,1,1,1,1] => 256
[2,1,1,1,1,1,1,1,1] => 512
[1,1,1,1,1,1,1,1,1,1] => 1024
[11] => 2
[10,1] => 4
[9,2] => 4
[9,1,1] => 8
[8,3] => 4
[8,2,1] => 8
[8,1,1,1] => 16
[7,4] => 4
[7,3,1] => 8
[7,2,2] => 8
[7,2,1,1] => 16
[7,1,1,1,1] => 32
[6,5] => 4
[6,4,1] => 8
[6,3,2] => 8
[6,3,1,1] => 16
[6,2,2,1] => 16
[6,2,1,1,1] => 32
[6,1,1,1,1,1] => 64
[5,5,1] => 8
[5,4,2] => 8
[5,4,1,1] => 16
[5,3,3] => 8
[5,3,2,1] => 16
[5,3,1,1,1] => 32
[5,2,2,2] => 16
[5,2,2,1,1] => 32
[5,2,1,1,1,1] => 64
[5,1,1,1,1,1,1] => 128
[4,4,3] => 8
[4,4,2,1] => 16
[4,4,1,1,1] => 32
[4,3,3,1] => 16
[4,3,2,2] => 16
[4,3,2,1,1] => 32
[4,3,1,1,1,1] => 64
[4,2,2,2,1] => 32
[4,2,2,1,1,1] => 64
[4,2,1,1,1,1,1] => 128
[4,1,1,1,1,1,1,1] => 256
[3,3,3,2] => 16
[3,3,3,1,1] => 32
[3,3,2,2,1] => 32
[3,3,2,1,1,1] => 64
[3,3,1,1,1,1,1] => 128
[3,2,2,2,2] => 32
[3,2,2,2,1,1] => 64
[3,2,2,1,1,1,1] => 128
[3,2,1,1,1,1,1,1] => 256
[3,1,1,1,1,1,1,1,1] => 512
[2,2,2,2,2,1] => 64
[2,2,2,2,1,1,1] => 128
[2,2,2,1,1,1,1,1] => 256
[2,2,1,1,1,1,1,1,1] => 512
[2,1,1,1,1,1,1,1,1,1] => 1024
[1,1,1,1,1,1,1,1,1,1,1] => 2048
[12] => 2
[11,1] => 4
[10,2] => 4
[10,1,1] => 8
[9,3] => 4
[9,2,1] => 8
[9,1,1,1] => 16
[8,4] => 4
[8,3,1] => 8
[8,2,2] => 8
[8,2,1,1] => 16
[8,1,1,1,1] => 32
[7,5] => 4
[7,4,1] => 8
[7,3,2] => 8
[7,3,1,1] => 16
[7,2,2,1] => 16
[7,2,1,1,1] => 32
[7,1,1,1,1,1] => 64
[6,6] => 4
[6,5,1] => 8
[6,4,2] => 8
[6,4,1,1] => 16
[6,3,3] => 8
[6,3,2,1] => 16
[6,3,1,1,1] => 32
[6,2,2,2] => 16
[6,2,2,1,1] => 32
[6,2,1,1,1,1] => 64
[6,1,1,1,1,1,1] => 128
[5,5,2] => 8
[5,5,1,1] => 16
[5,4,3] => 8
[5,4,2,1] => 16
[5,4,1,1,1] => 32
[5,3,3,1] => 16
[5,3,2,2] => 16
[5,3,2,1,1] => 32
[5,3,1,1,1,1] => 64
[5,2,2,2,1] => 32
[5,2,2,1,1,1] => 64
[5,2,1,1,1,1,1] => 128
[5,1,1,1,1,1,1,1] => 256
[4,4,4] => 8
[4,4,3,1] => 16
[4,4,2,2] => 16
[4,4,2,1,1] => 32
[4,4,1,1,1,1] => 64
[4,3,3,2] => 16
[4,3,3,1,1] => 32
[4,3,2,2,1] => 32
[4,3,2,1,1,1] => 64
[4,3,1,1,1,1,1] => 128
[4,2,2,2,2] => 32
[4,2,2,2,1,1] => 64
[4,2,2,1,1,1,1] => 128
[4,2,1,1,1,1,1,1] => 256
[4,1,1,1,1,1,1,1,1] => 512
[3,3,3,3] => 16
[3,3,3,2,1] => 32
[3,3,3,1,1,1] => 64
[3,3,2,2,2] => 32
[3,3,2,2,1,1] => 64
[3,3,2,1,1,1,1] => 128
[3,3,1,1,1,1,1,1] => 256
[3,2,2,2,2,1] => 64
[3,2,2,2,1,1,1] => 128
[3,2,2,1,1,1,1,1] => 256
[3,2,1,1,1,1,1,1,1] => 512
[3,1,1,1,1,1,1,1,1,1] => 1024
[2,2,2,2,2,2] => 64
[2,2,2,2,2,1,1] => 128
[2,2,2,2,1,1,1,1] => 256
[2,2,2,1,1,1,1,1,1] => 512
[2,2,1,1,1,1,1,1,1,1] => 1024
[2,1,1,1,1,1,1,1,1,1,1] => 2048
[1,1,1,1,1,1,1,1,1,1,1,1] => 4096
-----------------------------------------------------------------------------
Created: May 26, 2016 at 21:00 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Oct 29, 2017 at 21:35 by Martin Rubey