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Identifier
Values
[] => 0
[1] => 0
[2] => 1
[1,1] => 1
[3] => 0
[2,1] => 1
[1,1,1] => 3
[4] => 0
[3,1] => 0
[2,2] => 2
[2,1,1] => 2
[1,1,1,1] => 6
[5] => 0
[4,1] => 0
[3,2] => 1
[3,1,1] => 1
[2,2,1] => 2
[2,1,1,1] => 4
[1,1,1,1,1] => 10
[6] => 0
[5,1] => 0
[4,2] => 1
[4,1,1] => 1
[3,3] => 0
[3,2,1] => 1
[3,1,1,1] => 3
[2,2,2] => 3
[2,2,1,1] => 3
[2,1,1,1,1] => 7
[1,1,1,1,1,1] => 15
[7] => 0
[6,1] => 0
[5,2] => 1
[5,1,1] => 1
[4,3] => 0
[4,2,1] => 1
[4,1,1,1] => 3
[3,3,1] => 0
[3,2,2] => 2
[3,2,1,1] => 2
[3,1,1,1,1] => 6
[2,2,2,1] => 3
[2,2,1,1,1] => 5
[2,1,1,1,1,1] => 11
[1,1,1,1,1,1,1] => 21
[8] => 0
[7,1] => 0
[6,2] => 1
[6,1,1] => 1
[5,3] => 0
[5,2,1] => 1
[5,1,1,1] => 3
[4,4] => 0
[4,3,1] => 0
[4,2,2] => 2
[4,2,1,1] => 2
[4,1,1,1,1] => 6
[3,3,2] => 1
[3,3,1,1] => 1
[3,2,2,1] => 2
[3,2,1,1,1] => 4
[3,1,1,1,1,1] => 10
[2,2,2,2] => 4
[2,2,2,1,1] => 4
[2,2,1,1,1,1] => 8
[2,1,1,1,1,1,1] => 16
[1,1,1,1,1,1,1,1] => 28
[9] => 0
[8,1] => 0
[7,2] => 1
[7,1,1] => 1
[6,3] => 0
[6,2,1] => 1
[6,1,1,1] => 3
[5,4] => 0
[5,3,1] => 0
[5,2,2] => 2
[5,2,1,1] => 2
[5,1,1,1,1] => 6
[4,4,1] => 0
[4,3,2] => 1
[4,3,1,1] => 1
[4,2,2,1] => 2
[4,2,1,1,1] => 4
[4,1,1,1,1,1] => 10
[3,3,3] => 0
[3,3,2,1] => 1
[3,3,1,1,1] => 3
[3,2,2,2] => 3
[3,2,2,1,1] => 3
[3,2,1,1,1,1] => 7
[3,1,1,1,1,1,1] => 15
[2,2,2,2,1] => 4
[2,2,2,1,1,1] => 6
[2,2,1,1,1,1,1] => 12
[2,1,1,1,1,1,1,1] => 22
[1,1,1,1,1,1,1,1,1] => 36
[10] => 0
[9,1] => 0
[8,2] => 1
[8,1,1] => 1
>>> Load all 272 entries. <<<
[7,3] => 0
[7,2,1] => 1
[7,1,1,1] => 3
[6,4] => 0
[6,3,1] => 0
[6,2,2] => 2
[6,2,1,1] => 2
[6,1,1,1,1] => 6
[5,5] => 0
[5,4,1] => 0
[5,3,2] => 1
[5,3,1,1] => 1
[5,2,2,1] => 2
[5,2,1,1,1] => 4
[5,1,1,1,1,1] => 10
[4,4,2] => 1
[4,4,1,1] => 1
[4,3,3] => 0
[4,3,2,1] => 1
[4,3,1,1,1] => 3
[4,2,2,2] => 3
[4,2,2,1,1] => 3
[4,2,1,1,1,1] => 7
[4,1,1,1,1,1,1] => 15
[3,3,3,1] => 0
[3,3,2,2] => 2
[3,3,2,1,1] => 2
[3,3,1,1,1,1] => 6
[3,2,2,2,1] => 3
[3,2,2,1,1,1] => 5
[3,2,1,1,1,1,1] => 11
[3,1,1,1,1,1,1,1] => 21
[2,2,2,2,2] => 5
[2,2,2,2,1,1] => 5
[2,2,2,1,1,1,1] => 9
[2,2,1,1,1,1,1,1] => 17
[2,1,1,1,1,1,1,1,1] => 29
[1,1,1,1,1,1,1,1,1,1] => 45
[11] => 0
[10,1] => 0
[9,2] => 1
[9,1,1] => 1
[8,3] => 0
[8,2,1] => 1
[8,1,1,1] => 3
[7,4] => 0
[7,3,1] => 0
[7,2,2] => 2
[7,2,1,1] => 2
[7,1,1,1,1] => 6
[6,5] => 0
[6,4,1] => 0
[6,3,2] => 1
[6,3,1,1] => 1
[6,2,2,1] => 2
[6,2,1,1,1] => 4
[6,1,1,1,1,1] => 10
[5,5,1] => 0
[5,4,2] => 1
[5,4,1,1] => 1
[5,3,3] => 0
[5,3,2,1] => 1
[5,3,1,1,1] => 3
[5,2,2,2] => 3
[5,2,2,1,1] => 3
[5,2,1,1,1,1] => 7
[5,1,1,1,1,1,1] => 15
[4,4,3] => 0
[4,4,2,1] => 1
[4,4,1,1,1] => 3
[4,3,3,1] => 0
[4,3,2,2] => 2
[4,3,2,1,1] => 2
[4,3,1,1,1,1] => 6
[4,2,2,2,1] => 3
[4,2,2,1,1,1] => 5
[4,2,1,1,1,1,1] => 11
[4,1,1,1,1,1,1,1] => 21
[3,3,3,2] => 1
[3,3,3,1,1] => 1
[3,3,2,2,1] => 2
[3,3,2,1,1,1] => 4
[3,3,1,1,1,1,1] => 10
[3,2,2,2,2] => 4
[3,2,2,2,1,1] => 4
[3,2,2,1,1,1,1] => 8
[3,2,1,1,1,1,1,1] => 16
[3,1,1,1,1,1,1,1,1] => 28
[2,2,2,2,2,1] => 5
[2,2,2,2,1,1,1] => 7
[2,2,2,1,1,1,1,1] => 13
[2,2,1,1,1,1,1,1,1] => 23
[2,1,1,1,1,1,1,1,1,1] => 37
[1,1,1,1,1,1,1,1,1,1,1] => 55
[12] => 0
[11,1] => 0
[10,2] => 1
[10,1,1] => 1
[9,3] => 0
[9,2,1] => 1
[9,1,1,1] => 3
[8,4] => 0
[8,3,1] => 0
[8,2,2] => 2
[8,2,1,1] => 2
[8,1,1,1,1] => 6
[7,5] => 0
[7,4,1] => 0
[7,3,2] => 1
[7,3,1,1] => 1
[7,2,2,1] => 2
[7,2,1,1,1] => 4
[7,1,1,1,1,1] => 10
[6,6] => 0
[6,5,1] => 0
[6,4,2] => 1
[6,4,1,1] => 1
[6,3,3] => 0
[6,3,2,1] => 1
[6,3,1,1,1] => 3
[6,2,2,2] => 3
[6,2,2,1,1] => 3
[6,2,1,1,1,1] => 7
[6,1,1,1,1,1,1] => 15
[5,5,2] => 1
[5,5,1,1] => 1
[5,4,3] => 0
[5,4,2,1] => 1
[5,4,1,1,1] => 3
[5,3,3,1] => 0
[5,3,2,2] => 2
[5,3,2,1,1] => 2
[5,3,1,1,1,1] => 6
[5,2,2,2,1] => 3
[5,2,2,1,1,1] => 5
[5,2,1,1,1,1,1] => 11
[5,1,1,1,1,1,1,1] => 21
[4,4,4] => 0
[4,4,3,1] => 0
[4,4,2,2] => 2
[4,4,2,1,1] => 2
[4,4,1,1,1,1] => 6
[4,3,3,2] => 1
[4,3,3,1,1] => 1
[4,3,2,2,1] => 2
[4,3,2,1,1,1] => 4
[4,3,1,1,1,1,1] => 10
[4,2,2,2,2] => 4
[4,2,2,2,1,1] => 4
[4,2,2,1,1,1,1] => 8
[4,2,1,1,1,1,1,1] => 16
[4,1,1,1,1,1,1,1,1] => 28
[3,3,3,3] => 0
[3,3,3,2,1] => 1
[3,3,3,1,1,1] => 3
[3,3,2,2,2] => 3
[3,3,2,2,1,1] => 3
[3,3,2,1,1,1,1] => 7
[3,3,1,1,1,1,1,1] => 15
[3,2,2,2,2,1] => 4
[3,2,2,2,1,1,1] => 6
[3,2,2,1,1,1,1,1] => 12
[3,2,1,1,1,1,1,1,1] => 22
[3,1,1,1,1,1,1,1,1,1] => 36
[2,2,2,2,2,2] => 6
[2,2,2,2,2,1,1] => 6
[2,2,2,2,1,1,1,1] => 10
[2,2,2,1,1,1,1,1,1] => 18
[2,2,1,1,1,1,1,1,1,1] => 30
[2,1,1,1,1,1,1,1,1,1,1] => 46
[1,1,1,1,1,1,1,1,1,1,1,1] => 66
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Description
The number of invariant subsets of size 2 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):
    E = species.SetSpecies()
    E2 = species.CharacteristicSpecies(2)
    c = (E2*E).cycle_index_series()
    return c.count(la)
Created
May 26, 2016 at 20:55 by Martin Rubey
Updated
Oct 29, 2017 at 21:33 by Martin Rubey