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Identifier

St001899: Integer partitions ⟶ ℤ

Values

[1] => 1

[2] => 1

[1,1] => 1

[3] => 1

[2,1] => 2

[1,1,1] => 1

[4] => 2

[3,1] => 3

[2,2] => 2

[2,1,1] => 2

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

[5] => 5

[4,1] => 6

[3,2] => 4

[3,1,1] => 4

[2,2,1] => 4

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

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

[6] => 12

[5,1] => 15

[4,2] => 9

[4,1,1] => 9

[3,3] => 4

[3,2,1] => 12

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

[2,2,2] => 3

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

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

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

[7] => 33

[6,1] => 38

[5,2] => 23

[5,1,1] => 23

[4,3] => 18

[4,2,1] => 28

[4,1,1,1] => 10

[3,3,1] => 12

[3,2,2] => 10

[3,2,1,1] => 18

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

[2,2,2,1] => 7

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

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

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

[8] => 94

[7,1] => 109

[6,2] => 64

[6,1,1] => 62

[5,3] => 49

[5,2,1] => 76

[5,1,1,1] => 27

[4,4] => 24

[4,3,1] => 60

[4,2,2] => 24

[4,2,1,1] => 46

[4,1,1,1,1] => 10

[3,3,2] => 19

[3,3,1,1] => 21

[3,2,2,1] => 33

[3,2,1,1,1] => 20

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

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

[2,2,2,1,1] => 9

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

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

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

[9] => 290

[8,1] => 326

[7,2] => 187

[7,1,1] => 187

[6,3] => 141

[6,2,1] => 218

[6,1,1,1] => 75

[5,4] => 128

[5,3,1] => 169

[5,2,2] => 69

[5,2,1,1] => 128

[5,1,1,1,1] => 28

[4,4,1] => 80

[4,3,2] => 104

[4,3,1,1] => 104

[4,2,2,1] => 84

[4,2,1,1,1] => 54

[4,1,1,1,1,1] => 10

[3,3,3] => 16

[3,3,2,1] => 68

[3,3,1,1,1] => 25

[3,2,2,2] => 21

[3,2,2,1,1] => 54

[3,2,1,1,1,1] => 20

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

[2,2,2,2,1] => 12

[2,2,2,1,1,1] => 10

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

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

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

[10] => 949

[9,1] => 1054

[8,2] => 592

[8,1,1] => 592

[7,3] => 441

>>> Load all 811 entries. <<<

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Description

The total number of irreducible representations contained in the higher Lie character for an integer partition.

References

[1] Schocker, M. Multiplicities of higher Lie characters MathSciNet:1984625

Code

def statistic(la):
    s = SymmetricFunctions(ZZ).s()
    return sum(c for _, c in s.higher_lie_character(la))

Created

May 25, 2023 at 14:31 by Martin Rubey

Updated

May 25, 2023 at 14:31 by Martin Rubey