- FindStat

edit this statistic or download as text // json

Identifier

St001900: 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] => 5

[3,2] => 4

[3,1,1] => 4

[2,2,1] => 4

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

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

[6] => 8

[5,1] => 9

[4,2] => 7

[4,1,1] => 7

[3,3] => 4

[3,2,1] => 8

[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] => 13

[6,1] => 13

[5,2] => 12

[5,1,1] => 12

[4,3] => 11

[4,2,1] => 12

[4,1,1,1] => 8

[3,3,1] => 9

[3,2,2] => 9

[3,2,1,1] => 11

[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] => 20

[7,1] => 20

[6,2] => 19

[6,1,1] => 18

[5,3] => 18

[5,2,1] => 19

[5,1,1,1] => 15

[4,4] => 13

[4,3,1] => 18

[4,2,2] => 14

[4,2,1,1] => 18

[4,1,1,1,1] => 8

[3,3,2] => 12

[3,3,1,1] => 14

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

[3,2,1,1,1] => 13

[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] => 28

[8,1] => 28

[7,2] => 27

[7,1,1] => 27

[6,3] => 26

[6,2,1] => 27

[6,1,1,1] => 22

[5,4] => 26

[5,3,1] => 26

[5,2,2] => 24

[5,2,1,1] => 26

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

[4,4,1] => 23

[4,3,2] => 24

[4,3,1,1] => 24

[4,2,2,1] => 24

[4,2,1,1,1] => 21

[4,1,1,1,1,1] => 8

[3,3,3] => 15

[3,3,2,1] => 22

[3,3,1,1,1] => 17

[3,2,2,2] => 17

[3,2,2,1,1] => 23

[3,2,1,1,1,1] => 13

[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] => 40

[9,1] => 40

[8,2] => 39

[8,1,1] => 39

[7,3] => 38

>>> Load all 800 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 distinct 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(1 for _, c in s.higher_lie_character(la))

Created

May 25, 2023 at 14:37 by Martin Rubey

Updated

May 25, 2023 at 14:37 by Martin Rubey