Identifier
Identifier
• St000318: ⟶ ℤ (values match St000159The number of distinct parts of the integer partition., St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition.)
Values
[] => 1
[1] => 2
[2] => 2
[1,1] => 2
[3] => 2
[2,1] => 3
[1,1,1] => 2
[4] => 2
[3,1] => 3
[2,2] => 2
[2,1,1] => 3
[1,1,1,1] => 2
[5] => 2
[4,1] => 3
[3,2] => 3
[3,1,1] => 3
[2,2,1] => 3
[2,1,1,1] => 3
[1,1,1,1,1] => 2
[6] => 2
[5,1] => 3
[4,2] => 3
[4,1,1] => 3
[3,3] => 2
[3,2,1] => 4
[3,1,1,1] => 3
[2,2,2] => 2
[2,2,1,1] => 3
[2,1,1,1,1] => 3
[1,1,1,1,1,1] => 2
[7] => 2
[6,1] => 3
[5,2] => 3
[5,1,1] => 3
[4,3] => 3
[4,2,1] => 4
[4,1,1,1] => 3
[3,3,1] => 3
[3,2,2] => 3
[3,2,1,1] => 4
[3,1,1,1,1] => 3
[2,2,2,1] => 3
[2,2,1,1,1] => 3
[2,1,1,1,1,1] => 3
[1,1,1,1,1,1,1] => 2
[8] => 2
[7,1] => 3
[6,2] => 3
[6,1,1] => 3
[5,3] => 3
[5,2,1] => 4
[5,1,1,1] => 3
[4,4] => 2
[4,3,1] => 4
[4,2,2] => 3
[4,2,1,1] => 4
[4,1,1,1,1] => 3
[3,3,2] => 3
[3,3,1,1] => 3
[3,2,2,1] => 4
[3,2,1,1,1] => 4
[3,1,1,1,1,1] => 3
[2,2,2,2] => 2
[2,2,2,1,1] => 3
[2,2,1,1,1,1] => 3
[2,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1] => 2
[9] => 2
[8,1] => 3
[7,2] => 3
[7,1,1] => 3
[6,3] => 3
[6,2,1] => 4
[6,1,1,1] => 3
[5,4] => 3
[5,3,1] => 4
[5,2,2] => 3
[5,2,1,1] => 4
[5,1,1,1,1] => 3
[4,4,1] => 3
[4,3,2] => 4
[4,3,1,1] => 4
[4,2,2,1] => 4
[4,2,1,1,1] => 4
[4,1,1,1,1,1] => 3
[3,3,3] => 2
[3,3,2,1] => 4
[3,3,1,1,1] => 3
[3,2,2,2] => 3
[3,2,2,1,1] => 4
[3,2,1,1,1,1] => 4
[3,1,1,1,1,1,1] => 3
[2,2,2,2,1] => 3
[2,2,2,1,1,1] => 3
[2,2,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,1] => 2
[10] => 2
[9,1] => 3
[8,2] => 3
[8,1,1] => 3
[7,3] => 3
[7,2,1] => 4
[7,1,1,1] => 3
[6,4] => 3
[6,3,1] => 4
[6,2,2] => 3
[6,2,1,1] => 4
[6,1,1,1,1] => 3
[5,5] => 2
[5,4,1] => 4
[5,3,2] => 4
[5,3,1,1] => 4
[5,2,2,1] => 4
[5,2,1,1,1] => 4
[5,1,1,1,1,1] => 3
[4,4,2] => 3
[4,4,1,1] => 3
[4,3,3] => 3
[4,3,2,1] => 5
[4,3,1,1,1] => 4
[4,2,2,2] => 3
[4,2,2,1,1] => 4
[4,2,1,1,1,1] => 4
[4,1,1,1,1,1,1] => 3
[3,3,3,1] => 3
[3,3,2,2] => 3
[3,3,2,1,1] => 4
[3,3,1,1,1,1] => 3
[3,2,2,2,1] => 4
[3,2,2,1,1,1] => 4
[3,2,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1] => 3
[2,2,2,2,2] => 2
[2,2,2,2,1,1] => 3
[2,2,2,1,1,1,1] => 3
[2,2,1,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1,1] => 3
[1,1,1,1,1,1,1,1,1,1] => 2
[5,4,2] => 4
[5,4,1,1] => 4
[5,3,3] => 3
[5,3,2,1] => 5
[5,3,1,1,1] => 4
[5,2,2,2] => 3
[5,2,2,1,1] => 4
[4,4,3] => 3
[4,4,2,1] => 4
[4,4,1,1,1] => 3
[4,3,3,1] => 4
[4,3,2,2] => 4
[4,3,2,1,1] => 5
[4,2,2,2,1] => 4
[3,3,3,2] => 3
[3,3,3,1,1] => 3
[3,3,2,2,1] => 4
[6,4,2] => 4
[5,4,3] => 4
[5,4,2,1] => 5
[5,4,1,1,1] => 4
[5,3,3,1] => 4
[5,3,2,2] => 4
[5,3,2,1,1] => 5
[5,2,2,2,1] => 4
[4,4,3,1] => 4
[4,4,2,2] => 3
[4,4,2,1,1] => 4
[4,3,3,2] => 4
[4,3,3,1,1] => 4
[4,3,2,2,1] => 5
[3,3,3,2,1] => 4
[3,3,2,2,1,1] => 4
[5,4,3,1] => 5
[5,4,2,2] => 4
[5,4,2,1,1] => 5
[5,3,3,2] => 4
[5,3,3,1,1] => 4
[5,3,2,2,1] => 5
[4,4,3,2] => 4
[4,4,3,1,1] => 4
[4,4,2,2,1] => 4
[4,3,3,2,1] => 5
[5,4,3,2] => 5
[5,4,3,1,1] => 5
[5,4,2,2,1] => 5
[5,3,3,2,1] => 5
[4,4,3,2,1] => 5
[5,4,3,2,1] => 6
Description
The number of addable cells of the Ferrers diagram of an integer partition.
Code
def statistic(L):