Identifier
Identifier
Values
[2] generating graphics... => 0
[1,1] generating graphics... => 1
[3] generating graphics... => 0
[2,1] generating graphics... => 0
[1,1,1] generating graphics... => 1
[4] generating graphics... => 0
[3,1] generating graphics... => 0
[2,2] generating graphics... => 0
[2,1,1] generating graphics... => 0
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 0
[4,1] generating graphics... => 0
[3,2] generating graphics... => 0
[3,1,1] generating graphics... => 0
[2,2,1] generating graphics... => 0
[2,1,1,1] generating graphics... => 0
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 0
[5,1] generating graphics... => 0
[4,2] generating graphics... => 0
[4,1,1] generating graphics... => 0
[3,3] generating graphics... => 0
[3,2,1] generating graphics... => 0
[3,1,1,1] generating graphics... => 0
[2,2,2] generating graphics... => 0
[2,2,1,1] generating graphics... => 0
[2,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 0
[6,1] generating graphics... => 0
[5,2] generating graphics... => 0
[5,1,1] generating graphics... => 0
[4,3] generating graphics... => 0
[4,2,1] generating graphics... => 0
[4,1,1,1] generating graphics... => 0
[3,3,1] generating graphics... => 0
[3,2,2] generating graphics... => 0
[3,2,1,1] generating graphics... => 0
[3,1,1,1,1] generating graphics... => 0
[2,2,2,1] generating graphics... => 0
[2,2,1,1,1] generating graphics... => 0
[2,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 0
[7,1] generating graphics... => 0
[6,2] generating graphics... => 0
[6,1,1] generating graphics... => 0
[5,3] generating graphics... => 0
[5,2,1] generating graphics... => 0
[5,1,1,1] generating graphics... => 0
[4,4] generating graphics... => 0
[4,3,1] generating graphics... => 0
[4,2,2] generating graphics... => 0
[4,2,1,1] generating graphics... => 0
[4,1,1,1,1] generating graphics... => 0
[3,3,2] generating graphics... => 0
[3,3,1,1] generating graphics... => 0
[3,2,2,1] generating graphics... => 0
[3,2,1,1,1] generating graphics... => 0
[3,1,1,1,1,1] generating graphics... => 0
[2,2,2,2] generating graphics... => 0
[2,2,2,1,1] generating graphics... => 0
[2,2,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1] generating graphics... => 1
[9] generating graphics... => 0
[8,1] generating graphics... => 0
[7,2] generating graphics... => 0
[7,1,1] generating graphics... => 0
[6,3] generating graphics... => 0
[6,2,1] generating graphics... => 0
[6,1,1,1] generating graphics... => 0
[5,4] generating graphics... => 0
[5,3,1] generating graphics... => 0
[5,2,2] generating graphics... => 0
[5,2,1,1] generating graphics... => 0
[5,1,1,1,1] generating graphics... => 0
[4,4,1] generating graphics... => 0
[4,3,2] generating graphics... => 0
[4,3,1,1] generating graphics... => 0
[4,2,2,1] generating graphics... => 0
[4,2,1,1,1] generating graphics... => 0
[4,1,1,1,1,1] generating graphics... => 0
[3,3,3] generating graphics... => 0
[3,3,2,1] generating graphics... => 0
[3,3,1,1,1] generating graphics... => 0
[3,2,2,2] generating graphics... => 0
[3,2,2,1,1] generating graphics... => 0
[3,2,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,1] generating graphics... => 0
[2,2,2,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1] generating graphics... => 1
[10] generating graphics... => 0
[9,1] generating graphics... => 0
[8,2] generating graphics... => 0
[8,1,1] generating graphics... => 0
[7,3] generating graphics... => 0
[7,2,1] generating graphics... => 0
[7,1,1,1] generating graphics... => 0
[6,4] generating graphics... => 0
[6,3,1] generating graphics... => 0
[6,2,2] generating graphics... => 0
[6,2,1,1] generating graphics... => 0
[6,1,1,1,1] generating graphics... => 0
[5,5] generating graphics... => 0
[5,4,1] generating graphics... => 0
[5,3,2] generating graphics... => 0
[5,3,1,1] generating graphics... => 0
[5,2,2,1] generating graphics... => 0
[5,2,1,1,1] generating graphics... => 0
[5,1,1,1,1,1] generating graphics... => 0
[4,4,2] generating graphics... => 0
[4,4,1,1] generating graphics... => 0
[4,3,3] generating graphics... => 0
[4,3,2,1] generating graphics... => 0
[4,3,1,1,1] generating graphics... => 0
[4,2,2,2] generating graphics... => 0
[4,2,2,1,1] generating graphics... => 0
[4,2,1,1,1,1] generating graphics... => 0
[4,1,1,1,1,1,1] generating graphics... => 0
[3,3,3,1] generating graphics... => 0
[3,3,2,2] generating graphics... => 0
[3,3,2,1,1] generating graphics... => 0
[3,3,1,1,1,1] generating graphics... => 0
[3,2,2,2,1] generating graphics... => 0
[3,2,2,1,1,1] generating graphics... => 0
[3,2,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2] generating graphics... => 0
[2,2,2,2,1,1] generating graphics... => 0
[2,2,2,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[11] generating graphics... => 0
[10,1] generating graphics... => 0
[9,2] generating graphics... => 0
[9,1,1] generating graphics... => 0
[8,3] generating graphics... => 0
[8,2,1] generating graphics... => 0
[8,1,1,1] generating graphics... => 0
[7,4] generating graphics... => 0
[7,3,1] generating graphics... => 0
[7,2,2] generating graphics... => 0
[7,2,1,1] generating graphics... => 0
[7,1,1,1,1] generating graphics... => 0
[6,5] generating graphics... => 0
[6,4,1] generating graphics... => 0
[6,3,2] generating graphics... => 0
[6,3,1,1] generating graphics... => 0
[6,2,2,1] generating graphics... => 0
[6,2,1,1,1] generating graphics... => 0
[6,1,1,1,1,1] generating graphics... => 0
[5,5,1] generating graphics... => 0
[5,4,2] generating graphics... => 0
[5,4,1,1] generating graphics... => 0
[5,3,3] generating graphics... => 0
[5,3,2,1] generating graphics... => 0
[5,3,1,1,1] generating graphics... => 0
[5,2,2,2] generating graphics... => 0
[5,2,2,1,1] generating graphics... => 0
[5,2,1,1,1,1] generating graphics... => 0
[5,1,1,1,1,1,1] generating graphics... => 0
[4,4,3] generating graphics... => 0
[4,4,2,1] generating graphics... => 0
[4,4,1,1,1] generating graphics... => 0
[4,3,3,1] generating graphics... => 0
[4,3,2,2] generating graphics... => 0
[4,3,2,1,1] generating graphics... => 0
[4,3,1,1,1,1] generating graphics... => 0
[4,2,2,2,1] generating graphics... => 0
[4,2,2,1,1,1] generating graphics... => 0
[4,2,1,1,1,1,1] generating graphics... => 0
[4,1,1,1,1,1,1,1] generating graphics... => 0
[3,3,3,2] generating graphics... => 0
[3,3,3,1,1] generating graphics... => 0
[3,3,2,2,1] generating graphics... => 0
[3,3,2,1,1,1] generating graphics... => 0
[3,3,1,1,1,1,1] generating graphics... => 0
[3,2,2,2,2] generating graphics... => 0
[3,2,2,2,1,1] generating graphics... => 0
[3,2,2,1,1,1,1] generating graphics... => 0
[3,2,1,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2,1] generating graphics... => 0
[2,2,2,2,1,1,1] generating graphics... => 0
[2,2,2,1,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[12] generating graphics... => 0
[11,1] generating graphics... => 0
[10,2] generating graphics... => 0
[10,1,1] generating graphics... => 0
[9,3] generating graphics... => 0
[9,2,1] generating graphics... => 0
[9,1,1,1] generating graphics... => 0
[8,4] generating graphics... => 0
[8,3,1] generating graphics... => 0
[8,2,2] generating graphics... => 0
[8,2,1,1] generating graphics... => 0
[8,1,1,1,1] generating graphics... => 0
[7,5] generating graphics... => 0
[7,4,1] generating graphics... => 0
[7,3,2] generating graphics... => 0
[7,3,1,1] generating graphics... => 0
[7,2,2,1] generating graphics... => 0
[7,2,1,1,1] generating graphics... => 0
[7,1,1,1,1,1] generating graphics... => 0
[6,6] generating graphics... => 0
[6,5,1] generating graphics... => 0
[6,4,2] generating graphics... => 0
[6,4,1,1] generating graphics... => 0
[6,3,3] generating graphics... => 0
[6,3,2,1] generating graphics... => 0
[6,3,1,1,1] generating graphics... => 0
[6,2,2,2] generating graphics... => 0
[6,2,2,1,1] generating graphics... => 0
[6,2,1,1,1,1] generating graphics... => 0
[6,1,1,1,1,1,1] generating graphics... => 0
[5,5,2] generating graphics... => 0
[5,5,1,1] generating graphics... => 0
[5,4,3] generating graphics... => 0
[5,4,2,1] generating graphics... => 0
[5,4,1,1,1] generating graphics... => 0
[5,3,3,1] generating graphics... => 0
[5,3,2,2] generating graphics... => 0
[5,3,2,1,1] generating graphics... => 0
[5,3,1,1,1,1] generating graphics... => 0
[5,2,2,2,1] generating graphics... => 0
[5,2,2,1,1,1] generating graphics... => 0
[5,2,1,1,1,1,1] generating graphics... => 0
[5,1,1,1,1,1,1,1] generating graphics... => 0
[4,4,4] generating graphics... => 0
[4,4,3,1] generating graphics... => 0
[4,4,2,2] generating graphics... => 0
[4,4,2,1,1] generating graphics... => 0
[4,4,1,1,1,1] generating graphics... => 0
[4,3,3,2] generating graphics... => 0
[4,3,3,1,1] generating graphics... => 0
[4,3,2,2,1] generating graphics... => 0
[4,3,2,1,1,1] generating graphics... => 0
[4,3,1,1,1,1,1] generating graphics... => 0
[4,2,2,2,2] generating graphics... => 0
[4,2,2,2,1,1] generating graphics... => 0
[4,2,2,1,1,1,1] generating graphics... => 0
[4,2,1,1,1,1,1,1] generating graphics... => 0
[4,1,1,1,1,1,1,1,1] generating graphics... => 0
[3,3,3,3] generating graphics... => 0
[3,3,3,2,1] generating graphics... => 0
[3,3,3,1,1,1] generating graphics... => 0
[3,3,2,2,2] generating graphics... => 0
[3,3,2,2,1,1] generating graphics... => 0
[3,3,2,1,1,1,1] generating graphics... => 0
[3,3,1,1,1,1,1,1] generating graphics... => 0
[3,2,2,2,2,1] generating graphics... => 0
[3,2,2,2,1,1,1] generating graphics... => 0
[3,2,2,1,1,1,1,1] generating graphics... => 0
[3,2,1,1,1,1,1,1,1] generating graphics... => 0
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,2,2,2,2,2] generating graphics... => 0
[2,2,2,2,2,1,1] generating graphics... => 0
[2,2,2,2,1,1,1,1] generating graphics... => 0
[2,2,2,1,1,1,1,1,1] generating graphics... => 0
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 0
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
click to show generating function       
Description
The constant term of the character polynomial of an integer partition.
The definition of the character polynomial can be found in [1]. Indeed, this constant term is $0$ for partitions $\lambda \neq 1^n$ and $1$ for $\lambda = 1^n$.
References
[1] Garsia, A. M., Goupil, A. Character polynomials, their $q$-analogs and the Kronecker product MathSciNet:2576382
Code
def statistic(L):
    return L.character_polynomial()(*[0]*sum(L))
Created
Aug 07, 2017 at 13:59 by Christian Stump
Updated
Aug 07, 2017 at 20:05 by Christian Stump