Identifier
Values
=>
Cc0002;cc-rep
[2]=>0
[1,1]=>1
[3]=>0
[2,1]=>0
[1,1,1]=>1
[4]=>0
[3,1]=>0
[2,2]=>0
[2,1,1]=>0
[1,1,1,1]=>1
[5]=>0
[4,1]=>0
[3,2]=>0
[3,1,1]=>0
[2,2,1]=>0
[2,1,1,1]=>0
[1,1,1,1,1]=>1
[6]=>0
[5,1]=>0
[4,2]=>0
[4,1,1]=>0
[3,3]=>0
[3,2,1]=>0
[3,1,1,1]=>0
[2,2,2]=>0
[2,2,1,1]=>0
[2,1,1,1,1]=>0
[1,1,1,1,1,1]=>1
[7]=>0
[6,1]=>0
[5,2]=>0
[5,1,1]=>0
[4,3]=>0
[4,2,1]=>0
[4,1,1,1]=>0
[3,3,1]=>0
[3,2,2]=>0
[3,2,1,1]=>0
[3,1,1,1,1]=>0
[2,2,2,1]=>0
[2,2,1,1,1]=>0
[2,1,1,1,1,1]=>0
[1,1,1,1,1,1,1]=>1
[8]=>0
[7,1]=>0
[6,2]=>0
[6,1,1]=>0
[5,3]=>0
[5,2,1]=>0
[5,1,1,1]=>0
[4,4]=>0
[4,3,1]=>0
[4,2,2]=>0
[4,2,1,1]=>0
[4,1,1,1,1]=>0
[3,3,2]=>0
[3,3,1,1]=>0
[3,2,2,1]=>0
[3,2,1,1,1]=>0
[3,1,1,1,1,1]=>0
[2,2,2,2]=>0
[2,2,2,1,1]=>0
[2,2,1,1,1,1]=>0
[2,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1]=>1
[9]=>0
[8,1]=>0
[7,2]=>0
[7,1,1]=>0
[6,3]=>0
[6,2,1]=>0
[6,1,1,1]=>0
[5,4]=>0
[5,3,1]=>0
[5,2,2]=>0
[5,2,1,1]=>0
[5,1,1,1,1]=>0
[4,4,1]=>0
[4,3,2]=>0
[4,3,1,1]=>0
[4,2,2,1]=>0
[4,2,1,1,1]=>0
[4,1,1,1,1,1]=>0
[3,3,3]=>0
[3,3,2,1]=>0
[3,3,1,1,1]=>0
[3,2,2,2]=>0
[3,2,2,1,1]=>0
[3,2,1,1,1,1]=>0
[3,1,1,1,1,1,1]=>0
[2,2,2,2,1]=>0
[2,2,2,1,1,1]=>0
[2,2,1,1,1,1,1]=>0
[2,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1,1]=>1
[10]=>0
[9,1]=>0
[8,2]=>0
[8,1,1]=>0
[7,3]=>0
[7,2,1]=>0
[7,1,1,1]=>0
[6,4]=>0
[6,3,1]=>0
[6,2,2]=>0
[6,2,1,1]=>0
[6,1,1,1,1]=>0
[5,5]=>0
[5,4,1]=>0
[5,3,2]=>0
[5,3,1,1]=>0
[5,2,2,1]=>0
[5,2,1,1,1]=>0
[5,1,1,1,1,1]=>0
[4,4,2]=>0
[4,4,1,1]=>0
[4,3,3]=>0
[4,3,2,1]=>0
[4,3,1,1,1]=>0
[4,2,2,2]=>0
[4,2,2,1,1]=>0
[4,2,1,1,1,1]=>0
[4,1,1,1,1,1,1]=>0
[3,3,3,1]=>0
[3,3,2,2]=>0
[3,3,2,1,1]=>0
[3,3,1,1,1,1]=>0
[3,2,2,2,1]=>0
[3,2,2,1,1,1]=>0
[3,2,1,1,1,1,1]=>0
[3,1,1,1,1,1,1,1]=>0
[2,2,2,2,2]=>0
[2,2,2,2,1,1]=>0
[2,2,2,1,1,1,1]=>0
[2,2,1,1,1,1,1,1]=>0
[2,1,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1,1,1]=>1
[11]=>0
[10,1]=>0
[9,2]=>0
[9,1,1]=>0
[8,3]=>0
[8,2,1]=>0
[8,1,1,1]=>0
[7,4]=>0
[7,3,1]=>0
[7,2,2]=>0
[7,2,1,1]=>0
[7,1,1,1,1]=>0
[6,5]=>0
[6,4,1]=>0
[6,3,2]=>0
[6,3,1,1]=>0
[6,2,2,1]=>0
[6,2,1,1,1]=>0
[6,1,1,1,1,1]=>0
[5,5,1]=>0
[5,4,2]=>0
[5,4,1,1]=>0
[5,3,3]=>0
[5,3,2,1]=>0
[5,3,1,1,1]=>0
[5,2,2,2]=>0
[5,2,2,1,1]=>0
[5,2,1,1,1,1]=>0
[5,1,1,1,1,1,1]=>0
[4,4,3]=>0
[4,4,2,1]=>0
[4,4,1,1,1]=>0
[4,3,3,1]=>0
[4,3,2,2]=>0
[4,3,2,1,1]=>0
[4,3,1,1,1,1]=>0
[4,2,2,2,1]=>0
[4,2,2,1,1,1]=>0
[4,2,1,1,1,1,1]=>0
[4,1,1,1,1,1,1,1]=>0
[3,3,3,2]=>0
[3,3,3,1,1]=>0
[3,3,2,2,1]=>0
[3,3,2,1,1,1]=>0
[3,3,1,1,1,1,1]=>0
[3,2,2,2,2]=>0
[3,2,2,2,1,1]=>0
[3,2,2,1,1,1,1]=>0
[3,2,1,1,1,1,1,1]=>0
[3,1,1,1,1,1,1,1,1]=>0
[2,2,2,2,2,1]=>0
[2,2,2,2,1,1,1]=>0
[2,2,2,1,1,1,1,1]=>0
[2,2,1,1,1,1,1,1,1]=>0
[2,1,1,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1,1,1,1]=>1
[12]=>0
[11,1]=>0
[10,2]=>0
[10,1,1]=>0
[9,3]=>0
[9,2,1]=>0
[9,1,1,1]=>0
[8,4]=>0
[8,3,1]=>0
[8,2,2]=>0
[8,2,1,1]=>0
[8,1,1,1,1]=>0
[7,5]=>0
[7,4,1]=>0
[7,3,2]=>0
[7,3,1,1]=>0
[7,2,2,1]=>0
[7,2,1,1,1]=>0
[7,1,1,1,1,1]=>0
[6,6]=>0
[6,5,1]=>0
[6,4,2]=>0
[6,4,1,1]=>0
[6,3,3]=>0
[6,3,2,1]=>0
[6,3,1,1,1]=>0
[6,2,2,2]=>0
[6,2,2,1,1]=>0
[6,2,1,1,1,1]=>0
[6,1,1,1,1,1,1]=>0
[5,5,2]=>0
[5,5,1,1]=>0
[5,4,3]=>0
[5,4,2,1]=>0
[5,4,1,1,1]=>0
[5,3,3,1]=>0
[5,3,2,2]=>0
[5,3,2,1,1]=>0
[5,3,1,1,1,1]=>0
[5,2,2,2,1]=>0
[5,2,2,1,1,1]=>0
[5,2,1,1,1,1,1]=>0
[5,1,1,1,1,1,1,1]=>0
[4,4,4]=>0
[4,4,3,1]=>0
[4,4,2,2]=>0
[4,4,2,1,1]=>0
[4,4,1,1,1,1]=>0
[4,3,3,2]=>0
[4,3,3,1,1]=>0
[4,3,2,2,1]=>0
[4,3,2,1,1,1]=>0
[4,3,1,1,1,1,1]=>0
[4,2,2,2,2]=>0
[4,2,2,2,1,1]=>0
[4,2,2,1,1,1,1]=>0
[4,2,1,1,1,1,1,1]=>0
[4,1,1,1,1,1,1,1,1]=>0
[3,3,3,3]=>0
[3,3,3,2,1]=>0
[3,3,3,1,1,1]=>0
[3,3,2,2,2]=>0
[3,3,2,2,1,1]=>0
[3,3,2,1,1,1,1]=>0
[3,3,1,1,1,1,1,1]=>0
[3,2,2,2,2,1]=>0
[3,2,2,2,1,1,1]=>0
[3,2,2,1,1,1,1,1]=>0
[3,2,1,1,1,1,1,1,1]=>0
[3,1,1,1,1,1,1,1,1,1]=>0
[2,2,2,2,2,2]=>0
[2,2,2,2,2,1,1]=>0
[2,2,2,2,1,1,1,1]=>0
[2,2,2,1,1,1,1,1,1]=>0
[2,2,1,1,1,1,1,1,1,1]=>0
[2,1,1,1,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1,1,1,1,1]=>1
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
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 $\lambda = 1^n$.
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
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!