Symmetric function
In mathematics, a function of n {\displaystyle n} variables is symmetric if its value is the same no matter the order of its arguments. For example, a function f ( x 1 , x 2 ) {\displaystyle f\left(x_{1},x_{2}\right)} of two arguments is a symmetric function if and only if f ( x 1 , x 2 ) = f ( x 2 , x 1 ) {\displaystyle f\left(x_{1},x_{2}\right)=f\left(x_{2},x_{1}\right)} for all x 1 {\displaystyle x_{1}} and x 2 {\displaystyle x_{2}} such that ( x 1 , x 2 ) {\displaystyle \left(x_{1},x_{2}\right)} and ( x 2 , x 1 ) {\displaystyle \left(x_{2},x_{1}\right)} are in the domain of f .