Definition:Permutation on Polynomial

Definition
Let $f \paren {x_1, x_2, \ldots, x_n}$ denote a polynomial in $n$ variables $x_1, x_2, \ldots, x_n$.

Let $S_n$ denote the symmetric group on $n$ letters.

Let $\pi, \rho \in S_n$.

Then $\pi * f$ is the polynomial obtained by applying the permutation $\pi$ to the subscripts on the variables of $f$.

This is called the permutation on the polynomial $f$ by $\pi$, or the $f$-permutation by $\pi$.

Also known as
This is also called the permutation of the polynomial.

Also see

 * Permutation on Polynomial is Group Action