Definition:Permutation on Polynomial

Definition
Let $$f \left({x_1, x_2, \ldots, x_n}\right)$$ be 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 the permutation of the polynomial $$f$$ by $$\pi$$, or the $$f$$-permutation by $$\pi$$.

Also see

 * Permutation on a Polynomial is a Group Action