I am working with polynomials in several variables with the obvious action of $S_n$. That is, given a polynomial $f$ in the variables $x_1, \dots, x_n$, a permutation $\sigma \in S_n$ acts on $f$ by sending $x_i$ to $x_{\sigma(i)}$.
What I would like to do is to give Mathematica a polynomial, for example
$x_1^2x_2 + x_3$
and have it compute the image of this under the action of a particular element. For example, if I gave it $(123)$ it would output
$x_2^2x_3 + x_1$.
Thanks!