Notation for symmetric polynomials

Question

A symmetric polynomial is a polynomial $p \in \mathbb{R}[x_1, \ldots, x_n]$ such that, if any of the variables are interchanged, one obtains the same polynomial. Is there standard notation for saying "$p$ is a symmetric polynomial"?

Answer 1

The algebra of symmetric polynomials is usually denoted by $\mathbb{R}[x_1,\dots,x_n]^{S_n}$, so you can write $p \in \mathbb{R}[x_1,\dots,x_n]^{S_n}$ (see e.g. the wikipeda entry about invariant theory).