symmetric polynomial

A polynomial $f\in R[x_1,\mathrm{\dots },x_n]$ in $n$ variables with coefficients in a ring $R$ is symmetric if $\sigma (f)=f$ for every permutation $\sigma$ of the set $\{x_1,\mathrm{\dots },x_n\}$.

Every symmetric polynomial can be written as a polynomial expression in the elementary symmetric polynomials.