  The set $S(n)$ of all elementary symmetric polynomials in $n$ variables is a
minimal generating set for the algebra of symmetric polynomials in $n$
variables, but over a finite field ${\mathbb F}_q$ the set $S(n)$ is not a
minimal separating set for symmetric polynomials in general. We determined when
$S(n)$ is a minimal separating set for the algebra of symmetric polynomials
having the least possible number of elements.
