Definition:Symmetric Function/Elementary

Definition
Let $a, b \in \Z$ be integers such that $b \ge a$.

Let $U$ be a set of $n = b - a + 1$ numbers $\set {x_a, x_{a + 1}, \ldots, x_b}$.

Let $m \in \Z_{>0}$ be a (strictly) positive integer.

An elementary symmetric function of degree $m$ is a polynomial which can be defined by the formula:

That is, it is the sum of all products of $m$ distinct elements of $\set {x_a, x_{a + 1}, \dotsc, x_b}$.

Also see

 * Recursion Property of Elementary Symmetric Function