Definition:Symmetric Function/Elementary

Definition
An elementary symmetric function is a polynomial which can be defined by the formula:


 * $a_m = \displaystyle \sum_{a \mathop \le j_1 \mathop < j_2 \mathop < \mathop \cdots \mathop < j_m \mathop \le b} x_{j_1} x_{j_2} \cdots x_{j_m}$

for integers $a, b \in \Z$ such that $b \ge a$.