Definition:Elementary Symmetric Function/Notation

Notation for Elementary Symmetric Function
Let $U$ be established such that $\size U = n$.

It is commonplace for $U$ to be presented in the form $\set {x_1, x_2, \ldots, x_n}$.

Consequently, the elementary symmetric function of degree $m$ is often presented $\map {e_m} {\set {x_1, x_2, \ldots, x_n} }$, which is unwieldy.

Hence introduces the notation:
 * $E_{\tuple {m, n} } := \map {e_m} {\set {x_1, x_2, \ldots, x_n} }$