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 $\mathsf{Pr} \infty \mathsf{fWiki}$ introduces the notation:

$E_{\tuple {m, n} } := \map {e_m} {\set {x_1, x_2, \ldots, x_n} }$

The term $E_{\tuple {m, n} }$ was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$ in order to streamline the presentation of resources concerning elementary symmetric functions.

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.