Generating Function for Elementary Symmetric Function/Outline

Outline
Generating function discovery methods can find a formula for $\map G z$.

Let $n = 1$.

Then $U$ is a singleton:
 * $U = \set {x_1}$.

Expand the formal series:

Product of Generating Functions and experience with elementary symmetric functions suggests:


 * $\map G z = \paren {1 + x_1 z} \paren {1 + x_2 z} \cdots \paren {1 + x_n z}$