Is there a nice way to use generating functions to represent the formal sum of all size-$k$ subsets of a set $S$? Here I want to represent a subset by the product of its elements.
For example, if $S = \{a,b,c\}$ and $k = 2$ then then the formal sum is $ab + ac + bc$. Is there a nice way for arbitrary $k$ and $S = \{a_1,a_2,\dots,a_n\}$?
I'm trying to solve a more general problem, but my difficulty has boiled down to this.
Thanks for the help!