Q: What do ring homomorphisms, homogeneous and elementary symmetric functions, brick tabloids, and involutions have in common? A: If you mash them all together and stir them around, you can get some nice results for generating functions for various permutation statistics. In this talk, we'll define all the stuff we'll need to use. Then we will prove some famous results, as well as mention some not-so-famous results. It will be an example of how combinatorial objects can take a problem out of its current context (e.g. the ring of symmetric functions, or representation theory, or any number of other areas) to prove theorems in an accessible way.