A permutation of length n is a rearrangement of numbers from 1 through n, written as a list of those numbers. A principal permutation class is the set of all permutations that don’t contain a permutation as a pattern. For instance, with 321 as our pattern, the associated principal permutation class is the set of permutations that don’t contain 3 decreasing numbers when read from left to right. The primary topic of interest in this area is counting just how many permutations of each length are in a principal permutation class. Very little is known about exact counts. Instead, in this project, we investigate how some specific classes relate to each other.