Exact Pattern Containment in Restricted Growth Functions

In the mathematical field of enumerative combinatorics, we study the number of ways a pattern can emerge given certain constraints. In my research I examine the ways that a mathematical object called a “restricted growth function” (RGF) can be contained in another RGF and the distribution of certain “combinatorial statistics” on sets of RGF’s containing others. I find connections to many famous combinatorial objects such as set partitions, integer partitions, Fibonacci numbers, Pascal’s triangle, Catalan numbers, and more