### Faculty Member

Many combinatorial functions related to integer partitions have a surprising kind of regularity in their divisibility properties. For example, the Ramanujan Congruences say that p(5n+4) is a multiple of 5 for all n, where p(n) is the partition counting function. A combinatorial explanation of this fact is given by Dyson’s rank function, which splits the set of partitions of 5n+4 into 5 sets of equal size. We will use computational methods to explore some of the arithmetic patterns related to ranks of partitions.

### Team Meetings

### Project Difficulty

### Undergrad Prerequisites

Students should have some experience with discrete math via 213 or 347 or something similar, either previously or concurrently. Experience with modular arithmetic and/or combinatorics would be particularly helpful.

We will use Mathematica throughout the semester. Experience programming would be very helpful.