A unified method to prove Rogers-Ramanujan generalizations

A unified method to prove Rogers-Ramanujan generalizations

The first of the famous Rogers-Ramanujan identities states that the number of partitions of a positive integer n into distinct non-consecutive parts equals the number of partitions of n into parts that are 1 or 4 mod 5. Gordon later extended this theorem for partitions into repeated parts with some limit on the number of occurrences. There have been many generalizations since then. We will describe a unified method of proving Rogers-Ramanujan-Gordon generalizations. Our starting point is Andrews' recent paper "Parity in Partitions" and we will work with larger moduli. As time allows, we will show how to apply the method in some results involving overpartitions.