Special Seminar by Prof. Dr. Brian Preston Hopkins
Title: Integer Partitions and Parity
Speaker: Prof. Dr. Brian Preston Hopkins
Mathematics Department, Saint Peter’s University, NJ, USA
Date: Wednesday, 31 January 2024
Time: 16:00-17:00 PM
Integer partitions are a “basic science” mathematical concept with applications in many fields of mathematics and also physics and genetics. Their study began with Euler, who eventually established a recurrence relation for the number of partitions of a given sum, but many basic questions remain unanswered to this day. Data suggest that half of all sums have an even number of partitions, yet there are only limited general results towards establishing this basic fact. After surveying this situation, we will focus on a generalization called overpartitions. For a certain class of these overpartitions, we can show that the number for almost every sum is not only even, but a multiple of four. The proofs use combinatorial techniques, many from the late 1800s.