On the Unexpected Connections in the Arithmetic Properties of POND and PEND Partitions
Date: 09/04/2025
Time: 14:00 - 16:00
Time: 14:00 - 16:00
Location: RISC, Seminarroom, Castle of Hagenberg
Recently, Ballantine and Welch considered two classes of integer partitions which they labeled POND and PEND partitions. These are integer partitions wherein the odd parts (respectively, the even parts) *cannot* be distinct. In recent work, I studied these two types of partitions from an arithmetic perspective and proved infinite families of mod 3 congruences satisfied by the two corresponding enumerating functions. I will talk about the generating functions for these enumerating functions, and I will also highlight the elementary proofs that I utilized. In the latter portion of the talk, I will discuss unexpected connections between these divisibility properties for POND and PEND partitions by considering modified versions of the generating functions in question and relating these new generating functions in a natural way via Atkin-Lehner involutions. This part of the talk is joint work with Nicolas Smoot (University of Vienna).