On partitions with bounded largest part and fixed integral GBG-rank modulo primesMPIM

by Aritram Dhar (University of Florida)

Tuesday Feb 3, 2026, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

In 2009, Berkovich and Garvan introduced a new partition statistic called the GBG-rank modulo t which is a generalization of the well-known BG-rank.
In this talk, we explain the use of Littlewood decomposition of partitions to study partitions with bounded largest part and fixed integral value of  GBG-rank modulo prime t. As a consequence, we obtain new elegant generating function formulas for unrestricted partitions, self-conjugate partitions, and partitions whose parts repeat at most t − 1 times. This talk is based on joint work with my advisor Alexander Berkovich.