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

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.