  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 paper, we use the Littlewood decomposition of partitions to study
partitions with bounded largest part and fixed integral value of GBG-rank
modulo primes. As a consequence, we obtain new elegant generating function
formulas for unrestricted partitions, self-conjugate partitions, and partitions
whose parts repeat finite number of times.
