Buffered Frobenius representations of overpartitions

Abstract:

Overpartitions arise as a way to give combinatorial interpretation of the coefficients of qq-hypergeometric series. We generalize the first and second Frobenius representations of overpartitions into two infinite families, which in turn correspond to generalizations of the Dyson rank and M2M2-rank of overpartitions, the MdMd-ranks. The moments of these new rank functions give rise to mock modular forms, as is the case with the Dyson and M2M2-ranks.