Two Families of Buffered Frobenius Representations of Overpartitions

Abstract

We generalize the generating series of the Dyson ranks and $M_2$-ranks of overpartitions to obtain $k$-fold variants, and give a combinatorial interpretation of each. The $k$-fold generating series correspond to the full ranks of two families of buffered Frobenius representations, which generalize Lovejoy's first and second Frobenius representations of overpartitions, respectively.

Cited by in corpus (1)

• Variations of Andrews-Beck type congruences