# Two Families of Buffered Frobenius Representations of Overpartitions

## TL;DR

This paper introduces two new families of buffered Frobenius representations that generalize existing overpartition rank generating series, providing combinatorial interpretations for these extended structures.

## Contribution

It extends the generating series of overpartition ranks to k-fold variants and offers combinatorial interpretations for these new representations.

## Key findings

- Generalization of Dyson and M_2 ranks to k-fold variants
- Introduction of two families of buffered Frobenius representations
- Combinatorial interpretations for the new representations

## 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.