"Overpartitionized" Rogers--Ramanujan type identities

TL;DR

This paper explores algebraic manipulations of classical q-series identities, like Rogers-Ramanujan, to derive combinatorial interpretations involving overpartitions, supported by bijective proofs.

Contribution

It introduces new combinatorial interpretations of classical q-series identities through overpartitions and provides bijective proofs for these interpretations.

Findings

New combinatorial interpretations in terms of overpartitions

Algebraic manipulations of classical q-series identities

Bijective proofs of the identities

Abstract

Many classical $q$-series identities, such as the Rogers--Ramanujan identities, yield combinatorial interpretations in terms of integer partitions. Here we consider algebraically manipulating some of the classical $q$-series to yield natural combinatorial interpretations in terms of overpartitions. Bijective proofs are supplied as well.