Signed Partitions and Rogers-Ramanujan type Identities

George Andrews [\emph{Bull. Amer. Math. Soc.}, 2007, 561–573] introduced the idea of a \emph{signed partiton} of an integer; similar to an ordinary integer partitions, but where some of the parts could be negative. Further, Andrews reinterpreted the classical Göllnitz–Gordon partition identities in terms of signed partitions. In the present work, we provide interpretations of the sum sides of Rogers–Ramanujan type identities, including a new signed partition interpretation of the Göllnitz–Gordon identities, different from that of Andrews. Both analytic and bijective proofs are presented.