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We examine an identity originally stated in Ramanujan's ``lost notebook'' andfirst proven algebraically by Andrews and combinatorially by Kim. We give twoindependent combinatorial proofs and interpretations of this identity, whichalso extends an identity recently proven by Pak and Waarnar related to theproduct of partial theta functions: First, we give a direct combinatorialproof, using the involution principle, of a special case of the identity, andextend this into a direct combinatorial proof of the full identity as written.Second, we show that the identity can be rewritten, using minor algebraicmanipulation, into an identity that can be proven with a direct bijection. Weprovide such a bijection using a generalization of a standard bijection frompartition theory.

Combinatorial Proofs of an Identity from Ramanujan's Lost Notebook and its Variations