On a theorem of Alladi and Gordon and the gaussian polynomials

Alladi and Gordon [J. Combin. Theory Ser. A 63 (1993), 275–300] have recently proved a general partition identity which generalized earlier results by Bressoud and Göllnitz by analyzing a continued fraction introduced by Ramanujan. This result was the motivation for the investigation of the sets of partitions and bipartitions defined in this article. We construct explicit bijections between the sets of partitions and bipartitions under consideration, giving a new proof of the formula for the Gaussian polynomials and leading to a strong refinement of the theorem by Alladi and Gordon.