On a theorem of Alladi and Gordon and the Gaussian polynomials
By analyzing a continued fraction of Ramanujan, the reviewer and \textit{B. Gordon} [J. Comb. Theory, Ser. A 63, No. 2, 275-300 (1993; Zbl 0781.05006)] obtained a general partition identity in the form of an equality between three partition functions \(A\), \(B\) and \(C\). This generalized earlier results due to Bressoud and Göllnitz. The reviewer and Gordon established the equality \(A= C\) combinatorially by constructing a bijective, but to prove \(A= B\) they utilized Ramanujan's continued fraction. In this paper, the author constructs an explicit bijection between \(A\) and \(B\). In doing so, not only a strong refinement of the Alladi-Gordon theorem is obtained, but some new insights into certain Gaussian polynomial formulas are revealed.
scientific article; zbMATH DE number 720832