Lattice paths and multiple basic hypergeometric series

Abstract

While each side of equations (0.1) and (0.2) is easily interpreted as a generating function for certain restricted partitions, the interpretation of the left-hand side of equation (0.3) presents more of a problem. It was William Burge [Bur 1, Bur 2] who demonstrated that the most natural interpretation is in terms of weighted binary words. He was then able to establish one-to-one correspondences between his binary words of weight n and several different sets of partitions of n, thus providing new proofs of partition identities of Basil Gordon [Gor] and George Andrews [And 2]. Burge also gave interpretations of two other multiple basic hypergeometric series, and Andrews and Bressoud [A&B] have interpreted a