Partition identities and a continued fraction of Ramanujan

Abstract

We study the numerator and denominator of a continued fraction R( a, b) of Ramanujan and establish the equality of various restricted partition functions. We use the continued fraction to give a unified approach to several partition identities some of which generalize results of Bressoud and Göllnitz. We also give a combinatorial interpretation for the coefficients in the power series expansion of the reciprocal 1 R (−a, −b) , extending a result of Odlyzko and Wilf.