Three Aspects of

In this paper we shall discuss three topics in partitions. Section 2 is devoted to partitions with difference conditions and is an elucidation of joint work with J. B. Olsson [16]. In Section 3 we discuss certain partition problems which have their origins in statistical mechanics. We take as the theme for this section Euler’s article: Exemplum Memorabile Inductionis Fallacis [23]. The material for this section is closely related to the work in [10]. Section 4 contains a discussion of some of Ramanujan’s formulas from both his Notebooks and lost Notebook. More extensive accounts of this topic are found in [8] and [11].