Properties of integer partitions and plane partitions

Abstract

Generating functions and asymptotic analysis have been used in four di er- ent situations to establish new results for extremely well studied structures. Later in this thesis a more detailed individual abstract for each of these studies is provided. The four situations are: A. Durfee square areas in integer partitions. B. A study of the relationship between integer compositions and their constituent partitions by specifying the asymptotic expectation of the number of such partitions in arbitrary composition. C. Similar to B above but focusing more on the generating functions rather than on the expectations derived therefrom. D. In the area of plane partitions with additional structure imposed upon them.