Blecher, Aubrey2013-08-072013-08-072013-08-07http://hdl.handle.net/10539/13015A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy (by production of original research) in Mathematics School of Mathematics University of the Witwatersrand Johannesburg December 2012Generating 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.enGeometry, Plane.Arbitrage - Mathematical models.Thesis