Combinatorial generalizations and refinements of Euler's partition theorem
Ndlovu, Miehleketo Brighton
The aim of this research project is to survey and elaborate on various generalizations and re nements of Euler's celebrated distinct-odd partition theorem which asserts the equality of the numbers of partitions of a positive integer into distinct summands and into odd summands. Although the work is not originally my own, I give clarity where there is obscurity by bridging the gaps on the already existing work. I touch on combinatorial proofs, which are either bijective or involutive. In some cases I give both combinatorial and analytic proofs. The main source of this dissertation is [22, 5, 6, 8]. I start by rst summarizing some methods and techniques used in partition theory.
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. 9 December 2014.