3. Electronic Theses and Dissertations (ETDs) - All submissions

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Combinatorial generalizations and refinements of Euler's partition theorem
(2015-05-06) 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.