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. / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/17641 |
| Date | 06 May 2015 |
| Creators | Ndlovu, Miehleketo Brighton |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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