Combinatorial generalizations and refinements of Euler's partition theorem

• Main Author: Ndlovu, Miehleketo Brighton
• Format: Others
• Language: en
• Published: 2015
• Subjects: Partitions (Mathematics); Combinations.
• Online Access: http://hdl.handle.net/10539/17641

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.