Overpartition analogues of q-binomial coefficients and their applications
| dc.contributor.author | Ngubane, Siphephelo | |
| dc.date.accessioned | 2022-03-30T20:43:55Z | |
| dc.date.available | 2022-03-30T20:43:55Z | |
| dc.date.issued | 2018 | |
| dc.description | A dissertation submitted in fulfillment of the requirement of the degree of Master of Science (M.Sc.) in Pure Mathematics to the Faculty of Science, University of the Witwatersrand, 2018 | en_ZA |
| dc.description.abstract | In partition theory it is well known that the Gaussian polynomials ( or q binomial coefficients) [m:,n] generate integer partitions that fit inside an mxn rectangle, that is, partitions with largest part at most m and the number of parts does not exceed n. In this dissertation , we study the overpartition extension of these polynomials known as over q-binomial coefficients. These are ge11 erati11g fuuctio11s that enumerate overpartitio11s fitting inside au m, x n rectangle. First we discuss the ordinary q-binomial coefficients. Then we examine the over q-hiuomial coefficients with respect to their motivations, q-analogues of classical identities, and various combinatorial and analytic applications. | en_ZA |
| dc.description.librarian | TL (2022) | en_ZA |
| dc.faculty | Faculty of Science | en_ZA |
| dc.identifier.uri | https://hdl.handle.net/10539/32839 | |
| dc.language.iso | en | en_ZA |
| dc.title | Overpartition analogues of q-binomial coefficients and their applications | en_ZA |
| dc.type | Thesis | en_ZA |