Overpartition analogues of q-binomial coefficients and their applications
Date
2018
Authors
Ngubane, Siphephelo
Journal Title
Journal ISSN
Volume Title
Publisher
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.
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