Analytic and combinatorial explorations of partitions associated with the Rogers-Ramanujan identities and partitions with initial repetitions
Date
2016-09-16
Authors
Nyirenda, Darlison
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
In this thesis, various partition functions with respect to Rogers-Ramanujan identities
and George Andrews' partitions with initial repetitions are studied.
Agarwal and Goyal gave a three-way partition theoretic interpretation of the Rogers-
Ramanujan identities. We generalise their result and establish certain connections
with some work of Connor. Further combinatorial consequences and related partition
identities are presented.
Furthermore, we re ne one of the theorems of George Andrews on partitions with
initial repetitions. In the same pursuit, we construct a non-diagram version of the
Keith's bijection that not only proves the theorem, but also provides a clear proof
of the re nement.
Various directions in the spirit of partitions with initial repetitions are discussed
and results enumerated. In one case, an identity of the Euler-Pentagonal type is
presented and its analytic proof given.
Description
A thesis submitted to the Faculty of Science, University of the
Witwatersrand, Johannesburg, in ful lment of the requirements for
the degree of Doctor of Philosophy.
Johannesburg, 2016.