*Electronic Theses and Dissertations (Masters)
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Item Enumeration of binary strings and applications to compositions and partitions(University of the Witwatersrand, Johannesburg, 2023) Raphadu, MalekaIn this dissertation we first introduce binary strings and give a historical background. Then we discus some techniques for enumerating restricted sets of binary strings ,with several example . We employ mainly the symbolic method and recursive techniques, among others, to obtain our results. A chapter is devoted to a discussion of some published case studies on bit string enumerations which are relevant to our project. Then we consider how the study of binary string may facilitate the enumeration of selected classes of compositions and integer partitions.Item On polarity-based semantics for non-distributive modal logics(University of the Witwatersrand, Johannesburg, 2023) Clingman, R.; Conradie, WillemThis masters study builds upon recent research in polarity-based semantics for non-distributive modal logics (NDMLs). Current formulations of polarity-based semantics for NDML impose compatibility requirements on additional relations of polarity-based frames, hindering applicability of the semantics, as arbitrary frames need not be compatible. In this study we develop a polarity-based semantics for NDML with modalites that are, in general, neither normal nor distributive and without the imposition of compatibility requirements. We provide a sound and complete axiomatization of this logic. The second half of the thesis focuses on a special class of enriched polarities, those who are in a sense liftings of Kripke frames. The compatibility of these liftings combined with the intuitive nature of the underlying Kripke frames makes for a useful case study in which to explore p-morphisms between enriched polarities, and enriched polarity-based models, from a relational perspective.Item Resolvability of groups(University of the Witwatersrand, Johannesburg, 2020) Ndhlalane, MororisengA topological group is called resolvable if it can be partitioned into two dense subsets. A group is absolutely resolvable if it can be partitioned into two subsets dense in any nondescript group topology. The aim of this dissertation is to give a unified exposition of some major results about resolvability of groups. In particular, we show that; 1. Every countable nondescript topological group not containing an open Boolean subgroup is resolvable, 2. Every infinite Abelian group not containing an infinite Boolean subgroup is absolutely resolvable.