In this dissertation, we examine the nature of embeddings with regard to both combinatorial and geometric configurations. A combinatorial [r,k]-configuration is a collection of abstract points and sets (referred to as blocks) such that each point is a member of r blocks, each block is of size k, and these objects satisfy a linearity criterion: no two blocks intersect in more than one point. A geometric configuration requires that the points and blocks be realized as points and lines within the Euclidean plane. We provide improvements on the current bounds for the asymptotic existence of both combinatorial and geometric configurations. In addition, we examine the largely new problem of embedding configurations within larger configurations possessing regularity properties. Additionally, previously undiscovered geometric [r,k]-configurations are found as near-coverings of combinatorial configurations. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/6049 |
| Date | 29 April 2015 |
| Creators | Flowers, Garret |
| Contributors | Dukes, Peter |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web, http://creativecommons.org/publicdomain/zero/1.0/ |
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