A linear space is a set of points and lines such that any pair of points lie on exactly one line together. This is equivalent to a pairwise balanced design PBD(v, K), where there are v points, lines are regarded as blocks, and K ⊆ Z≥2 denotes the set of allowed block sizes. The dimension of a linear space is the maximum integer d such that any set of d points is contained in a proper subspace. Specifically for K = {3, 4, 5}, we determine which values of v admit PBD(v,K) of dimension at least three for all but a short list of possible exceptions under 50. We also observe that dimension can be reduced via a substitution argument. / Graduate / 0405 / jniezen@uvic.ca
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/5102 |
| Date | 20 December 2013 |
| Creators | Niezen, Joanna |
| Contributors | Dukes, Peter |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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