Pairwise Balanced Designs of Dimension Three
| dc.contributor.author | Niezen, Joanna | |
| dc.contributor.supervisor | Dukes, Peter | |
| dc.date.accessioned | 2013-12-20T18:53:48Z | |
| dc.date.available | 2013-12-20T18:53:48Z | |
| dc.date.copyright | 2013 | en_US |
| dc.date.issued | 2013-12-20 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | 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. | en_US |
| dc.description.proquestcode | 0405 | en_US |
| dc.description.proquestemail | jniezen@uvic.ca | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/5102 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights.temp | Available to the World Wide Web | en_US |
| dc.subject | pairwise balanced design | en_US |
| dc.subject | PBD | en_US |
| dc.subject | Latin square | en_US |
| dc.subject | MOLS | en_US |
| dc.subject | GDD | en_US |
| dc.subject | dimension | en_US |
| dc.subject | linear space | en_US |
| dc.subject | game of Set | en_US |
| dc.subject | Steiner triple system | en_US |
| dc.subject | STS | en_US |
| dc.subject | Steiner space | en_US |
| dc.subject | subspace | en_US |
| dc.subject | Wilson's construction | en_US |
| dc.title | Pairwise Balanced Designs of Dimension Three | en_US |
| dc.type | Thesis | en_US |