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This thesis shows results on 3 different problems involving partial difference sets (PDS) in abelian groups, and uses PDS to study partial geometries with an abelian Singer group. First, the last two undetermined cases of PDS on abelian groups with k ≤ 100, both of order 216, were shown not to exist. Second, new parameter bounds for k and Δ were found for PDS on abelian groups of order pn , p an odd prime, n odd. A parameter search on p5 in particular was conducted, and only 5 possible such cases remain for p < 250. Lastly, the existence of rigid type partial geometries with an abelian Singer group are examined; existence is left undetermined for 11 cases with α ≤ 200. This final study led to the determination of nonexistence for an infinite class of cases which impose a negative Latin type PDS.
| Advisor: | Wang, Zeying |
| Commitee: | Onder, Nilufer, Tonchev, Vladimir |
| School: | Michigan Technological University |
| Department: | Mathematical Sciences |
| School Location: | United States -- Michigan |
| Source: | MAI 58/05M(E), Masters Abstracts International |
| Source Type: | DISSERTATION |
| Subjects: | Mathematics |
| Keywords: | Partial difference set, Partial geometry, Strongly regular graph |
| Publication Number: | 13863113 |
| ISBN: | 978-1-392-17339-8 |
