Date of Award
2019
Document Type
Open Access Master's Thesis
Degree Name
Master of Science in Mathematical Sciences (MS)
Administrative Home Department
Department of Mathematical Sciences
Advisor 1
Zeying Wang
Committee Member 1
Vladimir Tonchev
Committee Member 2
Nilufer Onder
Abstract
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 ∆ were found for PDS on abelian groups of order p^n , p an odd prime, n odd. A parameter search on p^5 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.
Recommended Citation
Neubert, Eric J. Jr, "Some results on partial difference sets and partial geometries", Open Access Master's Thesis, Michigan Technological University, 2019.