Date of Award
Bachelor of Science
Dr. James A. Davis
The work consists of three parts. The first is a study of Cameron-Liebler line classes which receive much attention recently. We studied a new construction of infinite family of Cameron-Liebler line classes presented in the paper by Tao Feng, Koji Momihara, and Qing Xiang (rst introduced in 2014), and summarized our attempts to generalize this construction to discover any new Cameron-Liebler line classes or partial difference sets (PDSs) resulting from the Cameron-Liebler line classes. The second is our approach to finding PDS in non-elementary abelian groups. Our attempt eventually led to the same general construction of PDS presented in John Polhill's PhD Thesis. The third presents a proof that any PDS in Z3p for p 3 mod 4 must be trivial, and any PDS in Z3 p for p 1 mod 4 must be a Paley-type PDS. We also show that nding all PDSs in Z3 p for p 1 mod 4 reduces to a computational problem of solving a linear equation under some integer constraints. Up to the writing and best of the author's knowledge, the result of the third part is new to the Mathematics community.
Tantipongipat, Uthaipon, "Cameron-Liebler line classes and partial difference sets" (2016). Honors Theses. 929.