Degree Type

Dissertation

Date of Award

2017

Degree Name

Doctor of Philosophy

Department

Mathematics

Major

Mathematics

First Advisor

Sung-Yell Song

Abstract

In this dissertation, we intended to construct some q-analogue t-designs and association schemes in symplectic vector spaces over finite fields. In this process of searching for designs and association schemes, we found two new families of association schemes, both of which are families of Schurian association schemes. They are obtained from the action of finite symplectic groups or their subgroups

(i) on the sets of totally isotropic projective lines, and

(ii) on subconstituents of the generalized symplectic graphs which are defined on the sets of totally isotropic projective lines as their vertex sets.

The studies of these associations schemes are treated in Chapter 3. We describe these schemes in terms of their character tables and their fusion relations. We also present some tables to list other combinatorial objects that are associated with our association schemes.

Copyright Owner

Robert Lazar

Language

en

File Format

application/pdf

File Size

169 pages

Included in

Mathematics Commons

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