Date of Award

8-2021

Document Type

Thesis

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Aikin, Jeremy

Abstract

A matroid is a mathematical object that generalizes and connects notions of independence that arise in various branches of mathematics. Some matroids can be represented by a matrix whose entries are from some field; whereas, other matroids cannot be represented in this way. However, every matroid can be partially represented by a matrix over the field GF(2). In fact, for a given matroid, many different partial representations may exist, each providing a different collection of information about the matroid with which they are associated. Such a partial representation of a matroid usually does not uniquely determine the matroid on its own. That is, if we are given a partial representation P and seek to find a unique matroid having P as one of its partial representations, we may not be able to do so. On the other hand, the more partial representations we are given, the more likely it is that this collection of partial representations uniquely determines a matroid. In this thesis, we investigate matroids that can be uniquely determined by two partial representations. Specifically, we provide a characterization of the rank-3 matroids for which there exist two distinct partial representations that combine to encode all of the matroid information.

Download

  Contact Author

Included in

Mathematics Commons

Share

COinS