Date of Award
2020
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
First Advisor
Spencer Backman
Second Advisor
David Darais
Abstract
A matroid abstracts the notions of dependence common to linear algebra, graph theory, and geometry. We show the equivalence of some of the various axiom systems which define a matroid and examine the concepts of matroid minors and duality before moving on to those matroids which can be represented by a matrix over any field, known as regular matroids. Placing an orientation on a regular matroid allows us to define certain lattices (discrete groups) associated to the matroid. These allow us to construct the Jacobian group of a regular matroid analogous to the Jacobian group of a graph. We then survey some recent work characterizing the matroid Jacobian. Finally we extend some results due to Eppstein concerning the Jacobian group of a graph to the case of regular matroids.
Language
en
Number of Pages
83 p.
Recommended Citation
Mullins, Patrick, "The circuit and cocircuit lattices of a regular matroid" (2020). Graduate College Dissertations and Theses. 1234.
https://scholarworks.uvm.edu/graddis/1234