Browsing Theses by Supervisor "Nelson, Peter"
Now showing items 14 of 4

Counting Pentagons in Trianglefree Binary Matroids
(University of Waterloo, 20200730)A rankn binary matroid is a spanning subset E of F₂ⁿ\{0}, a triangle is a set of three elements from E which sum to zero, and the density of a rankn binary matroid is E/2ⁿ. We begin by giving a new exposition of a ... 
Induced Binary Submatroids
(University of Waterloo, 20210721)The notion of induced subgraphs is extensively studied in graph theory. An example is the famous Gy\'{a}rf\'{a}sSumner conjecture, which asserts that given a tree $T$ and a clique $K$, there exists a constant $c$ such ... 
On The Density of Binary Matroids Without a Given Minor
(University of Waterloo, 20161221)This thesis is motivated by the following question: how many elements can a simple binary matroid with no $\PG(t,2)$minor have? This is a natural analogue of questions asked about the density of graphs in minorclosed ... 
Quadratically Dense Matroids
(University of Waterloo, 20200708)This thesis is concerned with finding the maximum density of rank$n$ matroids in a minorclosed class. The extremal function of a nonempty minorclosed class $\mathcal M$ of matroids which excludes a rank2 uniform ...