Browsing Combinatorics and Optimization by Supervisor "Nelson, Peter"
Now showing items 17 of 7

Clique minors in dense matroids
(University of Waterloo, 20220923)The objective of this thesis is to bound the number of points a $U_{2,\ell+2}$ and $M(K_{k+1})$minorfree matroid has. We first prove that a sufficiently large matroid will contain a structure called a tower. We then use ... 
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 ... 
Enumerating matroid extensions
(University of Waterloo, 20230901)This thesis investigates the problem of enumerating the extensions of certain matroids. A matroid M is an extension of a matroid N if M delete e is equal to N for some element e of M. Similarly, a matroid M is a coextension ... 
Formalizing the Excluded Minor Characterization of Binary Matroids in the Lean Theorem Prover
(University of Waterloo, 20240123)A matroid is a mathematical object that generalizes the notion of linear independence of a set of vectors to an abstract independence of sets, with applications to optimization, linear algebra, graph theory, and algebraic ... 
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 ...