Now showing items 1-7 of 7

    • Clique minors in dense matroids 

      Rivera Omana, Fernanda (University of Waterloo, 2022-09-23)
      The objective of this thesis is to bound the number of points a $U_{2,\ell+2}$- and $M(K_{k+1})$-minor-free matroid has. We first prove that a sufficiently large matroid will contain a structure called a tower. We then use ...
    • Counting Pentagons in Triangle-free Binary Matroids 

      Brown, Adam (University of Waterloo, 2020-07-30)
      A rank-n 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 rank-n binary matroid is |E|/2ⁿ. We begin by giving a new exposition of a ...
    • Enumerating matroid extensions 

      Redlin Hume, Shayla (University of Waterloo, 2023-09-01)
      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 

      Gusakov, Alena (University of Waterloo, 2024-01-23)
      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 

      Nomoto, Kazuhiro (University of Waterloo, 2021-07-21)
      The notion of induced subgraphs is extensively studied in graph theory. An example is the famous Gy\'{a}rf\'{a}s-Sumner 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 

      Walsh, Zachary (University of Waterloo, 2016-12-21)
      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 minor-closed ...
    • Quadratically Dense Matroids 

      Walsh, Zachary (University of Waterloo, 2020-07-08)
      This thesis is concerned with finding the maximum density of rank-$n$ matroids in a minor-closed class. The extremal function of a non-empty minor-closed class $\mathcal M$ of matroids which excludes a rank-2 uniform ...


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