Browsing Theses by Subject "matroid"
Now showing items 1-5 of 5
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Clique minors in dense matroids
(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 Bases
(University of Waterloo, 2004)A theorem of Edmonds characterizes when a pair of matroids has a common basis. Enumerating the common bases of a pair of matroid is a much harder problem, and includes the #P-complete problem of counting the number of ... -
Enumerating matroid extensions
(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 ... -
Infinite graphs, graph-like spaces and B-matroids
(University of Waterloo, 2011-01-19)The central theme of this thesis is to prove results about infinite mathematical objects by studying the behaviour of their finite substructures. In particular, we study B-matroids, which are an infinite generalization ... -
Negative Correlation Properties for Matroids
(University of Waterloo, 2008-12-23)In pursuit of negatively associated measures, this thesis focuses on certain negative correlation properties in matroids. In particular, the results presented contribute to the search for matroids which satisfy $$P(\{X:e,f\in ...