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dc.contributor.advisorMartin, Jeremy
dc.contributor.authorEnkosky, Thomas
dc.date.accessioned2011-09-22T01:55:38Z
dc.date.available2011-09-22T01:55:38Z
dc.date.issued2011-05-18
dc.date.submitted2011
dc.identifier.otherhttp://dissertations.umi.com/ku:11634
dc.identifier.urihttp://hdl.handle.net/1808/8062
dc.description.abstractThe slope variety of a graph G is an algebraic variety whose points correspond to the slopes arising from point-line configurations of G. We start by reviewing the background material necessary to understand the theory of slope varieties. We then move on to slope varieties over finite fields and determine the size of this set. We show that points in this variety correspond to graphs without an induced path on four vertices. We then establish a bijection between graphs without an induced path on four vertices and series-parallel networks. Next, we study the defining polynomials of the slope variety in more detail. The polynomials defining the slope variety are understood but we show that those of minimal degree suffice to define the slope variety set theoretically. We conclude with some remarks on how we would define the slope variety for point-line configurations in higher dimensions.
dc.format.extent67 pages
dc.language.isoen
dc.publisherUniversity of Kansas
dc.rightsThis item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
dc.subjectMathematics
dc.titleEnumerative and Algebraic Aspects of Slope Varieties
dc.typeDissertation
dc.contributor.cmtememberBayer, Margaret
dc.contributor.cmtememberDao, Hailong
dc.contributor.cmtememberHuneke, Craig
dc.contributor.cmtememberGleason, Jennifer
dc.thesis.degreeDisciplineMathematics
dc.thesis.degreeLevelPh.D.
kusw.oastatusna
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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