dc.contributor.advisor Martin, Jeremy dc.contributor.author Enkosky, Thomas dc.date.accessioned 2011-09-22T01:55:38Z dc.date.available 2011-09-22T01:55:38Z dc.date.issued 2011-05-18 dc.date.submitted 2011 dc.identifier.other http://dissertations.umi.com/ku:11634 dc.identifier.uri http://hdl.handle.net/1808/8062 dc.description.abstract The 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.extent 67 pages dc.language.iso en dc.publisher University of Kansas dc.rights This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author. dc.subject Mathematics dc.title Enumerative and Algebraic Aspects of Slope Varieties dc.type Dissertation dc.contributor.cmtemember Bayer, Margaret dc.contributor.cmtemember Dao, Hailong dc.contributor.cmtemember Huneke, Craig dc.contributor.cmtemember Gleason, Jennifer dc.thesis.degreeDiscipline Mathematics dc.thesis.degreeLevel Ph.D. kusw.oastatus na kusw.oapolicy This item does not meet KU Open Access policy criteria. dc.rights.accessrights openAccess
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