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Enumerative and Algebraic Aspects of Slope Varieties
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. | |
kusw.bibid | 7643084 | |
dc.rights.accessrights | openAccess |
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Dissertations [4889]
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Mathematics Dissertations and Theses [179]