Geometric combinatorics in discrete settings

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Geometric combinatorics in discrete settings

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/15768

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dc.contributor.advisor Iosevich, Alex, 1967- en_US
dc.contributor.author Covert, David
dc.contributor.other University of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2011 Dissertations en_US
dc.date.accessioned 2012-10-18T15:51:22Z
dc.date.available 2012-10-18T15:51:22Z
dc.date.issued 2011
dc.date.submitted 2011 Spring en_US
dc.identifier.other CovertD-042011-D5439
dc.identifier.uri http://hdl.handle.net/10355/15768
dc.description Title from PDF of title page (University of Missouri--Columbia, viewed on October 18, 2012). en_US
dc.description The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. en_US
dc.description Dissertation advisor: Dr. Alex Iosevich en_US
dc.description Includes bibliographical references. en_US
dc.description Vita. en_US
dc.description Ph. D. University of Missouri--Columbia 2011. en_US
dc.description Dissertations, Academic -- University of Missouri--Columbia -- Mathematics en_US
dc.description "May 2011" en_US
dc.description.abstract This thesis is a compilation of work in which the author studies geometric configurations in finite fields and the integers modulo q. The results of this dissertation are threefold. First, we prove a finite field analog of the Furstenberg-Katznelson-Weiss theorem on triangles in R2. Second, we study volume sets in Fd/q and discuss some applications to sum-product problems. Finally, we study geometric combinatorics in Z/qZ. We generalize a result of Hart and Iosevich [27] which has applications to sum-product problems. Finally, we show that the Zd/q analogue of a sphere with unital radius is qd−1-dimensional. en_US
dc.format.extent v, 52 pages en_US
dc.language.iso en_US en_US
dc.publisher University of Missouri--Columbia en_US
dc.relation.ispartof 2011 Freely available dissertations (MU) en_US
dc.subject geometric combinatorics en_US
dc.subject finite fields en_US
dc.subject sum-product problem en_US
dc.title Geometric combinatorics in discrete settings en_US
dc.type Thesis en_US
thesis.degree.discipline Mathematics en_US
thesis.degree.grantor University of Missouri--Columbia en_US
thesis.degree.name Ph. D. en_US
thesis.degree.level Doctoral en_US


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