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dc.contributor.authorBorenstein, Evanen_US
dc.date.accessioned2009-08-26T17:44:00Z
dc.date.available2009-08-26T17:44:00Z
dc.date.issued2009-05-19en_US
dc.identifier.urihttp://hdl.handle.net/1853/29664
dc.description.abstractWe will survey some of the major directions of research in arithmetic combinatorics and their connections to other fields. We will then discuss three new results. The first result will generalize a structural theorem from Balog and Szemerédi. The second result will establish a new tool in incidence geometry, which should prove useful in attacking combinatorial estimates. The third result evolved from the famous sum-product problem, by providing a partial categorization of bivariate polynomial set functions which induce exponential expansion on all finite sets of real numbers.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectArithmetic combinatoricsen_US
dc.subjectAdditive combinatoricsen_US
dc.subjectCombinatoricsen_US
dc.subjectIncidence geometryen_US
dc.subjectSum-product inequalitiesen_US
dc.subjectStructural theoremsen_US
dc.subject.lcshCombinatorial analysis
dc.subject.lcshCombinatorial geometry
dc.subject.lcshSet functions
dc.titleAdditive stucture, rich lines, and exponential set-expansionen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Croot, Ernie; Committee Member: Costello, Kevin; Committee Member: Lyall, Neil; Committee Member: Tetali, Prasad; Committee Member: Yu, XingXingen_US


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