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dc.contributor.advisorCroot, Ernest
dc.contributor.authorBush, Albert
dc.date.accessioned2015-09-21T14:27:15Z
dc.date.available2015-09-21T14:27:15Z
dc.date.created2015-08
dc.date.issued2015-07-22
dc.date.submittedAugust 2015
dc.identifier.urihttp://hdl.handle.net/1853/53950
dc.description.abstractWe prove a new bound on a version of the sum-product problem studied by Chang. By introducing several combinatorial tools, this expands upon a method of Croot and Hart which used the Tarry-Escott problem to build distinct sums from polynomials with specific vanishing properties. We also study other aspects of the sum-product problem such as a method to prove a dual to a result of Elekes and Ruzsa and a conjecture of J. Solymosi on combinatorial geometry. Lastly, we study two combinatorial problems on sumsets over the reals. The first involves finding Freiman isomorphisms of real-valued sets that also preserve the order of the original set. The second applies results from the former in proving a new Balog-Szemeredi type theorem for real-valued sets.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectAdditive combinatorics
dc.subjectSum-product inequalities
dc.titleMultifold sums and products over R, and combinatorial problems on sumsets
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentMathematics
thesis.degree.levelDoctoral
dc.contributor.committeeMemberLacey, Michael
dc.contributor.committeeMemberLyall, Neil
dc.contributor.committeeMemberTetali, Prasad
dc.contributor.committeeMemberTrotter, William
dc.date.updated2015-09-21T14:27:15Z


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