Title:
Multifold sums and products over R, and combinatorial problems on sumsets
Multifold sums and products over R, and combinatorial problems on sumsets
| dc.contributor.advisor | Croot, Ernest | |
| dc.contributor.author | Bush, Albert | |
| dc.contributor.committeeMember | Lacey, Michael | |
| dc.contributor.committeeMember | Lyall, Neil | |
| dc.contributor.committeeMember | Tetali, Prasad | |
| dc.contributor.committeeMember | Trotter, William | |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2015-09-21T14:27:15Z | |
| dc.date.available | 2015-09-21T14:27:15Z | |
| dc.date.created | 2015-08 | |
| dc.date.issued | 2015-07-22 | |
| dc.date.submitted | August 2015 | |
| dc.date.updated | 2015-09-21T14:27:15Z | |
| dc.description.abstract | We 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.description.degree | Ph.D. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/53950 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | Additive combinatorics | |
| dc.subject | Sum-product inequalities | |
| dc.title | Multifold sums and products over R, and combinatorial problems on sumsets | |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.advisor | Croot, Ernest | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
| relation.isAdvisorOfPublication | 12d5c098-10ae-4a65-883e-60e8f1325f62 | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 | |
| thesis.degree.level | Doctoral |