We 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.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/29664 |
| Date | 19 May 2009 |
| Creators | Borenstein, Evan |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Detected Language | English |
| Type | Dissertation |
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