学位论文详细信息
Additive stucture, rich lines, and exponential set-expansion | |
Arithmetic combinatorics;Additive combinatorics;Combinatorics;Incidence geometry;Sum-product inequalities;Structural theorems | |
Borenstein, Evan ; Mathematics | |
University:Georgia Institute of Technology | |
Department:Mathematics | |
关键词: Arithmetic combinatorics; Additive combinatorics; Combinatorics; Incidence geometry; Sum-product inequalities; Structural theorems; | |
Others : https://smartech.gatech.edu/bitstream/1853/29664/1/borenstein_evan_s_200908_phd.pdf | |
美国|英语 | |
来源: SMARTech Repository | |
【 摘 要 】
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.
【 预 览 】
Files | Size | Format | View |
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Additive stucture, rich lines, and exponential set-expansion | 313KB | download |