ARITHMETIC PROGRESSIONS IN SETS OF SMALL DOUBLING
| Autor: | Kevin Henriot |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
11B30 Mathematics - Number Theory General Mathematics 010102 general mathematics 0102 computer and information sciences 01 natural sciences 010201 computation theory & mathematics Arithmetic progression FOS: Mathematics Mathematics - Combinatorics Coset Combinatorics (math.CO) Number Theory (math.NT) 0101 mathematics Abelian group Mathematics |
| Zdroj: | Mathematika. 62:587-613 |
| ISSN: | 2041-7942 0025-5793 |
| DOI: | 10.1112/s002557931500039x |
| Popis: | We show that if a finite, large enough subset A of an arbitrary abelian group satisfies the small doubling condition |A + A| < (log |A|)^{1 - epsilon} |A|, then A must contain a three-term arithmetic progression whose terms are not all equal, and A + A must contain an arithmetic progression or a coset of a subgroup, either of which of size at least exp^[ c (log |A|)^{delta} ]. This extends analogous results obtained by Sanders and, respectively, by Croot, Laba and Sisask in the case where the group is that of the integers or a finite field. 30 pages, improved exposition |
| Databáze: | OpenAIRE |
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