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C O ] 1 5 M ay 2 01 8 Improved Bounds for Progression-Free Sets in C n 8
| Content Provider | Semantic Scholar |
|---|---|
| Author | Petrov, Fedor Pohoata, Cosmin |
| Copyright Year | 2018 |
| Abstract | Let G be a finite group, and let r3(G) represent the size of the largest subset of G without non-trivial three-term progressions. In a recent breakthrough, Croot, Lev and Pach proved that r3(C n 4 ) 6 (3.61) , where Cm denotes the cyclic group of order m. For finite abelian groups G ∼= ∏n i=1 Cmi , where m1, . . . ,mn denote positive integers such that m1| . . . |mn, this also yields a bound of the form r3(G) 6 (0.903)rk4(G)|G|, with rk4(G) representing the number of indices i ∈ {1, . . . , n} with 4 | mi. In particular, r3(C n 8 ) 6 (7.22) . In this paper, we provide an exponential improvement for this bound, namely r3(C n 8 ) ≤ (7.09). |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://export.arxiv.org/pdf/1805.05549 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
