On sets with small doubling
| dc.creator | Shkredov, I. D. | |
| dc.date | 2007-03-11 | |
| dc.date.accessioned | 2026-07-07T07:51:26Z | |
| dc.date.available | 2026-07-07T07:51:26Z | |
| dc.description | Let G be an arbitrary Abelian group and let A be a finite subset of G. A has small additive doubling if |A+A| < K|A| for some K>0. These sets were studied in papers of G.A. Freiman, Y. Bilu, I. Ruzsa, M.C.--Chang, B. Green and T.Tao. In the article we prove that if we have some minor restrictions on K then for any set with small doubling there exists a set Lambda, |Lambda| << K log |A| such that |A\cap Lambda| >> |A| / K^{1/2 + c}, where c > 0. In contrast to the previous results our theorem is nontrivial for large K. For example one can take K equals |A|^η, where η>0. We use an elementary method in our proof. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703309 | |
| dc.identifier | http://arxiv.org/abs/math/0703309 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125508 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.title | On sets with small doubling | |
| dc.type | text |