Compressions, convex geometry and the Freiman-Bilu theorem
| dc.creator | Green, Ben | |
| dc.creator | Tao, Terence | |
| dc.date | 2005-11-03 | |
| dc.date | 2006-03-03 | |
| dc.date.accessioned | 2026-07-07T06:50:42Z | |
| dc.date.available | 2026-07-07T06:50:42Z | |
| dc.description | We note a link between combinatorial results of Bollobás and Leader concerning sumsets in the grid, the Brunn-Minkowski theorem and a result of Freiman and Bilu concerning the structure of sets of integers with small doubling. Our main result is the following. If eps > 0 and if A is a finite nonempty subset of a torsion-free abelian group with |A + A| <= K|A|, then A may be covered by exp(K^C) progressions of dimension [log_2 K + eps] and size at most |A|. | |
| dc.description | 9 pages, slight revisions in the light of comments from the referee. To appear in Quarterly Journal of Mathematics, Oxford | |
| dc.identifier | https://arxiv.org/abs/math/0511069 | |
| dc.identifier | http://arxiv.org/abs/math/0511069 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104747 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.title | Compressions, convex geometry and the Freiman-Bilu theorem | |
| dc.type | text |