Sets with small sumset and rectification
| dc.creator | Green, Ben | |
| dc.creator | Ruzsa, Imre Z. | |
| dc.date | 2004-03-21 | |
| dc.date | 2005-01-28 | |
| dc.date.accessioned | 2026-07-07T05:06:35Z | |
| dc.date.available | 2026-07-07T05:06:35Z | |
| dc.description | We study the extent to which sets A in Z/NZ, N prime, resemble sets of integers from the additive point of view (``up to Freiman isomorphism''). We give a direct proof of a result of Freiman, namely that if |A + A| < K|A| and |A| < c(K)N then A is Freiman isomorphic to a set of integers. Because we avoid appealing to Freiman's structure theorem, we get a reasonable bound: we can take c(K) > exp(-cK^2 log K). As a byproduct of our argument we obtain a sharpening of the second author's result on sets with small sumset in torsion groups. For example if A is a subset of F_2^n, and if |A + A| < K|A|, then A is contained in a coset of a subspace of size no more than 2^{CK^2}|A|. | |
| dc.description | 9 pages, minor corrections made | |
| dc.identifier | https://arxiv.org/abs/math/0403338 | |
| dc.identifier | http://arxiv.org/abs/math/0403338 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70524 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.title | Sets with small sumset and rectification | |
| dc.type | text |