Sets with small sumset and rectification

dc.creatorGreen, Ben
dc.creatorRuzsa, Imre Z.
dc.date2004-03-21
dc.date2005-01-28
dc.date.accessioned2026-07-07T05:06:35Z
dc.date.available2026-07-07T05:06:35Z
dc.descriptionWe 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.description9 pages, minor corrections made
dc.identifierhttps://arxiv.org/abs/math/0403338
dc.identifierhttp://arxiv.org/abs/math/0403338
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70524
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.titleSets with small sumset and rectification
dc.typetext

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