Compressions, convex geometry and the Freiman-Bilu theorem

dc.creatorGreen, Ben
dc.creatorTao, Terence
dc.date2005-11-03
dc.date2006-03-03
dc.date.accessioned2026-07-07T06:50:42Z
dc.date.available2026-07-07T06:50:42Z
dc.descriptionWe 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.description9 pages, slight revisions in the light of comments from the referee. To appear in Quarterly Journal of Mathematics, Oxford
dc.identifierhttps://arxiv.org/abs/math/0511069
dc.identifierhttp://arxiv.org/abs/math/0511069
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/104747
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.titleCompressions, convex geometry and the Freiman-Bilu theorem
dc.typetext

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