Compressions, convex geometry and the Freiman-Bilu theorem

BJ Green, TC Tao

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)

Abstract

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 A {subseteq} Z with small doubling. Our main result is the following. If {varepsilon} > 0 and if A is a finite non-empty subset of a torsion-free abelian group with |A + A| ≤ K|A|, then A may be covered by eKO(1) progressions of dimension {lfloor} log 2 K + {varepsilon} {rfloor} and size at most |A|.
Translated title of the contributionCompressions, convex geometry and the Freiman-Bilu theorem
Original languageEnglish
Pages (from-to)495 - 504
Number of pages10
JournalQuarterly Journal of Mathematics
Volume57 (4)
DOIs
Publication statusPublished - Dec 2006

Bibliographical note

Publisher: Oxford University Press
Other: http://arxiv.org/abs/math/0511069

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