Journal article
Compressions, convex geometry and the Freiman-Bilu theorem
- Abstract:
- We note a link between combinatorial results of Bollob\'as 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|.
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- Publication date:
- 2005-11-03
- Keywords:
- Pubs id:
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pubs:398494
- UUID:
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uuid:0a9a3b3c-584d-445a-9eb0-0e9c1bffacb2
- Local pid:
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pubs:398494
- Source identifiers:
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398494
- Deposit date:
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2013-11-16
- ARK identifier:
Terms of use
- Copyright date:
- 2005
- Notes:
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9 pages, slight revisions in the light of comments from the referee.
To appear in Quarterly Journal of Mathematics, Oxford
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