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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:
pubs:398494
UUID:
uuid:0a9a3b3c-584d-445a-9eb0-0e9c1bffacb2
Local pid:
pubs:398494
Source identifiers:
398494
Deposit date:
2013-11-16

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