Compressions, Convex Geometry and the Freiman-bilu Theorem
نویسنده
چکیده
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 ⊆ Z with small doubling. Our main result is the following. If ε > 0 and if A is a finite nonempty subset of a torsion-free abelian group with |A + A| 6 K|A|, then A may be covered by e O(1) progressions of dimension ⌊log 2 K + ε⌋ and size at most |A|.
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تاریخ انتشار 2006