In this paper, we study the linear structure of sets A ⊂ F n2 with doubling constant (A) < 2, where σ(A):=|A+A|/|A|. In particular, we show that A is contained in a small affine subspace. We also show that A can be covered by at most four shifts of some subspace V with |V| ≤ |A|. Finally, we classify all binary sets with small doubling constant.
|Original language||English (US)|
|Number of pages||8|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|State||Published - Mar 1 2009|
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