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Freiman–Ruzsa-type theory for small doubling constant
Published online by Cambridge University Press: 01 March 2009
Abstract
In this paper, we study the linear structure of sets A ⊂ with doubling constant σ(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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 2 , March 2009 , pp. 269 - 276
- Copyright
- Copyright © Cambridge Philosophical Society 2008
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