Freiman–Ruzsa-type theory for small doubling constant

Abstract

Abstract In this paper, we study the linear structure of sets A ⊂ $\mathbb{F}_2^n$ 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.

Locations

• arXiv (Cornell University) - View - PDF
• Mathematical Proceedings of the Cambridge Philosophical Society - View
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