TY - JOUR

T1 - Freiman-ruzsa-type theory for small doubling constant

AU - Diao, Hansheng

N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2009/3

Y1 - 2009/3

N2 - 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.

AB - 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.

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U2 - 10.1017/S0305004108001898

DO - 10.1017/S0305004108001898

M3 - Article

AN - SCOPUS:68349133943

SN - 0305-0041

VL - 146

SP - 269

EP - 276

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 2

ER -