Freiman-ruzsa-type theory for small doubling constant

Hansheng Diao

doi:10.1017/S0305004108001898

Freiman-ruzsa-type theory for small doubling constant

Hansheng Diao

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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)
Pages (from-to)	269-276
Number of pages	8
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	146
Issue number	2
DOIs	https://doi.org/10.1017/S0305004108001898
State	Published - Mar 2009

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/S0305004108001898

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title = "Freiman-ruzsa-type theory for small doubling constant",

abstract = "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.",

author = "Hansheng Diao",

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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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M3 - Article

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JO - Mathematical Proceedings of the Cambridge Philosophical Society

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IS - 2

ER -

Freiman-ruzsa-type theory for small doubling constant

Abstract

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