Freiman-ruzsa-type theory for small doubling constant

Hansheng Diao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish (US)
Pages (from-to)269-276
Number of pages8
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number2
StatePublished - Mar 2009

All Science Journal Classification (ASJC) codes

  • General Mathematics


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