A robust version of Freiman's 3k-4 Theorem and applications

Xuancheng Shao, Wenqiang Xu

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We prove a robust version of Freiman's 3k - 4 theorem on the restricted sumset A+ΓB, which applies when the doubling constant is at most (3+)/2 in general and at most 3 in the special case when A = -B. As applications, we derive robust results with other types of assumptions on popular sums, and structure theorems for sets satisfying almost equalities in discrete and continuous versions of the Riesz-Sobolev inequality.

Original languageEnglish
Pages (from-to)567-581
Number of pages15
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
StatePublished - May 1 2019

Bibliographical note

Publisher Copyright:
© Copyright Cambridge Philosophical Society 2018.

ASJC Scopus subject areas

  • General Mathematics


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