Hyper-Atoms Applied to the Critical Pair Theory

  • Yahya O. Hamidoune


The isoperimetric method is often useful for proving results regarding sumsets. Here, we introduce the notion of a hyper-atom into the method, which overcomes a previous weakness when dealing with atoms that are cosets. To show the utility of this new object, we give a new isoperimetric proof of the cornerstone of classical critical pair theory: The Kemperman Structure Theorem, proved in its so-called “dual” formulation.


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The author is grateful to an anonymous referee for many valuable comments on the first two drafts.


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Copyright information

© Janos Bolyai Mathematical Society and Springer-Verlag 2019

Authors and Affiliations

  • Yahya O. Hamidoune
    • 1
  1. 1.UPMC Univ Paris 06, E. CombinatoireParisFrance

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