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Sumsets and the Convex Hull

  • Máté MatolcsiEmail author
  • Imre Z. Ruzsa
Chapter

Summary

We extend Freiman’s inequality on the cardinality of the sumset of a d-dimensional set. We consider different sets related by an inclusion of their convex hull, and one of them added possibly several times.

Keywords

Multidimensional sumsets 

Notes

Acknowledgements

The authors profited much from discussions with Katalin Gyarmati and Károly Böröczky.

References

  1. 1.
    G. Freiman, Foundations of a structural theory of set addition, Am. Math. Soc., 1973.Google Scholar
  2. 2.
    K. Gyarmati, M. Matolcsi, and I. Z. Ruzsa, A superadditivity and submultiplicativity property for cardinalities of sumsets, Combinatorica, to appear.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Alfréd Rényi Institute of MathematicsBudapestHungary
  2. 2.BME Department of AnalysisBudapestHungary

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