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Annals of Combinatorics

, Volume 19, Issue 2, pp 235–242 | Cite as

Another Ham Sandwich in the Plane

  • Alexey Balitskiy
  • Alexey Garber
  • Roman Karasev
Article
  • 100 Downloads

Abstract

We show that every two nice measures in the plane can be partitioned into equal halves by translation of an angle from any k-fan when k is odd and in some cases when k is even. We also give some counterexamples for certain fans and measures.

Keywords

ham sandwich theorem 

Mathematics Subject Classification

52C35 60D05 

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References

  1. 1.
    Steinhaus H.: Sur la division des ensembles de l’espace par les plans et des ensembles plans par les cercles. Fund. Math. 33, 245–263 (1945)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Stone A.H., Tukey J.W.: Generalized "sandwich" theorems. Duke Math. J. 9(2), 356–359 (1942)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Živaljević, R.: Illumination complexes, Δ-zonotopes, and the polyhedral curtain theorem. Comput. Geom. 48(3), 225–236 (2015)Google Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Alexey Balitskiy
    • 1
  • Alexey Garber
    • 2
  • Roman Karasev
    • 1
    • 3
  1. 1.Department of MathematicsMoscow Institute of Physics and TechnologyDolgoprudnyRussia
  2. 2.Department of MathematicsThe University of Texas at BrownsvilleBrownsvilleUSA
  3. 3.Institute for Information Transmission Problems RASMoscowRussia

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