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Another Ham Sandwich in the Plane

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.

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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)

    MATH  MathSciNet  Google Scholar 

  2. 2.

    Stone A.H., Tukey J.W.: Generalized "sandwich" theorems. Duke Math. J. 9(2), 356–359 (1942)

    Article  MATH  MathSciNet  Google Scholar 

  3. 3.

    Živaljević, R.: Illumination complexes, Δ-zonotopes, and the polyhedral curtain theorem. Comput. Geom. 48(3), 225–236 (2015)

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Correspondence to Alexey Garber.

Additional information

The work of A. Garber is supported by the Russian Foundation of Basic Research grants 11-01-00633-a and 11-01-00735-a, and the Russian government project 11.G34.31.0053.

The work of R. Karasev is supported by the Dynasty foundation, the President’s of Russian Federation grant MD-352.2012.1, and the Russian government project 11.G34.31.0053.

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Balitskiy, A., Garber, A. & Karasev, R. Another Ham Sandwich in the Plane. Ann. Comb. 19, 235–242 (2015). https://doi.org/10.1007/s00026-015-0270-0

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Mathematics Subject Classification

  • 52C35
  • 60D05

Keywords

  • ham sandwich theorem