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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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
Mathematics Subject Classification
- ham sandwich theorem