Another ham sandwich in the plane
Alexey Balitskiy, Alexey Garber, Roman Karasev
TL;DR
This paper demonstrates that for certain configurations, two measures in the plane can be equally partitioned using translations of angles from k-fans, with some limitations and counterexamples provided.
Contribution
It introduces new partitioning results for measures using k-fans and explores conditions under which such partitions are possible or impossible.
Findings
Partitioning is possible for odd k-fans.
Counterexamples show limitations for certain measures and fans.
Results extend understanding of geometric measure partitioning.
Abstract
We show that every two nice measures in the plane can be partitioned into equal halves by translation of an angle from arbitrary 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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