• Corpus ID: 235828764

Generalizations of the Yao-Yao partition theorem and the central transversal theorem

  title={Generalizations of the Yao-Yao partition theorem and the central transversal theorem},
  author={Michael N. Manta and Pablo Sober'on},
We generalize the Yao–Yao partition theorem by showing that for any smooth measure in Rd there exist equipartitions using (t+ 1)2d−1 convex regions such that every hyperplane misses the interior of at least t regions. In addition, we present tight bounds on the smallest number of hyperplanes whose union contains the boundary of an equipartition of a measure into n regions. We also present a simple proof of a Borsuk–Ulam type theorem for Stiefel manifolds that allows us to generalize the central… 
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