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

@inproceedings{Manta2021GeneralizationsOT, title={Generalizations of the Yao-Yao partition theorem and the central transversal theorem}, author={Michael N. Manta and Pablo Sober'on}, year={2021} }

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…

## 2 Citations

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