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arXiv · 1711.11496

Tverberg partitions as weak epsilon-nets

Pablo Soberón
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Abstract

We prove a Tverberg-type theorem using the probabilistic method. Given $\varepsilon >0$, we find the smallest number of partitions of a set $X$ in $R^d$ into $r$ parts needed in order to induce at least one Tverberg partition on every subset of $X$ with at least $\varepsilon |X|$ elements. This generalizes known results about Tverberg's theorem with tolerance.

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Pablo Soberón. 2018-06-10. Tverberg partitions as weak epsilon-nets. https://arxiv.org/abs/1711.11496

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