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arXiv · 1009.2384

Radon partitions in convexity spaces

Boris Bukh
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Abstract

Tverberg's theorem asserts that every (k-1)(d+1)+1 points in R^d can be partitioned into k parts, so that the convex hulls of the parts have a common intersection. Calder and Eckhoff asked whether there is a purely combinatorial deduction of Tverberg's theorem from the special case k=2. We dash the hopes of a purely combinatorial deduction, but show that the case k=2 does imply that every set of O(k^2 log^2 k) points admits a Tverberg partition into k parts.

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Boris Bukh. 2010-09-13. Radon partitions in convexity spaces. https://arxiv.org/abs/1009.2384

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