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arXiv · 2604.18485

An elementary proof of Sierksma's conjecture for seven points in the plane

Pablo Soberón
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Abstract

We give a new simple geometric proof that any seven points in the plane have four Tverberg partitions into three sets. This is the only confirmed non-trivial case of Sierksma's conjecture. Earlier proofs, by Stephan Hell, relied on topological arguments.

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Pablo Soberón. 2026-04-20. An elementary proof of Sierksma's conjecture for seven points in the plane. https://arxiv.org/abs/2604.18485

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