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arXiv · 2609.37876

The topological Bárány-Larman conjecture for prime numbers

Pablo Soberón
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Abstract

The Bárány-Larman conjecture states that for any $d+1$ sets of $r$ points each in $\mathbb{R}^d$, considered as color classes, we can partition their union into $r$ rainbow $(d+1)$-tuples whose convex hulls intersect. We prove that the topological version of this conjecture holds when $r$ is a prime number. We also show that the optimal colorful Tverberg theorem of Blagojević, Matschke, and Ziegler cannot be extended to prime powers.

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Pablo Soberón. 2026-09-29. The topological Bárány-Larman conjecture for prime numbers. https://arxiv.org/abs/2609.37876

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