Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Soberón, Pablo
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214975633