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The topological Bárány-Larman conjecture for prime numbers
Abstract
The Bárány-Larman conjecture states that for any d+1 sets of r points each in ℝd, 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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BibTeX
@misc{soberon2026topological,
title = {{The topological Bárány-Larman conjecture for prime numbers}},
author = {Pablo Soberón},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37876},
eprint = {2609.37876},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37876},
}
RIS
TY - UNPB
TI - The topological Bárány-Larman conjecture for prime numbers
AU - Pablo Soberón
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37876
UR - https://arxiv.org/abs/2609.37876
AB - The Bárány-Larman conjecture states that for any d+1 sets of r points each in 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.
ER -