Author

Pablo Soberón

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Preprint Sep 2026

The topological B\'ar\'any-Larman conjecture for prime numbers

The B\'ar\'any-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...

Pablo Soberón · 0 citations

Preprint Aug 2026

Blocking codimension-one simplices on the moment curve

We study $b_d(n)$, the minimum number of points needed to meet the relative interior of every $(d-1)$-simplex spanned by an $n$-point set in general position in $\mathbb{R}^d$. In the plane, this is the parameter from the Blocking Conjecture. We improve the best known general planar lower bound to $ b_2(n)\ge \frac{41}...

Pablo Soberón · 0 citations