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arXiv · 2608.27189

Helly and Radon theorems for convex intersections containing $k$-flats

Sarah Ludwigson·Pablo Soberón
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Abstract

We study versions of results in combinatorial geometry related to families of convex sets in $\mathbb{R}^d$ whose intersection contains a $k$-dimensional affine space. We prove generalizations of the colorful Radon theorem, the fractional Helly theorem, the colorful Helly theorem, and the selection-structure Helly theorem. When $k=0$, our arguments give new proofs of the corresponding versions for points.

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Sarah Ludwigson, Pablo Soberón. 2026-08-27. Helly and Radon theorems for convex intersections containing $k$-flats. https://arxiv.org/abs/2608.27189

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