2026
2026 · preprint
Helly and Radon theorems for convex intersections containing k-flats
Abstract
We study versions of results in combinatorial geometry related to families of convex sets in ℝᵈ 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.
With student coauthor Sarah Ludwigson.
BibTeX citation
A minimal citation using the imported metadata. Journal references are retained in the note field.
@misc{soberon-2026-helly-radon-flats,
title = {{Helly and Radon theorems for convex intersections containing k-flats}},
author = {Sarah Ludwigson and Pablo Soberón},
year = {2026},
eprint = {2608.27189},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27189}
}
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