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arXiv · 2503.22571

Helly-type theorems for monotone properties of boxes

Nóra Frankl·Attila Jung
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Abstract

We present a unified approach to prove Helly-type theorems for monotone properties of boxes, such as having large volume or containing points from a given set. As a corollary, we obtain new proofs for several earlier results regarding specific monotone properties. Our results generalise to $H$-convex sets as well.

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Nóra Frankl, Attila Jung. 2025-03-28. Helly-type theorems for monotone properties of boxes. https://arxiv.org/abs/2503.22571

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