Helly-type theorems for monotone properties of boxes

Fuente: arXiv
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Main Authors: Frankl, Nóra, Jung, Attila
Format: Preprint
Published: 2025
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author Frankl, Nóra
Jung, Attila
author_facet Frankl, Nóra
Jung, Attila
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2503_22571
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Helly-type theorems for monotone properties of boxes
Frankl, Nóra
Jung, Attila
Combinatorics
52A35
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.
title Helly-type theorems for monotone properties of boxes
topic Combinatorics
52A35
url https://arxiv.org/abs/2503.22571