Helly-type theorems for monotone properties of boxes
Combinatorics
2025-03-31 v1
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 -convex sets as well.
Cite
@article{arxiv.2503.22571,
title = {Helly-type theorems for monotone properties of boxes},
author = {Nóra Frankl and Attila Jung},
journal= {arXiv preprint arXiv:2503.22571},
year = {2025}
}
Comments
10 pages