Helly-type theorems for monotone properties of boxes

2025/03/28 by Nóra Frankl, Frankl, Nóra, Attila Jung +1 · 1 citation
Computer Science · Mathematics · #52A35 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2503.22571

openalex publication_date 2025/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Strong invariants and Tverberg numbers in convexity spaces

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