3 papers
math.CO2026
Strong invariants and Tverberg numbers in convexity spaces
Minho Cho, Andreas F. Holmsen, Attila Jung +1
Helly, Carathéodory, and Radon numbers encode three kinds of finite certificates in a convexity space: for the emptiness of an intersection, for membership in a convex hull, and fo…
math.CO2025
Helly-type theorems for monotone properties of boxes
Nóra Frankl, Attila Jung
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 o…
math.CO2024
A note on infinite versions of -theorems
Attila Jung, Dömötör Pálvölgyi
We prove that fractional Helly and -theorems imply -theorems in an entirely abstract setting. We give a plethora of applications, including reproving almost al…