Andreas F. Holmsen

collaborators

6 papers

math.CO2026

Strong invariants and Tverberg numbers in convexity spaces

Minho Cho, Andreas F. Holmsen, Attila Jung +1

Helly, CarathÃ©odory, 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 f…

cs.CG2026

Intersection patterns in spaces with a forbidden homological minor

Xavier Goaoc, Andreas F. Holmsen, Zuzana PatÃ¡kovÃ¡

In this paper we study generalizations of classical results on intersection patterns of set systems in $R^{d}$ , such as the fractional Helly theorem or the $(p, q)$ -theorem,…

math.CO2026

Piercing all maximum cliques in hypergraphs

Andreas Holmsen, Attila Jung, BalÃ¡zs Keszegh +5

Graphs whose maximum clique size exceeds half of the total number of vertices satisfy a classical property: the family of their maximum sized cliques can be pierced by a single ver…

math.CO2025

The fractional Helly number for separable convexity spaces

Andreas F. Holmsen, Zuzana PatÃ¡kovÃ¡

A convex lattice set in $Z^{d}$ is the intersection of a convex set in $R^{d}$ with the integer lattice $Z^{d}$ . A classical theorem of Doignon states that the…

math.CO2025

Helly type problems in convexity spaces

Andreas F. Holmsen

We report on some recent progress regarding combinatorial properties in convexity spaces with a bounded Radon number. In particular, we discuss the relationship between the Radon n…

math.CO2025

A topological product Tverberg Theorem

Andreas F. Holmsen, Grace McCourt, Daniel McGinnis +1

We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let $I^$ denote the 8-dimensional simplex viewed as an…