1 citations · 2 across the 3 of their papers we have counts for
5 papers
Intersection patterns in spaces with a forbidden homological minor
Xavier Goaoc, Andreas F. Holmsen, Zuzana Patáková
In this paper we study generalizations of classical results on intersection patterns of set systems in , such as the fractional Helly theorem or the -theorem,…
Barycentric cuts through a convex body
Zuzana Patáková, Martin Tancer, Uli Wagner
Let be a convex body in (i.e., a compact convex set with nonempty interior). Given a point in the interior of , a hyperplane passing through is ca…
Bounding Radon numbers via Betti numbers
Zuzana Patáková
We prove general topological Radon-type theorems for sets in or on a surface. Combined with a recent result of Holmsen and Lee, we also obtain fractional Helly theore…
Intersection patterns of planar sets
Gil Kalai, Zuzana Patáková
Let be a family of sets in the plane. For , denote by the number of subsets of of cardinality that sa…
Colorful simplicial depth, Minkowski sums, and generalized Gale transforms
Karim Adiprasito, Philip Brinkmann, Arnau Padrol +3
The colorful simplicial depth of a collection of d+1 finite sets of points in Euclidean d-space is the number of choices of a point from each set such that the origin is contained…