Zuzana Pat'akov'a

activity

20162021

most citedIntersection patterns of planar sets

1 citations · 2 across the 3 of their papers we have counts for

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4 papers · 1 filter

math.CO2020

Barycentric cuts through a convex body

Zuzana Patáková, Martin Tancer, Uli Wagner

Let $K$ be a convex body in $R^{n}$ (i.e., a compact convex set with nonempty interior). Given a point $p$ in the interior of $K$ , a hyperplane $h$ passing through $p$ is ca…

math.CO2019★ 1 cited

Bounding Radon numbers via Betti numbers

Zuzana Patáková

We prove general topological Radon-type theorems for sets in $R^{d}$ or on a surface. Combined with a recent result of Holmsen and Lee, we also obtain fractional Helly theore…

math.CO2019★ 1 cited

Intersection patterns of planar sets

Gil Kalai, Zuzana Patáková

Let $A = {A_{1}, \dots, A_{n}}$ be a family of sets in the plane. For $0 \leq i < n$ , denote by $f_{i}$ the number of subsets $σ$ of ${1, \dots, n}$ of cardinality $i + 1$ that sa…

math.CO2016

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…