8 citations · 65 across the 30 of their papers we have counts for
6 papers · 1 filter
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,…
A Universality Theorem for Nested Polytopes
Michael G. Dobbins, Andreas Holmsen, Tillmann Miltzow
In a nutshell, we show that polynomials and nested polytopes are topological, algebraic and algorithmically equivalent. Given two polytops and a number , the Nest…
An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial Lifting
Xavier Goaoc, Andreas Holmsen, Cyril Nicaud
We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in . We show that this question,…
Smoothed Analysis of the Art Gallery Problem
Michael Gene Dobbins, Andreas Holmsen, Tillmann Miltzow
In the Art Gallery Problem we are given a polygon on vertices and a number . We want to find a guard set of size , such that each point in is s…
Lower Bounds for Pinning Lines by Balls
Otfried Cheong, Xavier Goaoc, Andreas Holmsen
A line L is a transversal to a family F of convex objects in R^d if it intersects every member of F. In this paper we show that for every integer d>2 there exists a family of 2d-1…
Hadwiger and Helly-type theorems for disjoint unit spheres
Otfried Cheong, Xavier Goaoc, Andreas Holmsen +1
We prove Helly-type theorems for line transversals to disjoint unit balls in . In particular, we show that a family of disjoint unit balls in has a line…