4 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,…
Intersection patterns of set systems on manifolds with slowly growing homological shatter functions
Sergey Avvakumov, Marguerite Bin, Xavier Goaoc
A theorem of MatouÅ¡ek asserts that for any , any set system whose shatter function is enjoys a fractional Helly theorem of order : in the -wise intersectio…
An asymptotic rigidity property from the realizability of chirotope extensions
Xavier Goaoc, Arnau Padrol
Let be a finite full-dimensional point configuration in . We show that if a point configuration has the property that all finite chirotopes realizable by addi…
Hitting and Covering Affine Families of Convex Polyhedra, with Applications to Robust Optimization
Jean Cardinal, Xavier Goaoc, Sarah Wajsbrot
Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set…