19 citations · 59 across the 23 of their papers we have counts for
12 papers · 1 filter
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…
A colorful Goodman-Pollack-Wenger theorem
Andreas F. Holmsen
Hadwiger's transversal theorem gives necessary and sufficient conditions for the existence of a line transversal to a family of pairwise disjoint convex sets in the plane. These co…
No weak epsilon nets for lines and convex sets in space
Otfried Cheong, Xavier Goaoc, Andreas F. Holmsen
We prove that there exist no weak -nets of constant size for lines and convex sets in .
On a transversal theorem of Montejano and Karasev
Andreas F. Holmsen
We give a new proof of a theorem of Montejano and Karasev regarding -dimensional transversals to small families of convex sets. While their proof uses technical algebraic and to…
Limits of Order Types
Xavier Goaoc, Alfredo Hubard, Rémi de Joannis de Verclos +2
We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obta…
Shellability is NP-complete
Xavier Goaoc, Pavel Paták, Zuzana Patáková +2
We prove that for every , deciding if a pure, -dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Dan…