Projekte pro Jahr
Abstract
Let S be a k-colored (finite) set of n points in Rd, d≥3, in general position, that is, no (d+1) points of S lie in a common (d−1)-dimensional hyperplane. We count the number of empty monochromatic d-simplices determined by S, that is, simplices which have only points from one color class of S as vertices and no points of S in their interior. For 3≤k≤d we provide a lower bound of Ω(nd−k+1+2−d)
and strengthen this to Ω(n d−2/3) for k=2.
On the way we provide various results on triangulations of point sets in Rd
. In particular, for any constant dimension d≥3, we prove that every set of n points (n sufficiently large), in general position in Rd, admits a triangulation with at least dn+Ω(logn) simplices.
and strengthen this to Ω(n d−2/3) for k=2.
On the way we provide various results on triangulations of point sets in Rd
. In particular, for any constant dimension d≥3, we prove that every set of n points (n sufficiently large), in general position in Rd, admits a triangulation with at least dn+Ω(logn) simplices.
Originalsprache | englisch |
---|---|
Seiten (von - bis) | 362-393 |
Fachzeitschrift | Discrete & Computational Geometry |
Jahrgang | 52 |
Ausgabenummer | 2 |
DOIs | |
Publikationsstatus | Veröffentlicht - 2014 |
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Theoretical
Fingerprint
Untersuchen Sie die Forschungsthemen von „Empty Monochromatic Simplices“. Zusammen bilden sie einen einzigartigen Fingerprint.-
Discrete and Computational Geometry
Hackl, T., Aigner, W., Pilz, A., Vogtenhuber, B., Kornberger, B. & Aichholzer, O.
1/01/05 → …
Projekt: Arbeitsgebiet
-
FWF - ComPoSe - EuroGIGA_Varianten von Erdös-Szekeres Problemen auf gefärbten Punktmengen und kompatible Graphen
1/10/11 → 31/12/15
Projekt: Forschungsprojekt
-
FWF - CPGG - Kombinatorische Probleme auf geometrischen Graphen
Hackl, T.
1/09/11 → 31/12/15
Projekt: Forschungsprojekt