Carathéodory-type Theorems à la Bárány

Carathéodory-type Theorems à la Bárány

We generalise the famous Helly–Lovász theorem leading to a generalisation of the Bárány–Carathéodory theorem for oriented matroids in dimension ≤3. We also provide a non-metric proof of the latter colourful theorem for arbitrary dimensions and explore some generalisations in dimension 2.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Discrete & computational geometry 2011-03, Vol.45 (2), p.261-271
Hauptverfasser: Bokowski, Jürgen, Bracho, Javier, Strausz, Ricardo
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Computational geometry
Computational Mathematics and Numerical Analysis
Geometry
Mathematics
Mathematics and Statistics
Proving
Theorems
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We generalise the famous Helly–Lovász theorem leading to a generalisation of the Bárány–Carathéodory theorem for oriented matroids in dimension ≤3. We also provide a non-metric proof of the latter colourful theorem for arbitrary dimensions and explore some generalisations in dimension 2.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-010-9290-z