Fulltext

Point Configurations in d -Space without Large Subsetsin Convex Position

Károlyi, Gyula ; Valtr, Pavel

In: Discrete & Computational Geometry, 2003, vol. 30, no. 2, p. 277-286

Ajouter à la liste personnelle
    Titre
    • Point Configurations in d -Space without Large Subsetsin Convex Position
    Auteur
    • Károlyi, Gyula. IFOR, Department of Mathematics, ETH Zurich, Zurich, Switzerland and Department of Algebra and Number Theory, Eötvös University, Postafiók 120, H-1518 Budapest, Hungary
    • Valtr, Pavel. Department of Applied Mathematics, Charles University and Institute for Theoretical Computer Science (ITI), Charles University, Malostransk'en'am. 25, 118 00 Praha 1, Czech Republic
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Discrete & Computational Geometry, 2003, vol. 30, no. 2, p. 277-286. Springer-Verlag; www.springer-ny.com
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:314483
    Summary
    In this paper we give a lower bound for the Erd\H os-Szekeres number in higher dimensions. Namely, in two different ways we construct, for every $n>d\ge 2$, a configuration of $n$ points in general position in $\R^d$ containing at most $c_d(\log n)^{d-1}$ points in convex position. (Points in $\R^d$ are in convex position if none of them lies in the convex hull of the others.)