|
|||||
|
|
Point Configurations in <Emphasis Type="Italic">d</Emphasis>-Space without Large Subsets in Convex Position |
|
| Authors: | |
| Institution: | (1) IFOR, Department of Mathematics, ETH Zurich, Zurich, Switzerland and Department of Algebra and Number Theory, Eötvös University, Postafiók 120, H-1518 Budapest, Hungary;(2) Department of Applied Mathematics, Charles University and Institute for Theoretical Computer Science (ITI), Charles University, Malostransk enam. 25, 118 00 Praha 1, Czech Republic |
| Abstract: | 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.) |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |