Planar point sets with a small number of empty convex polygons-Reference-Cited by-同舟云学术

Planar point sets with a small number of empty convex polygons

Published:2004-05-01 Issue:2 Volume:41 Page:243-269
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
language:
Short-container-title:

Author:

Bárány Imre¹,Valtr Pável²

Affiliation:

1. 1 I: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences II: Department of Mathematics, University College London I: H-1364 Budapest, P.O.B. 127, Hungary II: Gower Street, London Wc1e 6bt, England

2. 2 Institute for Theoretical Computer Science and Department of Applied Mathematics, Charles University Malostranské Nám. 25, 118 00 Praha 1, Czech Republic

Abstract

A subset A of a finite set P of points in the plane is called an empty polygon, if each point of A is a vertex of the convex hull of A and the convex hull of A contains no other points of P. We construct a set of n points in general position in the plane with only ˜1.62n2 empty triangles, ˜1.94n2 empty quadrilaterals, ˜1.02n2 empty pentagons, and ˜0.2n2 empty hexagons.

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://www.akademiai.com/doi/pdf/10.1556/sscmath.41.2004.2.4

Reference13 articles.

1. Empty simplices in Euclidean space;I. Bárány;Canadian Math. Bull.,1987

2. Problems and results around the erdös-szekeres convex polygon theorem;I. Bárány;Lect. notes comput. sci.,2001

3. Planar sets with few empty convex polygons;A. Dumitrescu;Stud. Sci. Math. Hung.,2000

4. Counting the interior of a point configuration;P. Edelman;Discrete Comput. Geom.,2000

5. On some problems of elementary and combinatorial geometry;P. Erdős;Ann. Mat. Pura. Appl.,1975

Cited by 39 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Erdős–Szekeres-Type Problems in the Real Projective Plane;Discrete & Computational Geometry;2024-09-09

2. No selection lemma for empty triangles;Acta Mathematica Hungarica;2024-05-23

3. Stars of empty simplices;Illinois Journal of Mathematics;2024-04-01

4. Growth Rate of the Number of Empty Triangles in the Plane;Lecture Notes in Computer Science;2024

5. Growth Rates of the Number of Empty Triangles and Tetrahedrons;2024