Geodesic
On the number of points in general position in the plane
Discrete analysis (2018)
Cet article a éte moissonné depuis la source Scholastica

Voir la notice de l'article

In this paper we study some Erdos type problems in discrete geometry. Our main result is that we show that there is a planar point set of n points such that no four are collinear but no matter how we choose a subset of size $n^{5/6+o(1)} $ it contains a collinear triple. Another application studies epsilon-nets in a point-line system in the plane. We prove the existence of some geometric constructions with a new tool, the so-called Hypergraph Container Method.
Publié le : 
@article{DAS_2018_a5,
     author = {Jozsef Balogh and Jozsef Solymosi},
     title = {On the number of points in general position in the plane},
     journal = {Discrete analysis},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2018_a5/}
}
TY  - JOUR
AU  - Jozsef Balogh
AU  - Jozsef Solymosi
TI  - On the number of points in general position in the plane
JO  - Discrete analysis
PY  - 2018
UR  - http://geodesic.mathdoc.fr/item/DAS_2018_a5/
LA  - en
ID  - DAS_2018_a5
ER  - 
%0 Journal Article
%A Jozsef Balogh
%A Jozsef Solymosi
%T On the number of points in general position in the plane
%J Discrete analysis
%D 2018
%U http://geodesic.mathdoc.fr/item/DAS_2018_a5/
%G en
%F DAS_2018_a5
Jozsef Balogh; Jozsef Solymosi. On the number of points in general position in the plane. Discrete analysis (2018). http://geodesic.mathdoc.fr/item/DAS_2018_a5/