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

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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/