AbstractDe Bruijn and Erdös proved that every noncollinear set of n points in the plane determines at least n distinct lines. We suggest a possible generalization of this theorem in the framework of metric spaces and provide partial results on related extremal combinatorial problems
According to the Erdős–Szekeres theorem, for every n, a sufficiently large set of points in general ...
This thesis consists of three papers, each addressing a different collection of problems on the extr...
Abstract. Let P be a set of n points in the plane, not all on a line. We show that if n is large the...
summary:A special case of a combinatorial theorem of De Bruijn and Erdős asserts that every noncolli...
International audienceA special case of a combinatorial theorem of De Bruijn and Erd˝ os asserts tha...
The de Bruijn-Erdos Theorem from combinatorial geometry states that every set of $n$ noncollinear po...
AbstractA theorem of de Bruijn and Erdös [2] asserts that every finite geometry (see section 1 for d...
International audienceA set of n points in the plane which are not all collinear defines at least n ...
AbstractWe prove that if X1, X2,…, Xk are pairwise disjoint sets of points in a linear space, each o...
In 1951, Gabriel Dirac conjectured that every non-collinear set P of n points in the plane contains ...
We prove a conjecture of Erdős, Purdy, and Straus on the number of distinct areas of triangles dete...
Abstract Erd""os, Purdy, and Straus conjectured that the number of distinct (nonze...
The Sylvester-Gallai theorem asserts that any non-collinear point set in the plane de-termines a lin...
Based on a ternary betweenness relation, Coxeter introduced the notion of a line in ordered geometri...
In this paper, we prove that a set of N points in R^2 has at least c^N_(logN) distinct distances, th...
According to the Erdős–Szekeres theorem, for every n, a sufficiently large set of points in general ...
This thesis consists of three papers, each addressing a different collection of problems on the extr...
Abstract. Let P be a set of n points in the plane, not all on a line. We show that if n is large the...
summary:A special case of a combinatorial theorem of De Bruijn and Erdős asserts that every noncolli...
International audienceA special case of a combinatorial theorem of De Bruijn and Erd˝ os asserts tha...
The de Bruijn-Erdos Theorem from combinatorial geometry states that every set of $n$ noncollinear po...
AbstractA theorem of de Bruijn and Erdös [2] asserts that every finite geometry (see section 1 for d...
International audienceA set of n points in the plane which are not all collinear defines at least n ...
AbstractWe prove that if X1, X2,…, Xk are pairwise disjoint sets of points in a linear space, each o...
In 1951, Gabriel Dirac conjectured that every non-collinear set P of n points in the plane contains ...
We prove a conjecture of Erdős, Purdy, and Straus on the number of distinct areas of triangles dete...
Abstract Erd""os, Purdy, and Straus conjectured that the number of distinct (nonze...
The Sylvester-Gallai theorem asserts that any non-collinear point set in the plane de-termines a lin...
Based on a ternary betweenness relation, Coxeter introduced the notion of a line in ordered geometri...
In this paper, we prove that a set of N points in R^2 has at least c^N_(logN) distinct distances, th...
According to the Erdős–Szekeres theorem, for every n, a sufficiently large set of points in general ...
This thesis consists of three papers, each addressing a different collection of problems on the extr...
Abstract. Let P be a set of n points in the plane, not all on a line. We show that if n is large the...
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