Add to ORKGLet P be a set of n points in R 3, not all of which are in a plane and no three on a line. We partially answer a question of Scott (1970) by showing that the connecting lines of P assume at least 2n − 3 different directions if n is even and at least 2n − 2 if n is odd. These bounds are sharp. The proof is based on a far-reaching generalization of Ungar’s theorem concerning the analogous problem in the plane.
Abstract. A three-dimensional analogue of the classical direction problem is proposed and an asympto...
AbstractIt is generally believed that the minimum number of distinct distances determined by a set o...
Abstract. Some improved bounds on the number of directions not determined by a point set in the affi...
AbstractLet P be a set of n points in R3, not all of which are in a plane and no three on a line. We...
AbstractP.R. Scott posed the problem of determining the minimum number of directions determined by n...
In this article we prove a theorem about the number of direc-tions determined by less then q affine ...
AbstractIt has been known for a long time that a p-element point set in AG(2,p), which is not a line...
AbstractA three-dimensional analogue of the classical direction problem is proposed and an asymptoti...
AbstractWe extend (and somewhat simplify) the algebraic proof technique of Guth and Katz (2010) [9],...
Abstract Erd""os, Purdy, and Straus conjectured that the number of distinct (nonze...
Let p1, p2, p3 be three noncollinear points in the plane, and let P be a set of n other points in th...
AbstractA classical problem in combinatorial geometry is that of determining the minimum number f(n)...
AbstractGiven a set of n points which span an ordered projective space P3, W. Bonnice and L.M. Kelly...
We give a fairly elementary and simple proof that shows that the number of inci-dences between m poi...
We examine the number of triangulations that any set of n points in the plane must have, and prove t...
Abstract. A three-dimensional analogue of the classical direction problem is proposed and an asympto...
AbstractIt is generally believed that the minimum number of distinct distances determined by a set o...
Abstract. Some improved bounds on the number of directions not determined by a point set in the affi...
AbstractLet P be a set of n points in R3, not all of which are in a plane and no three on a line. We...
AbstractP.R. Scott posed the problem of determining the minimum number of directions determined by n...
In this article we prove a theorem about the number of direc-tions determined by less then q affine ...
AbstractIt has been known for a long time that a p-element point set in AG(2,p), which is not a line...
AbstractA three-dimensional analogue of the classical direction problem is proposed and an asymptoti...
AbstractWe extend (and somewhat simplify) the algebraic proof technique of Guth and Katz (2010) [9],...
Abstract Erd""os, Purdy, and Straus conjectured that the number of distinct (nonze...
Let p1, p2, p3 be three noncollinear points in the plane, and let P be a set of n other points in th...
AbstractA classical problem in combinatorial geometry is that of determining the minimum number f(n)...
AbstractGiven a set of n points which span an ordered projective space P3, W. Bonnice and L.M. Kelly...
We give a fairly elementary and simple proof that shows that the number of inci-dences between m poi...
We examine the number of triangulations that any set of n points in the plane must have, and prove t...
Abstract. A three-dimensional analogue of the classical direction problem is proposed and an asympto...
AbstractIt is generally believed that the minimum number of distinct distances determined by a set o...
Abstract. Some improved bounds on the number of directions not determined by a point set in the affi...