AbstractLet δ(n) denote the minimum diameter of a set of n points in the plane in which any two positive distances, if they are different, differ by at least one. Erdős conjectured that for n sufficiently big we have δ(n) = n − 1, the extremal configuration being n equidistant points on a line. In this note we prove an asymptotic version of this conjecture for the special case of sets which lie in a parallel half-strip
AbstractThe well-known three-distance theorem states that there are at most three distinct gaps betw...
Let C be a convex body in the Euclidean plane. The relative distance of points p and q is twice the ...
We consider the problem of computing the outer-radii of point sets. In this problem, we are given in...
AbstractLet δ(n) denote the minimum diameter of a set of n points in the plane in which any two posi...
AbstractA point set is separated if the minimum distance between its elements is 1. We call two real...
AbstractWe investigate the problem of finding the smallest diameterD(n) of a set ofnpoints such that...
AbstractA point set is separated if the minimum distance between its elements is one. Two numbers ar...
A set of points in d-dimensional Euclidean space is almost equidistant if among any three points of ...
In this note we study the existence of finite point-sets in the plane which have a prescribed set of...
International audienceA set of points in d-dimensional Euclidean space is almost equidistant if, amo...
We show the following two results on a set of n points in the plane, thus answering questions posed ...
AbstractLet 1 = d1 < d2 < ⋯ < dk denote the distinct distances determined by a set of n points in th...
AbstractA proof is given of the (known) result that, if real n-dimensional Euclidean space Rn is cov...
AbstractWe derive a new estimate of the size of finite sets of points in metric spaces with few dist...
AbstractA classical problem in combinatorial geometry is that of determining the minimum number f(n)...
AbstractThe well-known three-distance theorem states that there are at most three distinct gaps betw...
Let C be a convex body in the Euclidean plane. The relative distance of points p and q is twice the ...
We consider the problem of computing the outer-radii of point sets. In this problem, we are given in...
AbstractLet δ(n) denote the minimum diameter of a set of n points in the plane in which any two posi...
AbstractA point set is separated if the minimum distance between its elements is 1. We call two real...
AbstractWe investigate the problem of finding the smallest diameterD(n) of a set ofnpoints such that...
AbstractA point set is separated if the minimum distance between its elements is one. Two numbers ar...
A set of points in d-dimensional Euclidean space is almost equidistant if among any three points of ...
In this note we study the existence of finite point-sets in the plane which have a prescribed set of...
International audienceA set of points in d-dimensional Euclidean space is almost equidistant if, amo...
We show the following two results on a set of n points in the plane, thus answering questions posed ...
AbstractLet 1 = d1 < d2 < ⋯ < dk denote the distinct distances determined by a set of n points in th...
AbstractA proof is given of the (known) result that, if real n-dimensional Euclidean space Rn is cov...
AbstractWe derive a new estimate of the size of finite sets of points in metric spaces with few dist...
AbstractA classical problem in combinatorial geometry is that of determining the minimum number f(n)...
AbstractThe well-known three-distance theorem states that there are at most three distinct gaps betw...
Let C be a convex body in the Euclidean plane. The relative distance of points p and q is twice the ...
We consider the problem of computing the outer-radii of point sets. In this problem, we are given in...
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