AbstractHere we have an example for six points in the plane no three on a line no four on a circle, and no one equidistant from three others, such that they determine 5 distinct distances, one occurring once, one twice, one three times, one four times, and one five times, and the configuration does not contain equilateral triangles
AbstractLet δ(n) denote the minimum diameter of a set of n points in the plane in which any two posi...
AbstractWe prove that among n points in the plane in general position, the shortest distance can occ...
We begin by revisiting a paper of Erd\H{o}s and Fishburn, which posed the following question: given ...
AbstractHere we have an example for six points in the plane no three on a line no four on a circle, ...
We study the structure of planar point sets that determine a small number of distinct distances. Spe...
Improving an old result of Clarkson et al., we show that the number of distinct distances determined...
AbstractIt is generally believed that the minimum number of distinct distances determined by a set o...
Improving an old result of Clarkson et al., we show that the number of distinct distances determined...
Erd\H{o}s and Fishburn studied the maximum number of points in the plane that span $k$ distances and...
Let p1, p2, p3 be three noncollinear points in the plane, and let P be a set of n other points in th...
AbstractMaximum planar sets that determine k distances are identified for k ⩽ 5. Evidence is present...
Abstract. In 1989, Erdős conjectured that for a sufficiently large n it is impossible to place n po...
AbstractLet g(k) be the smallest integer n for which there are n planar points each of which has k o...
AbstractThe question of how often the same distance can occur between k distinct points in n-dimensi...
We establish the following result related to Erdős’s problem on distinct distances. Let V be an n-el...
AbstractLet δ(n) denote the minimum diameter of a set of n points in the plane in which any two posi...
AbstractWe prove that among n points in the plane in general position, the shortest distance can occ...
We begin by revisiting a paper of Erd\H{o}s and Fishburn, which posed the following question: given ...
AbstractHere we have an example for six points in the plane no three on a line no four on a circle, ...
We study the structure of planar point sets that determine a small number of distinct distances. Spe...
Improving an old result of Clarkson et al., we show that the number of distinct distances determined...
AbstractIt is generally believed that the minimum number of distinct distances determined by a set o...
Improving an old result of Clarkson et al., we show that the number of distinct distances determined...
Erd\H{o}s and Fishburn studied the maximum number of points in the plane that span $k$ distances and...
Let p1, p2, p3 be three noncollinear points in the plane, and let P be a set of n other points in th...
AbstractMaximum planar sets that determine k distances are identified for k ⩽ 5. Evidence is present...
Abstract. In 1989, Erdős conjectured that for a sufficiently large n it is impossible to place n po...
AbstractLet g(k) be the smallest integer n for which there are n planar points each of which has k o...
AbstractThe question of how often the same distance can occur between k distinct points in n-dimensi...
We establish the following result related to Erdős’s problem on distinct distances. Let V be an n-el...
AbstractLet δ(n) denote the minimum diameter of a set of n points in the plane in which any two posi...
AbstractWe prove that among n points in the plane in general position, the shortest distance can occ...
We begin by revisiting a paper of Erd\H{o}s and Fishburn, which posed the following question: given ...
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