On the Erdös-diameter of sets
Let \(\delta(n)\) be 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. The best general upper bound is given by \(n\) equidistant points on a line. P. Erdös conjectured that \(\delta(n) = n - 1\) for \(n\) sufficiently big. [See also \textit{A. Baker} et al., `A tribute to Paul Erdös' (1990; Zbl 0706.00007) and \textit{P. Erdös}, A tribute to Paul Erdös, 467-478 (1990; Zbl 0709.11003)]. In this note the author proves an interesting asymptotic version of this Erdös conjecture for the special case of sets which lie in a parallel half-strip.
scientific article; zbMATH DE number 896020
scientific article