On distinct distances among points in general position and other related problems
The author studies some variants of Erdős classical and famous problem asking for the minimum number of distinct distances determined by \(n\) points in the plane. For instance, it is shown that there exist \(n\)-element point sets in strong general position and which do not contain the vertices of a parallelogram that determine only \(O(n^2/\sqrt{\log n})\) distinct distances. For more information on distance problems, we refer to \textit{P. Brass, W. Moser} and \textit{J. Pach} [Research problems in discrete geometry, New York, Springer (2005; Zbl 1086.52001)].
scientific article; zbMATH DE number 5651906
scientific article