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CCCG
2008

On distinct distances among points in general position and other related problems

9 years 4 months ago
On distinct distances among points in general position and other related problems
A set of points in the plane is said to be in general position if no three of them are collinear and no four of them are cocircular. If a point set determines only distinct vectors, it is called parallelogram free. We show that there exist n-element point sets in the plane in general position, and parallelogram free, that determine only O(n2 / log n) distinct distances. This answers a question of Erdos, Hickerson and Pach. We then revisit an old problem of Erdos : given any n points in the plane (or in d dimensions), how many of them can one select so that the distances which are determined are all distinct? -- and provide (make explicit) some new bounds in one and two dimensions. Other related distance problems are also discussed.
Adrian Dumitrescu
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2008
Where CCCG
Authors Adrian Dumitrescu
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