On the unit distance problem

Jozsef Solymosi
University of British Columbia

The classical unit distance problem of Erdos asks for the
maximum number of unit distances determined by $n$ points in the plane.
For some metrics (given by symmetric strictly convex set) this number
can be as large as $n^{4/3}$. In this talk we will show some new examples
for such metrics and we will give some conditions that under those
restrictions the number of unit distances is $o(n^{4/3})$.

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