Uniformly Distributed Distances – a Geometric Application of Janson's Inequality

denote the distances determined by n points in the plane. It is shown that , where the minimum is taken over all point sets with minimal distance . This bound is asymptotically tight.

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Received: September 4, 1997

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Pach, J., Spencer, J. Uniformly Distributed Distances – a Geometric Application of Janson's Inequality. Combinatorica 19, 111–124 (1999). https://doi.org/10.1007/s004930050048

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  • AMS Subject Classification (1991) Classes:  52C10, 05C80