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

Combinatorica volume 19, pages111–124(1999)Cite this article

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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Affiliations

  1. City College, CUNY; and Courant Institute, NYU; E-mail: pach@math-inst.hu, HU

    János Pach

  2. Courant Institute, NYU; E-mail: spencer@cs.nyu.edu, US

    Joel Spencer

Authors
  1. János Pach
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  2. Joel Spencer
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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