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Near optimal bounds for the Erdős distinct distances problem in high dimensions

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Abstract

We show that the number of distinct distances in a set of n points in ℝd is Ω(n 2/d − 2 / d(d + 2)), d ≥ 3. Erdős’ conjecture is Ω(n 2/d).

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Authors and Affiliations

  1. Department of Mathematics, UBC, Vancouver, BC, V6T 1Z2, Canada

    József Solymosi

  2. Department of Mathematics Rutgers, Piscataway, NJ, 08854-8019, USA

    Van H. Vu

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  1. József Solymosi
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  2. Van H. Vu
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Correspondence to József Solymosi.

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Solymosi, J., Vu, V.H. Near optimal bounds for the Erdős distinct distances problem in high dimensions. Combinatorica 28, 113–125 (2008). https://doi.org/10.1007/s00493-008-2099-1

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  • DOI: https://doi.org/10.1007/s00493-008-2099-1

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