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Periodica Mathematica Hungarica

, Volume 38, Issue 3, pp 173–177 | Cite as

A Note on the Number of Distinct Distances

  • G. Elekes
Article

Abstract

We refine a method introduced in [1] and [2] for studying the number of distinct values taken by certain polynomials of two real variables on Cartesian products. We apply it to prove a "gap theorem", improving a recent lower bound on the number of distinct distances between two collinear point sets in the Euclidean space.

Keywords

Euclidean Space Real Variable Collinear Point Distinct Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    GyÖrgy Elekes, On linear combinatories I, Combinatorica, 17(4) (1997), 447–458.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    GyÖrgy Elekes and Lajos RÓnyai, A combinatorial problem on polynomials and rational functions, Journal of Combinatorial Theory, series A, to appear.Google Scholar
  3. [3]
    Paul ErdŐs, On sets of distances of n points, Amer. Math. Monthly, 53: (1946), 248–250.MathSciNetCrossRefGoogle Scholar
  4. [4]
    William Fulton, Algebraic Curves, W. A. Benjamin Inc., New York-Amsterdam, 1969.Google Scholar
  5. [5]
    Leo Moser and JÁnos Pach, Research Problems in Combinatorial Geometry, Mimeographed notes, McGill University, Montreal, 1995.Google Scholar
  6. [6]
    JÁnos Pach and Pankaj K Agarwal, Combinatorial Geometry, J. Wiley and Sons, New York, 1995.Google Scholar
  7. [7]
    JÁnos Pach and Micha Sharir, Repeated angles in the plane and related problems, Journal of Combinatorial Theory, series A, 59 (1990), 12–22.MathSciNetCrossRefGoogle Scholar
  8. [8]
    JÁnos Pach and Micha Sharir, On the number of incidences between points and curves, Combinatorics, Probability and Computing, to appear.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • G. Elekes
    • 1
  1. 1.Eötvös Loránd UniversityBudapestHungary

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