Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  663.05013
Autor:  Erdös, Paul
Title:  Some old and new problems in combinatorial geometry. (In English)
Source:  Applications of discrete mathematics, Proc. 3rd SIAM Conf., Clemson/South Carolina 1986, 32-44 (1988).
Review:  [For the entire collection see Zbl 655.00007.]
Let x1,x2,...,xn be n distinct points in a metric space. Usually we will restrict ourselves to the plane. Denote by D(x1,...,xn) the number of distinct distances determined by x1,...,xn. Assume that the points are in r-dimensional space. Denote by

fr(n) = maxx1,...,xnD(x1,..,xn).

I conjectured more than 40 years ago that f2(n) > c1n(log n) ½. The lattice points show that this if true is best possible. In this paper we discuss problems related to the conjecture and other questions related to this parameter.
Classif.:  * 05B25 Finite geometries (combinatorics)
                   05-02 Research monographs (combinatorics)
                   00A07 Problem books
Keywords:  distances; lattice points
Citations:  Zbl 655.00007

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