##
**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 x_{1},x_{2},...,x_{n} be n distinct points in a metric space. Usually we will restrict ourselves to the plane. Denote by D(x_{1},...,x_{n}) the number of distinct distances determined by x_{1},...,x_{n}. Assume that the points are in r-dimensional space. Denote by f_{r}(n) = **max**_{x1,...,xn}D(x_{1},..,x_{n}). I conjectured more than 40 years ago that f_{2}(n) > c_{1}n(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

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag