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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 874.52010

**Autor: ** Erdös, Paul; Pach, János

**Title: ** Are there many distances that occur few times? (In English)

**Source: ** Geombinatorics 6, No.3, 77-78 (1997).

**Review: ** Let x_{1},...,x_{n} be points in the plane and let **{**d_{1},...,d_{k}**}** denote the different distances occurring between these points. It is known that the diameter D: = **max** d_{i} occurs at most n times. The authors conject that there is at least one other d_{j} which occurs at most n times as well. They also state a conjecture concerning the sum of all the distances whose multiplicities are \leq n.

**Reviewer: ** B.Kind (Bochum)

**Classif.: ** * 52C10 Erdoes problems and related topics of discrete geometry

**Keywords: ** distances in finite planar sets

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