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**Zentralblatt MATH**

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

**Zbl.No: ** 233.05017

**Autor: ** Erdös, Paul

**Title: ** On a problem of Grünbaum. (In English)

**Source: ** Can. Math. Bull. 15, 23-25 (1972).

**Review: ** The following problem is stated by Grünbaum: Determine the sequence of integers m^{(n)}_{1} < m^{(n)}_{2} < ... so that for every i there is a set of n points in the plane which determine exactly m^{(n)}_{i} lines. The author proves that there is a c_{1} so that for every c_{1}n^{3/2} < m \leq \binom{n}{2}, m \ne \binom{n}{2}-1, m \ne \binom{n}{2}-3 there is a set of n points which determines exactly m lines. The result is best possible (apart from the value of c_{1}). The principal tool is a result of *L. M. Kella* and *W. O. J. Moser* [Can. J. Math. 10, 210-219 (1958; Zbl 081.15103)]. Several unsolved problems are stated.

**Classif.: ** * 11B83 Special sequences of integers and polynomials

00A07 Problem books

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