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**Zentralblatt MATH**

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

**Zbl.No: ** 606.05005

**Autor: ** Salamon, Peter; Erdös, Paul

**Title: ** The solution to a problem of Grünbaum. (In English)

**Source: ** Can. Math. Bull. 31, No.2, 129-138 (1988).

**Review: ** The paper characterizes the set of all possible values for the number of lines determined by n points for n sufficiently large. For \binom{k}{2} \leq (n-k), the lower bound of Kelly and Moser for the number of lines in a configuration with n-k collinear points is shown to be sharp and it is shown that all values between M_{max}(k) and M_{max}(k) are assumed with the exception of M_{max}-1 and M_{max}-3. Exact expressions are obtained for the lower end of the continuum of values leading down from \binom{n}{2}-4. In particular, the best value of c = 1 is obtained in Erdös' previous expression cn^{3/2} for this lower end of the continuum.

**Reviewer: ** P.Salamon

**Classif.: ** * 05A15 Combinatorial enumeration problems

05B25 Finite geometries (combinatorics)

51E20 Combinatorial structures in finite projective spaces

**Keywords: ** connecting lines; lines determined by points

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