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 Mmax(k) and Mmax(k) are assumed with the exception of Mmax-1 and Mmax-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 cn3/2 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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