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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