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 c1 so that for every c1n3/2 < 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 c1). 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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