Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  422.05023
Autor:  Erdös, Paul; Purdy, G.
Title:  Some combinatorial problems in the plane. (In English)
Source:  J. Comb. Theory, Ser. A 25, 205-210 (1978).
Review:  The author prove (among other things) the following remarkable theorem: Let S be a finite set of n points in the plane, not all on one line, and let ti denote the number of lines which contain exactly i points of S for i = 2,3,...,n-1. If n \geq 25, then max{t2,t3} \geq n-1. Also, for all n, if t2 < n-1, then t3 \geq (n2-12n-16)/24. Finally, max{t2,t3,...,tn-1} = max{t2,t3}. The paper includes results in a similar vein together with various conjectures and their current status.
Reviewer:  D.A.Klarner
Classif.:  * 05B25 Finite geometries (combinatorics)
                   51M05 Euclidean geometries (general) and generalizations
                   00A07 Problem books
Keywords:  finite set of points in the plane; lines
Index Words:  Problems

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