Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  428.05008
Autor:  Erdös, Paul
Title:  Some combinational problems in geometry. (In English)
Source:  Geometry and differential geometry, Proc. Conf., Haifa 1979, Lect. Notes Math. 792, 46-53 (1980).
Review:  [For the entire collection see Zbl 418.00010.]
In this short survey, results and conjectures for lower and upper bounds are given for (1) f2(n): = maximum number of pairs xi, xj satisfying d(xi,xj) = 1 in a set {x1,...,xn} of distinct points in the euclidean plane; (2) H(n): = smallest integer such that every set of H(n) points in the plane, no three on a line, contains the vertices of a convex n-gon; (3) tk(n): = largest integer such that there is a set of n points in the plane for which there are tk(n) lines containing exactly k of the points; (4) a multitude of further geometrically defined integer functions.
Reviewer:  H.Groh
Classif.:  * 05A20 Combinatorial inequalities
                   05A99 Classical combinatorial problems
                   05-02 Research monographs (combinatorics)
                   00A07 Problem books
                   05B25 Finite geometries (combinatorics)
                   52A99 General convexity
Keywords:  lower bounds; combinational geometry; survey; upper bounds
Citations:  Zbl.418.00010

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