maximum number of pairs x_{i}, x_{j} satisfying d(x_{i},x_{j}) = 1 in a set **{**x_{1},...,x_{n}**}** 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) t_{k}(n): = largest integer such that there is a set of n points in the plane for which there are t_{k}(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

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag