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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 403.52006

**Autor: ** Erdös, Paul; Purdy, George

**Title: ** Some extremal problems in geometry. V. (In English)

**Source: ** Proc. 8th southeast. Conf. on Combinatorics, graph theory, and computing, Baton Rouge 1977, 569-578 (1977).

**Review: ** [For the entire collection see Zbl 396.00002.]

The authors continue their investigation of bounds for several functions occuring in problems of Combinatorial Geometry (for part IV, see Proc. 7th south-east. Conf. Comb., Graph Theory, Comput.; Baton Rouge 1976, 307-322 (1976; Zbl 345.52007). Their results concern the number of different volumes of simplices formed from n given points in a Euclidean space, the number of planes determined by n given points, and the number of triangles determined by n points in the plane. Examples: Given n points in E^{3}, no three on a line, not all on a plane, there are at least cn^{3/4} distinct volumes of simplices formed from these points, where c is a constant. Then n vertices of polyhedron in E^{3} determine at least \binom{n-2}{2}+1 planes, provided n \geq 552.

**Reviewer: ** R.Schneider

**Classif.: ** * 52A37 Other problems of combinatorial convexity

**Keywords: ** simplices formed from n given points; number of different volumes of simplices; Euclidean space

**Citations: ** Zbl.396.00002; Zbl.345.52007

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