Alexander Kharazishvili

On Some Mutual Positions of Hyperplanes in a Finite-Dimensional Affine Space

Several combinatorial questions and facts connected with certain types of mutual positions of finitely many hyperplanes in a finite-dimensional affine space are considered. An application of one of such facts to a multi-dimensional version of the well-known Sylvester theorem is presented.

Affine space, hyperplane, admissible set, admissible simplex, Sylvester theorem.

MSC 2000: 52A10, 52C10, 52C35