Combinatorics: Trends and Examples

Combinatorics is currently a very active branch of mathematics, and there is good reason to believe that it will become even more active in the future. One trend in combinatorics is the increasing use of methods from other branches of mathematics to solve purely combinatorial questions. A wellknown example of this situation is the field of algebraic topology where topological questions are converted into algebraic ones and vice versa, an idea which has been used quite effectively in combinatorics, and which we will illustrate with two examples.