More Counting Techniques
In this chapter we study a few more elaborate counting techniques. We start by discussing the inclusion-exclusion principle, which, roughly speaking, is a formula for counting the number of elements of a finite union of finite sets. The presentation continues with the notion of double counting for, counting a certain number of configurations in two distinct ways, to infer some hidden result. Then, a brief discussion of equivalence relations and their role in counting problems follows. Among other interesting results, we illustrate it by proving a famous theorem of B. Bollobás, on extremal set theory. The chapter ends with a glimpse on the use of the language of metric spaces in certain specific counting problems.
- 25.Y. Kohayakawa, C.G.T. de A. Moreira, Tópicos em Combinatória Contemporânea (in Portuguese) (IMPA, Rio de Janeiro, 2001)Google Scholar