More Counting Techniques

  • Antonio Caminha Muniz Neto
Part of the Problem Books in Mathematics book series (PBM)


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.


  1. 25.
    Y. Kohayakawa, C.G.T. de A. Moreira, Tópicos em Combinatória Contemporânea (in Portuguese) (IMPA, Rio de Janeiro, 2001)Google Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Antonio Caminha Muniz Neto
    • 1
  1. 1.Universidade Federal do CearáFortalezaBrazil

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