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Three famous theorems on finite sets

  • Martin Aigner
  • Günter M. Ziegler
Chapter

Abstract

In this chapter we are concerned with a basic theme of combinatorics: properties and sizes of special families \(\mathcal{F}\) of subsets of a finite set N = {1, 2, . . . , n}. We start with two results which are classics in the field: the theorems of Sperner and of Erdős–Ko–Rado. These two results have in common that they were reproved many times and that each of them initiated a new field of combinatorial set theory. For both theorems, induction seems to be the natural method, but the arguments we are going to discuss are quite different and truly inspired.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 1
  1. 1.Institut für MathematikFreie Universität BerlinBerlinGermany

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