Counting Functions

  • Martin Aigner
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 234)


Consider the family of n-subsets of a set R or the family of r-partitions of a set N. In chapter I, these families were viewed as special patterns whereas in chapter II they appeared as levels of certain lattices. In this chapter we want to count patterns and lattice levels starting from table 1.13 on the one hand and the fundamental examples of section II.4 on the other. In accordance with the set-up of the book we shall concentrate more on deriving general counting principles rather than on supplying a large set of recursion and inversion formulae for well-known coefficients such as the binomial coefficients or various partition numbers. For a good collection of the latter the reader is referred to Riordan [1, 2] or to Knuth [1, vol. 1].


Basis Sequence Basis Operator Inversion Formula Young Tableau Order Function 
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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Martin Aigner
    • 1
  1. 1.II. Institut für MathematikFreie Universität BerlinBerlin 33Federal Republic of Germany

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