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Counting Functions

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

Abstract

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].

Keywords

Basis Sequence Basis Operator Inversion Formula Young Tableau Order Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

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  8. See also Crapo-Rota, Désarméniens-Kung-Rota, Doubilet-Rota-Stanley, Goldman-Rota, Harper-Rota, Mullin-Rota, Roman-Rota. Rothschild, B. L. See Graham-Rothschild, Graham-Leeb-Rothschild. Rutherford, D. E.: Substitutional Analysis. Edinburgh: Oliver and Body (1948).Google Scholar
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    Stanley, R. P.: Ordered structures and partitions. Memoirs Amer. Math. Soc. 119 (1972).Google Scholar
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    Knuth, D. E.: The Art of Computer Programming,vol. 1 (1968), vol. 2 (1969), vol. 3 (1973). Reading: Addison-Wesley.Google Scholar
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    Knuth, D. E.: Permutations, matrices and generalized Young tableaux. Pac. J. Math. 34, 709–727 (1970). Ko, C. See Erdös-Ko-Rado.Google Scholar
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    Schensted, C.: Longest increasing and decreasing subsequences. Can. J. Math. 13, 179–191 (1961).Google Scholar
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    Foata, D.-Schützenberger, M. P.: Théorie Géométrique des Polynômes Eulériens. Lectures Notes Math. 138, Springer-Verlag (1970). See also Cartier-Foata.Google Scholar
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    Stanley, R. P.: Theory and application of plane partitions. Studies in Appl. Math. I, 50, 167–188 (1971), II, 50, 259–279 (1971).MathSciNetzbMATHGoogle Scholar

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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