Advertisement

The Would-Be Method of Targeted Rings

  • Ottavio M. D’Antona
Part of the Progress in Mathematics book series (PM, volume 161)

Abstract

We describe the notion of an algebraic structure underlying a combinatorial identity or an inequality. In so doing, we supply an algebraic motivation for symbolic substitutions like x n x n ,x n → (x) n and others.

Keywords

Formal Power Series Associative Ring Factorial Moment Stirling Number Canonical Homomorphism 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Aigner, Combinatorial Theories, Springer, New York/Berlin, 1979.Google Scholar
  2. [2]
    S. Bertoluzza and O. D’Antona, Considerazioni di tipo algebrico sulla diseguaglianza di Bonferroni, Technical Report RIDIS 28–87, Dipartimento di Informatica e Sistemistica, Università di Pavia, 1987.Google Scholar
  3. [3]
    L. Comtet., Advanced Combinatorics, Birkäuser, 1974.MATHGoogle Scholar
  4. [4]
    H. H. Crapo, Rota’s “combinatorial theory,” in Gian-Carlo Rota on Combinatorics, J.P.S. Kung, ed., xix–xiii, Birkäuser, Boston 1995.Google Scholar
  5. [5]
    O. D’Antona, A ring underlying probabilistic identities, J. Math. Anal. Appl., 108:211–215, 1985.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    O. D’Antona, Combinatorial properties of the factorial ring, J. Math. Anal. Appl 117:303–309, 1986.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    O. D’Antona, Pseudo power series, Technical Report RIDIS 27–87, Dipartimento di Informatica e Sistemistica, Università di Pavia, 1987.Google Scholar
  8. [8]
    O. D’Antona and A. Pesci, Connecting two rings underlying the inclusion-exclusion principle, J. Combin. Theory Ser. A, 40:439–443, 1985.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    O. D’Antona and G.-C. Rota, Two rings connected with the inclusion-exclusion principle, J. Combin. Theory Ser. A, 24:65–72, 1978.MathSciNetGoogle Scholar
  10. [10]
    M. Fréchet, Les probabilités associées à un système d’événements compatible et dépendants, Vol. I, Herman, Paris, 1940.Google Scholar
  11. [11]
    J. Riordan, An Introduction to Combinatorial Analysis, J. Wiley & Sons, 1958.MATHGoogle Scholar
  12. [12]
    S. Roman, Umbral Calculus, Reidel, Dordrecht, 1984.MATHGoogle Scholar
  13. [13]
    G.-C. Rota, The number of partitions of a set, Amer . Math. Monthly, 71:498–505, 1964.MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    R. P. Stanley, Enumerative Combinatorics, Wadworth & Brooks, Monterey, 1986.MATHGoogle Scholar

Copyright information

© Birkhäuser 1998

Authors and Affiliations

  • Ottavio M. D’Antona
    • 1
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly

Personalised recommendations