Advertisement

Permutations, Partitions, and Power Series

  • Anthony Mendes
  • Jeffrey Remmel
Chapter
  • 1.2k Downloads
Part of the Developments in Mathematics book series (DEVM, volume 43)

Abstract

Statistics on permutations and rearrangements are defined and relationships between q-analogues of n, \(n!\), and \(\binom{n}{k}\) are proved. Integer partitions are defined and a few results concerning them are discussed. Generating functions are introduced as both elements of the ring of formal power series and complex valued functions.

References

  1. 4.
    Andrews, G.E.: The Theory of Partitions. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1998)[Reprint of the 1976 original]Google Scholar
  2. 18.
    Carlitz, L.: A combinatorial property of q-Eulerian numbers. Am. Math. Mon. 82, 51–54 (1975)CrossRefzbMATHGoogle Scholar
  3. 43.
    Foata, D.: Sur un énoncé de MacMahon. C. R. Acad. Sci. Paris 258, 1672–1675 (1964)MathSciNetzbMATHGoogle Scholar
  4. 44.
    Foata, D.: On the Netto inversion number of a sequence. Proc. Am. Math. Soc. 19, 236–240 (1968)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 81.
    Loehr, N.A.: Abacus proofs of Schur function identities. SIAM J. Discret. Math. 24(4), 1356–1370 (2010)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 83.
    Macdonald, I.G.: Symmetric Functions and Hall Polynomials, 2nd edn. Oxford Mathematical Monographs. The Clarendon Press/Oxford University Press, New York (1995) [With contributions by A. Zelevinsky, Oxford Science Publications]Google Scholar
  7. 109.
    Stanley, R.P.: Enumerative Combinatorics, vol. 2. Cambridge Studies in Advanced Mathematics, vol. 62. Cambridge University Press, Cambridge (1999)Google Scholar
  8. 117.
    White, D.E.: A bijection proving orthogonality of the characters of S n. Adv. Math. 50(2), 160–186 (1983)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Anthony Mendes
    • 1
  • Jeffrey Remmel
    • 2
  1. 1.Mathematics DepartmentCalifornia Polytechnic State UniversitySan Luis ObispoUSA
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA

Personalised recommendations