Annals of Combinatorics

, Volume 5, Issue 2, pp 241–250 | Cite as

Combinatorics of Geometrically Distributed Random Variables: Inversions and a Parameter of Knuth

  • Helmut Prodinger

Abstract.

For words of length n, generated by independent geometric random variables, we consider the mean and variance of the number of inversions and of a parameter of Knuth from permutation in situ. In this way, q-analogues for these parameters from the usual permutation model are obtained.

Keywords: geometric distribution, inversions, permutations, harmonic numbers, q-analogues 
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Copyright information

© Birkhäuser Verlag Basel, 2001

Authors and Affiliations

  • Helmut Prodinger
    • 1
  1. 1.The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathe-matics, University of the Witwatersrand, P. O. Wits, 2050 Johannesburg, South Africa, e-mail: helmut@gauss.cam.wits.ac.zaZA

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