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Combinatorics of Geometrically Distributed Random Variables: Inversions and a Parameter of Knuth
Helmut Prodinger
The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, P.O. Wits, 2050 Johannesburg, South Africa
helmut@gauss.cam.wits.ac.za
Annals of Combinatorics 5 (2) p.241-250 June, 2001
AMS Subject Classification: 05A15
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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