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On q-Olivier Functions
Helmut Prodinger and Tuwani A. Tshifhumulo
The John Knopfmacher Centre for Applicable Analysis and Number Theory
University of the Witwatersrand, Private Bag 3, WITS 2050, Johannesburg, South Africa
helmut@maths.wits.ac.za   tat@univen.ac.za
Annals of Combinatorics 6 (2) p.181-194 June, 2002
AMS Subject Classification: 05A15, 33D70, 60C05
Abstract:
We consider words with letters satisfying an up-up-down pattern like Attaching the (geometric) probability to the letter i (with p=1-q), every word gets a probability by assuming independence of letters. We are interested in the probability that a random word of length n satisfies the up-up-down condition. It turns out that one has to consider the 3 residue classes (mod 3) separately; then one can compute the associated probability generating function. They turn out to be q-analogues of so called Olivier functions.
Keywords: Olivier functions, permutations, geometric probabilities, words

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