On q-Olivier Functions |
| |
Authors: | Helmut Prodinger Tuwani A Tsifhumulo |
| |
Institution: | The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, Private Bag 3, WITS 2050, Johannesburg, South Africa, e-mail: helmut@maths.wits.ac.za; tat@univen.ac.za, ZA
|
| |
Abstract: | We consider words w1· · · wn with letters wi ? {1, 2, 3, ?} w_i \in \{1, 2, 3, \ldots\} satisfying an up-up-down pattern like a1 h a2 h a3 S a4 h a5 h a6 S · · · . Attaching the (geometric) probability pqi-1 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: | |
本文献已被 SpringerLink 等数据库收录! |
|