Brennan, Charlotte and Knopfmacher, Arnold - Descent variation of samples of geometric random variables

dmtcs:594 - Discrete Mathematics & Theoretical Computer Science, April 5, 2013, Vol. 15 no. 2
Descent variation of samples of geometric random variables

Authors: Brennan, Charlotte and Knopfmacher, Arnold

In this paper, we consider random words ω1ω2ω3⋯ωn of length n, where the letters ωi ∈ℕ are independently generated with a geometric probability such that Pωi=k=pqk-1 where p+q=1 . We have a descent at position i whenever ωi+1 < ωi. The size of such a descent is ωi-ωi+1 and the descent variation is the sum of all the descent sizes for that word. We study various types of random words over the infinite alphabet ℕ, where the letters have geometric probabilities, and find the probability generating functions for descent variation of such words.

Source : oai:HAL:hal-00980745v1
Volume: Vol. 15 no. 2
Section: Combinatorics
Published on: April 5, 2013
Submitted on: February 24, 2011
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]