## Charlotte Brennan ; Arnold Knopfmacher - Descent variation of samples of geometric random variables

dmtcs:594 - Discrete Mathematics & Theoretical Computer Science, April 5, 2013, Vol. 15 no. 2 - https://doi.org/10.46298/dmtcs.594
Descent variation of samples of geometric random variables

Authors: Charlotte Brennan ; Arnold Knopfmacher

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.

Volume: Vol. 15 no. 2
Section: Combinatorics
Published on: April 5, 2013
Accepted on: June 9, 2015
Submitted on: February 24, 2011
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]