### Descent variation of samples of geometric variables

*Charlotte Brennan, Arnold Knopfmacher*

#### Abstract

In this paper, we consider random words
ω

_{1}ω_{2}ω_{3}⋯ω_{n}of length n, where the letters ω_{i}∈ℕ are independently generated with a geometric probability such that P{ω_{i}=k}=pq^{k-1}where p+q=1 . We have a descent at position i whenever ω_{i+1}< ω_{i}. The size of such a descent is ω_{i}-ω_{i+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.Full Text: PDF PostScript