Discrete Mathematics & Theoretical Computer Science, Vol 15, No 2 (2013)

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Descent variation of samples of geometric variables

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 P{ωi=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 ωii+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.

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