q-Enumeration of words by their total variation
Ligia Loreta Cristea, Helmut Prodinger
Abstract
In recent work, Mansour [Discrete Math. Theoret. Computer
Science 11, 2009, 173—186] considers the problem of
enumerating all words of length n over
{1,2,…,k} (where k is a
given integer), that have the total variation equal to a
given integer m. In the present paper we study various
types of random words over the infinite alphabet ℕ,
where the letters have geometric probabilities. We are interested in
the probabilities of words of given type to have a given total
variation.
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