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- W2048233076 abstract "In this paper we study some relevant prefixes of coloured Motzkin walks (otherwise called coloured Motzkin words). In these walks, the three kinds of step can have α , β and γ colours, respectively. In particular, when α = β = γ = 1 we have the classical Motzkin walks while for α = γ = 1 and β = 0 we find the well-known Dyck walks. By using the concept of Riordan arrays and probability generating functions we find the average length of the relevant prefix in a walk of length n and the corresponding variance in terms of α , β and γ . This result is interesting from a combinatorial point of view and also provides an average case analysis of algorithms related to the problem of ranking and generating uniformly at random the coloured Motzkin words." @default.
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- W2048233076 date "2010-01-01" @default.
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- W2048233076 title "The relevant prefixes of coloured Motzkin walks: An average case analysis" @default.
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- W2048233076 doi "https://doi.org/10.1016/j.tcs.2009.09.021" @default.
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