Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
A calculus for the random generation of labelled combinatorial structures
Theoretical Computer Science
Riordan arrays and combinatorial sums
Discrete Mathematics
Uniform generation of a Motzkin word
Theoretical Computer Science
The random generation of underdiagonal walks
Proceedings of the 4th conference on Formal power series and algebraic combinatorics
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Ranking and unranking of lexicographically ordered words: an average-case analysis
Journal of Automata, Languages and Combinatorics
Random generation of trees and other combinatorial objects
Theoretical Computer Science - Special issue on Caen '97
Underdiagonal lattice paths with unrestricted steps
Discrete Applied Mathematics
Combinatorial algorithms: generation, enumeration, and search
ACM SIGACT News
Generating trees and proper Riordan arrays
Discrete Mathematics
A generic approach for the unranking of labeled combinatorial classes
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Combinatorial Algorithms: For Computers and Hard Calculators
Combinatorial Algorithms: For Computers and Hard Calculators
A bijection between ordered trees and 2-Motzkin paths and its many consequences
Discrete Mathematics
A Construction for Enumerating k-coloured Motzkin Paths
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Algebraic and Combinatorial Properties of Simple, Coloured Walks
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
A fast algorithm to generate necklaces with fixed content
Theoretical Computer Science
Boltzmann Samplers for the Random Generation of Combinatorial Structures
Combinatorics, Probability and Computing
Efficient iteration in admissible combinatorial classes
Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
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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 @a,@b and @c colours, respectively. In particular, when @a=@b=@c=1 we have the classical Motzkin walks while for @a=@c=1 and @b=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 @a,@b and @c. 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.