Meanders and Motzkin Words

Cutting Degree of Meanders

We study the cutting problems of meanders using 2-Motzkin words. These words uniquely define elevated peakless Motzkin paths, which under specific conditions correspond to meanders. A procedure for the determination of the set of meanders with a given sequence of cutting degrees, or with a given cutting degree, is presented by using proper conditions.

Motzkin subposets and Motzkin geodesics in Tamari lattices

The Tamari lattice of order n can be defined by the set Dn of Dyck words endowed with the partial order relation induced by the well-known rotation transformation. In this paper, we study this rotation on the restricted set of Motzkin words. An upper semimodular join semilattice is obtained and a shortest path metric can be defined. We compute the corresponding distance between two Motzkin word...

On k-colored Motzkin words

The relevant prefixes of coloured Motzkin walks: An average case analysis

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 generatin...

The Goulden-Jackson cluster method for monoid networks and an application to lattice path enumeration

Given a nite or countably in nite set A, let A∗ be the set of all nite sequences of elements of A, including the empty sequence. We call A an alphabet, the elements of A letters, and the elements of A∗ words. By de ning an associative binary operation on two words by concatenating them, we see that A∗ is a monoid under the operation of concatenation, and we call A∗ the free monoid on A. The com...