On the rotation distance in the lattice of binary trees
Information Processing Letters
On the structure of the lattice of noncrossing partitions
Discrete Mathematics
A shortest path metric on unlabeled binary trees
Pattern Recognition Letters
Discrete Mathematics
Right-arm rotation distance between binary trees
Information Processing Letters
Efficient lower and upper bounds of the diagonal-flip distance between triangulations
Information Processing Letters
The pruning-grafting lattice of binary trees
Theoretical Computer Science
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The Tamari lattice of order n can be defined by the set D"n 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 words in this structure. This distance can also be interpreted as the length of a geodesic between these Motzkin words in a Tamari lattice. So, a new upper bound is obtained for the classical rotation distance between two Motzkin words in a Tamari lattice. For some specific pairs of Motzkin words, this bound is exactly the value of the rotation distance in a Tamari lattice. Finally, enumerating results are given for join and meet irreducible elements, minimal elements and coverings.