Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647152 | Discrete Mathematics | 2015 | 9 Pages |
Abstract
The Tamari lattice of order n can be defined on the set Tn of binary trees endowed with the partial order relation induced by the well-known rotation transformation. In this paper, we restrict our attention to the subset Mn of Motzkin trees. This set appears as a filter of the Tamari lattice. We prove that its diameter is 2nâ5 and that its radius is nâ2. Enumeration results are given for join and meet irreducible elements, minimal elements and coverings. The set Mn endowed with an order relation based on a restricted rotation is then isomorphic to a ranked join-semilattice recently defined in Baril and Pallo (2014). As a consequence, we deduce an upper bound for the rotation distance between two Motzkin trees in Tn which gives the exact value for some specific pairs of Motzkin trees.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jean-Luc Baril, Jean-Marcel Pallo,