A Motzkin filter in the Tamari lattice
نویسندگان
چکیده
منابع مشابه
A Motzkin filter in the Tamari lattice
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 2n − 5 and that its radius is n − 2. Enumeration results are given for jo...
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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...
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We discuss some properties of a subposet of the Tamari lattice introduced by Pallo (1986), which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial...
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We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [T0, T1] where T0 and T1 are balanced trees are isomorphic as posets to a hypercube. We introduce tree patterns and synchronous grammars to get a functional equation of the generating series enumerating balanced tree intervals. Résumé. Nous montrons que l’ensemble des arbre...
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The Tamari lattice Tn was originally defined on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Although in several related lattices, the number of maximal chains is known, quoting Knuth, “The enumeration of such paths in Tamari lattices remains mysterious.” The lengths of maximal chains vary over a great range. In this paper, we focu...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2015
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.02.024