Balanced binary trees in the Tamari lattice

Details Balanced binary trees in the Tamari lattice Balanced binary trees in the Tamari lattice

2010-09-24

arxiv.org/abs/1009.4774v1

Formal Power Series and Algebraic Combinatorics 2010

Mathematics

Combinatorics

Scientific paper

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.

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