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Balanced binary trees in the Tamari lattice

Abstract : We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals $[T_0, T_1]$ where $T_0$ and $T_1$ 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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Samuele Giraudo. Balanced binary trees in the Tamari lattice. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.725-736, ⟨10.46298/dmtcs.2814⟩. ⟨hal-00790740v2⟩

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