Abstract
We show that the set of balanced binary trees is closed by interval in the Tamari lattice. We establish that the intervals [ T , T ′ ] , where T and T ′ are balanced binary trees are isomorphic as posets to a hypercube. We introduce synchronous grammars that allow to generate tree-like structures and obtain fixed-point functional equations to enumerate these. We also introduce imbalance tree patterns and show that they can be used to describe some sets of balanced binary trees that play a particular role in the Tamari lattice. Finally, we investigate other families of binary trees that are also closed by interval in the Tamari lattice.
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