Intervals of balanced binary trees in the Tamari lattice

Samuele Giraudo (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Domaines: Combinatoire [math.CO]

Samuele Giraudo. Intervals of balanced binary trees in the Tamari lattice. Theoretical Computer Science, 2012, 420, pp.1--27. ⟨hal-00786799⟩