%0 Journal Article
%T Intervals of balanced binary trees in the Tamari lattice
%A Samuele Giraudo
%J Mathematics
%D 2011
%I arXiv
%R 10.1016/j.tcs.2011.11.020
%X 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.
%U http://arxiv.org/abs/1107.3472v2