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. Nous montrons que l'ensemble des arbres équilibrés est clos par intervalle dans le treillis de Tamari. Nous caractérisons la forme des intervalles du type $[T_0, T_1]$ où $T_0$ et $T_1$ sont équilibrés en montrant qu'en tant qu'ensembles partiellement ordonnés, ils sont isomorphes à un hypercube. Nous introduisons la notion de motif d'arbre et de grammaire synchrone dans le but d'établir une équation fonctionnelle de la série génératrice qui dénombre les intervalles d'arbres équilibrés.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Discrete Mathematics & Theoretical Computer Science
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
