Sur le nombre d'intervalles dans les treillis de Tamari

TL;DR

This paper provides an enumeration of intervals in Tamari lattices using an inductive approach, introduces the concept of 'new intervals,' and computes related series inverses, advancing combinatorial understanding of these structures.

Contribution

It introduces an inductive description of Tamari lattice intervals and defines and enumerates 'new intervals,' offering new combinatorial insights.

Findings

Enumerated all intervals in Tamari lattices.

Defined and counted 'new intervals' within the Tamari lattices.

Computed inverses of specific series related to the lattice structure.

Abstract

We enumerate the intervals in the Tamari lattices. For this, we introduce an inductive description of the intervals. Then a notion of "new interval" is defined and these are also enumerated. A a side result, the inverse of two special series is computed in a group of tree-indexed series.