Non-ambiguous trees: new results and generalization

Jean-Christophe Aval (1) , Adrien Boussicault (1) , Bérénice Delcroix-Oger (2) , Florent Hivert (3) , Patxi Laborde-Zubieta (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 LRI - Laboratoire de Recherche en Informatique

We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differ- ential equation whose solution can be described combinatorially. This yield a new formula for the number of NATs. We also obtain q-versions of our formula. And we generalize NATs to higher dimension.

Domaines: Combinatoire [math.CO]

Jean-Christophe Aval, Adrien Boussicault, Bérénice Delcroix-Oger, Florent Hivert, Patxi Laborde-Zubieta. Non-ambiguous trees: new results and generalization. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6414⟩. ⟨hal-02173753⟩