Non-ambiguous trees: new results and generalisation
Jean-Christophe Aval, Adrien Boussicault, Berenice Delcroix-Oger, and Florent Hivert, Patxi Laborde-Zubieta
TL;DR
This paper introduces a new combinatorial definition of non-ambiguous trees, derives a differential equation for their enumeration, extends the formulas to q-analogues, and generalizes the concept to higher dimensions.
Contribution
It provides a novel definition of NATs, new enumeration formulas including q-versions, and a higher-dimensional generalization, advancing the combinatorial understanding of these structures.
Findings
Derived a differential equation for NAT enumeration
Established a new formula for counting NATs
Generalized NATs to higher dimensions
Abstract
We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differential 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.
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