Non-ambiguous trees: new results and generalisation (Full version)
B\'er\'enice Delcroix-Oger (IRIF), Florent Hivert (LRI), Patxi, Laborde-Zubieta (LaBRI), Jean-Christophe Aval (LaBRI), Adrien Boussicault, (LaBRI)
TL;DR
This paper introduces a new combinatorial framework for non-ambiguous trees, deriving a differential equation, new counting formulas, q-analogues, and higher-dimensional generalizations.
Contribution
It provides a novel definition of NATs, a differential equation characterization, and extends the concept to higher dimensions, enriching the combinatorial theory.
Findings
New formula for counting NATs
Differential equation describing NATs
Higher-dimensional generalizations
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 yields a new formula for the number of NATs. We also obtain q-versions of our formula. We finally generalise NATs to higher dimension.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Stochastic processes and statistical mechanics · Theoretical and Computational Physics