Continued Classification of 3D Lattice Models in the Positive Octant

Axel Bacher (1) , Manuel Kauers (2) , Rika Yatchak (2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 JKU - University of Linz - Johannes Kepler Universität Linz

We continue the investigations of lattice walks in the three-dimensional lattice restricted to the positive octant. We separate models which clearly have a D-finite generating function from models for which there is no reason to expect that their generating function is D-finite, and we isolate a small set of models whose nature remains unclear and requires further investigation. For these, we give some experimental results about their asymptotic behaviour, based on the inspection of a large number of initial terms. At least for some of them, the guessed asymptotic form seems to tip the balance towards non-D-finiteness.

Domaines: Combinatoire [math.CO]

Axel Bacher, Manuel Kauers, Rika Yatchak. Continued Classification of 3D Lattice Models in the Positive Octant. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6415⟩. ⟨hal-02173752⟩