Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Continued Classification of 3D Lattice Models in the Positive Octant
Axel Bacher  1  , Manuel Kauers  2  , Rika Yatchak  2  
1 : Laboratoire dÍnformatique de Paris-Nord  (LIPN)  -  Website
université Paris 13, Institut Galilée, Centre National de la Recherche Scientifique : UMR7030
Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, F-93430, Villetaneuse -  France
2 : Johannes Kepler University Linz [linz]  (JKU)  -  Website
Altenberger Straße 69, 4040 Linz -  Autriche

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. 

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