Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Monday 4
Karen Yeats
› 17:30 - 19:00 (1h30)
› SFU Harbour Center - Segal Centre Conference Rooms 1400 - 1410
Continued Classification of 3D Lattice Models in the Positive Octant
Axel Bacher  1  , Manuel Kauers  2  , Rika Yatchak  3  
1 : Laboratoire d'Informatique de Paris-Nord  (LIPN)
Université Sorbonne Paris Cité (USPC), Institut Galilée, université Paris 13, CNRS : UMR7030
2 : Institute for Algebra, Johannes Kepler University, Linz
3 : Institute for Algebra, Johannes Kepler University, Linz, Austria

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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