Continued Classification of 3D Lattice Walks in the Positive Octant
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2015
- DOI:
- arXiv:
- arXiv:1511.05763
- Bibcode:
- 2015arXiv151105763B
- Keywords:
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- Mathematics - Combinatorics;
- 05A16
- E-Print:
- 14 pages, FPSAC 2016 submission