Continued Classification of 3D Lattice Models in the Positive Octant

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 sma...

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Vydáno v:Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th...
Hlavní autoři: Bacher, Axel, Kauers, Manuel, Yatchak, Rika
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: DMTCS 22.04.2020
Discrete Mathematics & Theoretical Computer Science
Témata:
[math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
ISSN:1365-8050, 1462-7264, 1365-8050
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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.
AbstractList 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.
Author Yatchak, Rika
Kauers, Manuel
Bacher, Axel
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  organization: Johannes Kepler University Linz [Linz]
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Snippet We continue the investigations of lattice walks in the three-dimensional lattice restricted to the positive octant. We separate models which clearly have a...
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SubjectTerms [math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
Title Continued Classification of 3D Lattice Models in the Positive Octant
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