Walks in the Quarter Plane with Multiple Steps

We extend the classification of nearest neighbour walks in the quarter plane to models in which multiplicities are attached to each direction in the step set. Our study leads to a small number of infinite families that completely characterize all the models whose associated group is D4, D6, or D8. T...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 27th...; no. Proceedings; pp. 25 - 36
Main Authors: Kauers, Manuel, Yatchak, Rika
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2015
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
computer algebra
Computer Science
d-finiteness
Discrete Mathematics
lattice walks
Computer Algebra
D-finiteness
Lattice Walks
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary:We extend the classification of nearest neighbour walks in the quarter plane to models in which multiplicities are attached to each direction in the step set. Our study leads to a small number of infinite families that completely characterize all the models whose associated group is D4, D6, or D8. These families cover all the models with multiplicites 0, 1, 2, or 3, which were experimentally found to be D-finite — with three noteworthy exceptions. Nous étendons la classification des marches aux plus proches voisins dans le quart de plan à des modèles dans lesquels une multiplicité est attachée à chaque direction de l’ensemble des pas. Notre étude identifie un petit nombre de familles infinies qui caractérisent complétement tous les modèles dont le groupe est D4, D6 ou D8. Ces familles contiennent tous les modèles à multiplicités 0, 1, 2 ou 3 dont il a été prouvé expérimentalement qu’ils étaientD-finis —avec trois exceptions notables.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2463