Classifying lattice walks restricted to the quarter plane

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This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic, transcendental holonomic and non-holonomic. The principal results are a new algebraic class related to Kreweras' walks; two new non-holonomic classes; and enumerative data on some other classes. These results provide strong evidence for conjectures which use combinatorial criteria to classify the generating functions all nearest neighbour walks in the quarter plane.
17 pages, 2 Tables, 2 Figures

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Combinatorics, Primary 82B41; Secondary 05A15

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http://salesiana.dossiersoluciones.com/handle/123456789/119370

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611651
 http://arxiv.org/abs/math/0611651

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arXiv