Classifying lattice walks restricted to the quarter plane

Details Classifying lattice walks restricted to the quarter plane Classifying lattice walks restricted to the quarter plane

2006-11-21

arxiv.org/abs/math/0611651v1

Mathematics

Combinatorics

17 pages, 2 Tables, 2 Figures

Scientific paper

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.

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