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Two Non-holonomic Lattice Walks in the Quarter Plane

Marni Mishna·Andrew Rechnitzer
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Abstract

We present two classes of random walks restricted to the quarter plane whose generating function is not holonomic. The non-holonomy is established using the iterated kernel method, a recent variant of the kernel method. This adds evidence to a recent conjecture on combinatorial properties of walks with holonomic generating functions. The method also yields an asymptotic expression for the number of walks of length n.

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Marni Mishna, Andrew Rechnitzer. 2007-01-28. Two Non-holonomic Lattice Walks in the Quarter Plane. https://doi.org/10.1016/j.tcs.2009.04.008

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