Two non-holonomic lattice walks in the quarter plane

Authors:
Marni Mishna;Andrew Rechnitzer
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, Canada;Department of Mathematics, University of British Columbia, Vancouver, Canada
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We present two classes of random walks restricted to the quarter plane with non-holonomic generating functions. The non-holonomicity is established using the iterated kernel method, a variant of the kernel method. This adds evidence to a recent conjecture on combinatorial properties of walks with holonomic generating functions [M. Mishna, Classifying lattice walks in the quarter plane, J. Combin. Theory Ser. A 116 (2009) 460-477]. The method also yields an asymptotic expression for the number of walks of length n.