Two Non-holonomic Lattice Walks in the Quarter Plane
Combinatorics
2011-02-10 v1
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.
Cite
@article{arxiv.math/0701800,
title = {Two Non-holonomic Lattice Walks in the Quarter Plane},
author = {Marni Mishna and Andrew Rechnitzer},
journal= {arXiv preprint arXiv:math/0701800},
year = {2011}
}