Counting walks in a quadrant: a unified approach via boundary value problems

Details Counting walks in a quadrant: a unified approach via boundary value problems Counting walks in a quadrant: a unified approach via boundary value problems

2010-03-06

arxiv.org/abs/1003.1362v3

Mathematics

Combinatorics

28 pages; 6 figures

Scientific paper

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations as well as on the sign of the covariance of the walk

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