New steps in walks with small steps in the quarter plane
Combinatorics
2016-02-24 v3
Abstract
In this article we obtain new expressions for the generating functions counting (non-singular) walks with small steps in the quarter plane. Those are given in terms of infinite series, while in the literature, the standard expressions use solutions to boundary value problems. We illustrate our results with three examples (an algebraic case, a transcendental D-finite case, and an infinite group model).
Keywords
Cite
@article{arxiv.1307.0599,
title = {New steps in walks with small steps in the quarter plane},
author = {Irina Kurkova and Kilian Raschel},
journal= {arXiv preprint arXiv:1307.0599},
year = {2016}
}
Comments
47 pages, 8 figures, to appear in Annals of Combinatorics