Transcendence of generating functions of walks on the slit plane
Combinatorics
2007-05-23 v1
Abstract
Consider a single walker on the slit plane, that is, the square grid Z^2 without its negative x-axis, who starts at the origin and takes his steps from a given set S. Mireille Bousquet-Melou conjectured that -- excluding pathological cases -- the generating function counting the number of possible walks is algebraic if and only if the walker cannot cross the negative x-axis without touching it. In this paper we prove a special case of her conjecture.
Cite
@article{arxiv.math/0405188,
title = {Transcendence of generating functions of walks on the slit plane},
author = {Martin Rubey},
journal= {arXiv preprint arXiv:math/0405188},
year = {2007}
}
Comments
Accepted for MathInfo2004