Transcendence of generating functions of walks on the slit plane

Details Transcendence of generating functions of walks on the slit plane Transcendence of generating functions of walks on the slit plane

2004-05-11

arxiv.org/abs/math/0405188v1

Mathematics

Combinatorics

Accepted for MathInfo2004

Scientific paper

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.

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