2004/05/11 by Martin Rubey, Rubey, Martin
Biochemistry, Genetics and Molecular Biology · Mathematics · #05A16 #Combinatorics (math.CO) #Diffusion and Search Dynamics #FOS: Mathematics #math.CO #msc:05A16
paper · pdf · doi:10.48550/arxiv.math/0405188
Accepted for MathInfo2004
arxiv created 2004/05/11 · openalex publication_date 2004/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a single walker on the slit plane, that is, the square grid Z2 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.