2010/10/15 by Axel Bacher, Bacher, Axel, Mireille Bousquet‐Mélou +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · doi:10.48550/arxiv.1010.3200
openalex publication_date 2010/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a new family of self-avoiding walks (SAW) on the square lattice, called weakly directed walks. These walks have a simple characterization in terms of the irreducible bridges that compose them. We determine their generating function. This series has a complex singularity structure and in particular, is not D-finite. The growth constant is approximately 2.54 and is thus larger than that of all natural families of SAW enumerated so far (but smaller than that of general SAW, which is about 2.64). We also prove that the end-to-end distance of weakly directed walks grows linearly. Finally, we study a diagonal variant of this model.