Axel Bacher ; Mireille BousquetMélou

Weakly directed selfavoiding walks
dmtcs:2883 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2010,
DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)

https://doi.org/10.46298/dmtcs.2883
Weakly directed selfavoiding walksArticle
Authors: Axel Bacher ^{1}; Mireille BousquetMélou ^{2,}^{3}
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Axel Bacher;Mireille BousquetMélou
1 Laboratoire Bordelais de Recherche en Informatique
We define a new family of selfavoiding walks (SAW) on the square lattice, called $\textit{weakly directed walks}$. 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 Dfinite. 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 endtoend distance of weakly directed walks grows linearly. Finally, we study a diagonal variant of this model.