Weakly directed self-avoiding walks

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Bacher, Axel¹  Bousquet-Melou, Mireille¹ 

[1] Univ Bordeaux 1, LaBRI, CNRS, F-33405 Talence, France

关键词: Enumeration;    Self-avoiding walks;    Partially directed bridges;    Non-D-finite series;    Random generation;   

DOI  :  10.1016/j.jcta.2011.06.001

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free