On the number of spiral self-avoiding walks

Abstract

The authors consider the problem of spiral self-avoiding walks as recently introduced by Privman (1983). They prove that the number of n-step spiral self-avoiding walks is given by sn=exp(2 pi (n/3)12/)/ (n74/c)(1+O(1/ square root n)) where c= pi /(4.354/). Similar results for various subsets of these walks are also obtained.