Exact enumeration of self-avoiding walks

Abstract

This thesis concerns a recently developed method for exact enumeration of self-avoiding walks, called the length-doubling algorithm. This method was created by the author and the supervisors and it substantially improves the current methods for the exact enumeration of self-avoiding walks. The basis of the algorithm and the results for the simple cubic lattice are given in the article [2]. This thesis reiterates the basis of the algorithm with slightly different terminology, and provides a more in-depth look at the implementation of the algorithm. It also adds the results of the face-centered cubic (FCC) and body- centered cubic (BCC) lattice, which are as of today yet unpublished.