Introduction -- Self-avoiding walks and connective constants -- Graph height functions and bridges -- Self-avoiding walks on one-dimensional lattices -- Context-free languages -- The language of self-avoiding walks.
0
SUMMARY OR ABSTRACT
Text of Note
The connective constant of a quasi-transitive infinite graph is a measure for the asymptotic growth rate of the number of self-avoiding walks of length n from a given starting vertex. On edge-labelled graphs the formal language of self-avoiding walks is generated by a formal grammar, which can be used to calculate the connective constant of the graph. Christian Lindorfer discusses the methods in some examples, including the infinite ladder-graph and the sandwich of two regular infinite trees.