## Connective constants and height functions for Cayley graphs

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## Abstract

The connective constant

It is proved that a large class of Cayley graphs support unimodular graph height functions, that are in addition

Group height functions, as well as the graph height functions of the previous paragraph, are non-constant harmonic functions with linear growth and an additional property of having periodic differences. The existence of such functions on Cayley graphs is a topic of interest beyond their applications in the theory of self-avoiding walks.

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1088-6850