If counts the -step self-avoiding walks from a fixed vertex of a transitive lattice, the connective constant is the exponential growth rateSubmultiplicativity of and the Fekete lemma applied to prove existence of this limit.
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A self-avoiding walk (SAW) is a mathematical and combinatorial object used primarily in statistical mechanics and theoretical physics, as well as in computer science and graph theory. It is defined as a path that does not visit the same point more than once.