Self-avoiding walk generating function
= Self-avoiding walk generating function
{title2=$Z_v(x)=\sum_{n\geq0}\sigma_n(v)x^n$}
The <generating function> weights each <self-avoiding walk> by $x$ to the power of its length, including the zero-length walk. Its <radius of convergence> is the reciprocal of the upper exponential growth rate of the rooted counts, by the <Cauchy-Hadamard theorem>.