Let $f(n,k)$ count the number of self-avoiding walks of $n$ steps (beginning at the origin) in ${\mathbb{Z}}^k$ (i.e. those walks which do not intersect themselves). Determine$$C_k=\underset{n\to \infty }{\lim }f(n,k{)}^{1/n}.$$

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Write (c_n=f(n,k)) for the number of $n$-step self–avoiding walks (SAWs) in (\mathbb Z^k) starting at the origin.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.