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constants/38a.md

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@@ -8,6 +8,7 @@ A **self-avoiding walk (SAW)** on a graph $G=(V,E)$ is a walk that visits no ver
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<a href="#SSSY2014-Nv-ell">[SSSY2014-Nv-ell]</a>
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The **connective constant** (also called the SAW growth constant) of a graph $G$ is defined by
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$$
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\mu(G)\ :=\ \sup_{v\in V}\ \limsup_{\ell\to\infty} N(v,\ell)^{1/\ell}.
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$$
@@ -17,6 +18,7 @@ For **vertex-transitive** graphs, the $\limsup$ in the definition above can be r
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<a href="#SSSY2014-rem-vtx-limit">[SSSY2014-rem-vtx-limit]</a>
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For the square lattice $G=\mathbb{Z}^2$, let $c_n$ be the number of $n$-step SAWs starting at the origin. Then the **square-lattice SAW connective constant** is
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$$
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C_{38} := \mu_{\mathbb{Z}^2}\ :=\ \lim_{n\to\infty} c_n^{1/n}.
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$$

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