= Poisson limit for strictly balanced subgraph counts
{c}
{title2=$X_H(G(n,cn^{-v/e}))\Rightarrow\operatorname{Po}(c^e/a)$}
Here $v,e,a$ are the numbers of <vertices>, <edges> and <graph automorphisms> of $H$. Vertex-disjoint ordered $r$-tuples contribute $(n)_{rv}p^{re}/a^r\to(c^e/a)^r$ to the <factorial moment>. Adding a copy overlapping the previous union in $f$ <vertices> and $g$ <edges> changes the power of $n$ by $-f+(v/e)g\le0$, strictly when the intersection is a proper nonempty <subgraph>. The first overlap is strict because $H$ is connected and the previous copies are disjoint. Finitely many overlap types therefore contribute $o(1)$. The <factorial-moment criterion for Poisson convergence> gives the result.
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