USER:
don't search the internet.
This is a test to see how well you can craft non-trivial, novel and creative solutions given a "combinatorics" math problem. Provide a full solution to the problem.
Problem:
"A hypergraph $(V,E)$ has a \emph{partition of size $m$} if there exist $D\subseteq V$ and $P\subseteq E$ such that $|D|=m$ and every vertex of $D$ lies in exactly one edge of $P$.
Let $H(n)$ be the maximum $|V|$ over all hypergraphs $(V,E)$ with no isolated vertices and no partition of size greater than $n$.
It is known that
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