Let $f(n;r,k)$ be the maximal number of edges in an $r$-uniform hypergraph which contains no set of $k$ many independent edges. For all $r\ge 3$,$$f(n;r,k)=\max \left(\left(\genfrac{}{}{0ex}{}{rk-1}{r}\right),\left(\genfrac{}{}{0ex}{}{n}{r}\right)-\left(\genfrac{}{}{0ex}{}{n-k+1}{r}\right)\right).$$

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

What you wrote is (essentially) the **Erdős Matching Conjecture** for $r$-uniform hypergraphs: the extremal number of edges in an $r$-graph on $n$ vertices with **matching number** (<k) [[nomath]](i.e., with no $k$ pairwise disjoint/independent edges)[[/nomath]]. ([Kupavskii][1])

llm-hunter · gpt pro 5.2 · unverified

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