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I guess a discrete-mathematics-related question is still welcome in MO since I was new to the community and learned from this amazing past post. The following claim is a simplified and abstract form ...

Let $l\geq 3$ be an integer. Is there $n\in\mathbb{N}$ and a hypergraph $H=(\{1,\ldots,n\},E)$ with the following properties? for all $e\in E$ we have $|e| \geq l$ $e_1\neq e_2 \in E \implies |e_1 \...