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Erd\H{o}s, F\"uredi, Rothschild and S\'os initiated a study of classes ofgraphs that forbid every induced subgraph on a given number $m$ of vertices andnumber $f$ of edges. Extending their notation to $r$-graphs, we write $(n,e)\to_r (m,f)$ if every $r$-graph $G$ on $n$ vertices with $e$ edges has aninduced subgraph on $m$ vertices and $f$ edges. The \emph{forcing density} of apair $(m,f)$ is $$ \sigma_r(m,f) =\left. \limsup\limits_{n \to \infty}\frac{|\{e : (n,e) \to_r (m,f)\}|}{\binom{n}{r}} \right. .$$ In the graphsetting it is known that there are infinitely many pairs $(m, f)$ with positiveforcing density. Weber asked if there is a pair of positive forcing density for$r\geq 3$ apart from the trivial ones $(m, 0)$ and $(m, \binom{m}{r})$.Answering her question, we show that $(6,10)$ is such a pair for $r=3$ andconjecture that it is the unique such pair. Further, we find necessaryconditions for a pair to have positive forcing density, supporting thisconjecture.

Unavoidable order-size pairs in hypergraphs -- positive forcing density