## Hereditary properties of hypergraphs.(English)Zbl 1219.05104

Summary: A hereditary property $$\mathbf P^{(k)}$$ is a class of $$k$$-graphs closed under isomorphism and taking induced sub-hypergraphs. Let $$\mathbf P^{(k)}_n$$ denote those $$k$$-graphs of $$\mathbf P^{(k)}$$ on vertex set $$\{1,\ldots ,n\}$$. We prove an asymptotic formula for $$\log _2|\mathbf P^{(k)}_n|$$ in terms of a Turán-type function concerning forbidden induced sub-hypergraphs. This result complements several existing theorems for hereditary and monotone graph and hypergraph properties.

### MSC:

 05C65 Hypergraphs 05C75 Structural characterization of families of graphs
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### References:

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