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A property of uniform hypergraphs is hereditary if every induced subhypergraph of a hypergraph with that property also has the property. It is understood to be invariant under relabelling the vertex set. For example, excluding a specified induced hypergraph is hereditary. This permits counting restrictions to smaller vertex sets using the same counting function.

A subhypergraph restricts the vertex set of a hypergraph and retains some of its edges contained in that vertex set. Retaining every such edge gives an induced subhypergraph.