Hypergraph complement ($E(\overline{H})=\left(\genfrac{}{}{0ex}{}{V}{\ell }\right)\setminus E(H)$)

The complement of an $\ell$-uniform hypergraph on $V$ has all $\ell$-subsets of $V$ that are not hyperedges of the original hypergraph. An edge in every $r$-set of one hypergraph is equivalent to the absence of a complete $\ell$-uniform $r$-vertex hypergraph in its complement.