Approximate counting of regular hypergraphs

• We approximately count regular and uniform hypergraphs.
• Proofs are based on a configuration model.
• We extend to hypergraphs a switching technique of McKay and Wormald.

In this paper we asymptotically count d-regular k-uniform hypergraphs on n vertices, provided k   is fixed and d=d(n)=o(n1/2)d=d(n)=o(n1/2). In doing so, we extend to hypergraphs a switching technique of McKay and Wormald.