On Counting Independent Sets in Regular Hypergraphs

Balogh, Bollobás and Narayanan conjectured that among all finite simple $r$-uniform $d$-regular hypergraphs, the number of weak independent sets is maximized by a natural quasi-bipartite construction $H_{r,d}$. We give three types of evidence for this conjecture. For every fixed $r$, we prove the co