On the number of independent sets in uniform, regular, linear hypergraphs

We study the problems of bounding number weak and strong independent sets in r-uniform, d-regular, n-vertex linear hypergraphs with no cross-edges. In case sets, we provide an upper bound that is tight up to first order term for all (fixed) r≥3, d n going infinity. r=3, second term, improving on a result Ordentlich–Roth (2004). The tightness set established by explicit construction 3-uniform, cross-edge free, hypergraph vertices which could be interest other contexts. leave open general case(s) some conjectures. Our proofs use occupancy method introduced Davies, Jenssen, Perkins, Roberts (2017).