Independent Sets in Regular Hypergraphs and Multidimensional Runlength-Limited Constraints

Let G be a t uniform s regular linear hypergraph with r vertices It is shown that the number of independent sets I G in G satis es log I G r t O log ts s This leads to an improvement of a previous bound by Alon obtained for t i e for regular ordinary graphs It is also shown that for the Hamming graph H n q with vertices consisting of all n tuples over an alphabet of size q and edges connecting pairs of vertices with Hamming distance log I H n q q q O log qn qn The latter result is then applied to show that the Shannon capacity of the n dimensional d runlength limited RLL constraint converges to d as n goes to in nity Abbreviated Title Independent Sets in Regular Hypergraphs