Maximal independent sets in bipartite graphs obtained from Boolean lattices (Q607358)

Motivated by the problem of finding the number of maximal antichains in the Boolean lattice of all subsets of a set the authors study \(mis(n,k)\), the number of maximal independent sets in the bipartite graph whose parts consists of all \(k\)-subsets, and all \(k+1\)-subsets of an \(n\)-set, respectively, the adjecency given by the proper containment. In the paper the asymptotic value of \(\log_{2}mis(n,k)\) is found for the case \(k=o(n)\). If \(k\) is a constant proportion of \(n\), the upper and the lower bound on \(\log_{2}mis(n,k)\) given in the paper differ by a factor of \(1.3563\).