The Number of Maximal Independent Sets in the Hamming Cube

Let Qn be the n-dimensional Hamming cube and N = 2n. We prove that number of maximal independent sets in is asymptotically $$2n{2^{N/4}},$$ as was conjectured by Ilinca first author connection with a question Duffus, Frankl Rödl. The value natural lower bound derived from between induced matchings. proof it also an upper draws on various tools, among them “stability” results for set counts old new isoperimetric behavior Qn.