The Number of Maximal Independent Sets in the Hamming Cube

Let Qn be the n-dimensional Hamming cube and N = 2n. We prove that the number of maximal independent sets in Qn is asymptotically 2n2N/4,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2n{2^{N/4}},$$\end{document} as was conjectured by Ilinca and the first author in connection with a question of Duffus, Frankl and Rödl.