Let Q_n be the n-dimensional Hamming cube and N = 2ⁿ. We prove that the number of maximal independent sets in Q_n is asymptotically

$$2n{2^{N/4}},$$

as was conjectured by Ilinca and the first author in connection with a question of Duffus, Frankl and Rödl.

The value is a natural lower bound derived from a connection between maximal independent sets and induced matchings. The proof that it is also an upper bound draws on various tools, among them “stability” results for maximal independent set counts and old and new results on isoperimetric behavior in Q_n.

中文翻译：

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汉明立方中的最大独立集数

令Q _n为n维汉明立方且N = 2 ⁿ。我们证明了Q _n中的最大独立集的数量是渐近的

$$2n{2^{N/4}},$$

正如 Ilinca 和第一作者就 Duffus、Frankl 和 Rödl 的问题所推测的那样。

该值是从最大独立集和诱导匹配之间的连接得出的自然下限。它也是一个上限的证明利用了各种工具，其中包括最大独立集计数的“稳定性”结果以及Q _n中等周行为的新旧结果。