Partitioning the hypercube into smaller hypercubes
Abstract
Denote by Qd the d-dimensional hypercube. Addressing a recent question we estimate the number of ways the vertex set of Qd can be partitioned into vertex disjoint smaller cubes. Among other results, we prove that the asymptotic order of this function is not much larger than the number of perfect matchings of Qd. We also describe several new (and old) questions.
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