Speaker: Jozsef Balogh (UIUC)
Title: Partitioning the hypercube into smaller hypercubes
Abstract: Denote by Q_d the d-dimensional hypercube. Addressing a recent question, we estimate the number of ways the vertex set of Q_d 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 Q_d. We also describe several new (and old) questions. It is joint work with Noga Alon and Vladimir N. Potapov.
