On the number of partitions of the hypercube ${\mathbf{Z}}_q^n$ into large subcubes

Yuriy Tarannikov

We prove that the number of partitions of the hypercube ${\mathbf{Z}}_q^n$ into $q^m$ subcubes of dimension $n-m$ each for fixed $q$, $m$ and growing $n$ is asymptotically equal to $n^{…