Partitioning the hypercube into smaller hypercubes
Denote by Qd the d-dimensional hypercube. 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 larger than the number of perfect matchings of Qd by an exponential factor in the number of vertices, and not by a larger factor. We also describe and address several new (and old) related questions.
Authors
- Vladimir N. Potapov (ORCID: https://orcid.org/0000-0001-9461-2064)
- Noga Alon (ORCID: https://orcid.org/0000-0003-1332-4883)
- József Balogh (ORCID: https://orcid.org/0000-0003-4423-5859)
Institutions
- University of Illinois Urbana-Champaign (US)
- Tel Aviv University (IL)
- Princeton University (US)
Publication Details
- Journal
- Illinois Journal of Mathematics
- Published
- 2025-04-01
- DOI
- https://doi.org/10.1215/00192082-11792788
- Citations
- 1
- Primary Topic
- Interconnection Networks and Systems
- Type
- article
- Field-Weighted Citation Impact
- 1.49