TY - JOUR
T1 - Partitioning the hypercube into smaller hypercubes
AU - Alon, Noga
AU - Balogh, József
AU - Potapov, Vladimir N.
N1 - Publisher Copyright:
© 2025 by the University of Illinois Urbana-Champaign.
PY - 2025/4
Y1 - 2025/4
N2 - Abstract 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.
AB - Abstract 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.
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U2 - 10.1215/00192082-11792788
DO - 10.1215/00192082-11792788
M3 - Article
AN - SCOPUS:105005577492
SN - 0019-2082
VL - 69
SP - 109
EP - 122
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 1
ER -