Partitioning the hypercube into smaller hypercubes

Noga Alon; József Balogh; Vladimir N. Potapov

doi:10.1215/00192082-11792788

Partitioning the hypercube into smaller hypercubes

Noga Alon
, József Balogh
, Vladimir N. Potapov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Abstract Denote by Q_d the d-dimensional hypercube. 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 larger than the number of perfect matchings of Q_d 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.

Original language	English (US)
Pages (from-to)	109-122
Number of pages	14
Journal	Illinois Journal of Mathematics
Volume	69
Issue number	1
DOIs	https://doi.org/10.1215/00192082-11792788
State	Published - Apr 2025

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00192082-11792788

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title = "Partitioning the hypercube into smaller hypercubes",

abstract = "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.",

author = "Noga Alon and J{\'o}zsef Balogh and Potapov, \{Vladimir N.\}",

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AU - Potapov, Vladimir N.

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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

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JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

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Partitioning the hypercube into smaller hypercubes

Abstract

All Science Journal Classification (ASJC) codes

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