Decomposing cubes into smaller cubes
type: Item
instance of: scholarly article
title: Decomposing cubes into smaller cubes
zbMATH Open document ID: 1394.51007
author: Peter Connor
author: Phillip Marmorino
published in: Journal of Geometry
publication date: 2018-05-30T00:00:00Z
review text: Given a positive integer \(n\), let us define \(D(n)\) as the set of integers \(k\) such that an \(n\)-dimensional cube can be decomposed into \(k\) smaller \(n\)-dimensional cubes. In addition, let \(c(n)\) be the smallest integer (it is known to exist, for example \(c(2)=6\)) such that \(k\geq c(n) \Rightarrow k\in D(n)\). This paper presents some results dealing with \(c(n)\). In particular, it is proven that \(c(n)\geq 2^{n+1}+1\) for every \(n\geq 3\) and also that \(c(n)\leq e^2n^n\) if \(n+1\) is not a prime and \(c(n)\leq 1.8n^{n+1}\) if \(n+1\) is a prime.
Mathematics Subject Classification ID: 51M04
Mathematics Subject Classification ID: 11D45
Mathematics Subject Classification ID: 11H31
zbMATH DE Number: 6876764
zbMATH Keywords: tiling
zbMATH Keywords: partitions
zbMATH Keywords: hypercubes
zbMATH Keywords: cube
zbMATH Keywords: decomposition
reviewed by: Antonio M. Oller Marcén
MaRDI profile type: Publication
full work available at URL: s00022-018-0424-4
OpenAlex ID: W2791726212
cites work: On a Problem of Partitions
cites work: Dissecting \(d\)-cubes into smaller \(d\)-cubes
cites work: Decomposition of a Cube into Smaller Cubes
DOI: 10.1007/S00022-018-0424-4
description: scientific article; zbMATH DE number 6876764