On the structure of cube tilings and unextendible systems of cubes in low dimensions
type: Item
instance of: scholarly article
title: On the structure of cube tilings and unextendible systems of cubes in low dimensions
zbMATH Open document ID: 1241.52009
author: Magdalena Łysakowska
author: Krzysztof Przesławski
published in: European Journal of Combinatorics
publication date: 2011-11-29T00:00:00Z
review text: In the paper under review, cube tilings where each tile is a translate of the unit cube are studied. This topic is related to Keller's conjecture that in any cube tiling there are two cubes which share a hyperface. For the 3-dimensional space the authors prove that any cube tiling either is layered or has the structure as they describe. Also they classify the so-called unextendible systems of cubes in \(\mathbb{R}^3\), which can be applied in quantum information theory. For the 4-dimensional space it is proved that each cylinder of a cube tiling contains a column, and it is shown by an example that the latter result does not hold in \(\mathbb{R}^5\).
reviewed by: Elizaveta Zamorzaeva
Mathematics Subject Classification ID: 52C22
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 5982486
zbMATH Keywords: cube tilings
zbMATH Keywords: layered structure
zbMATH Keywords: cube packings
Wikidata QID: Q56699792
describes a project that uses: QETLAB
MaRDI profile type: Publication
full work available at URL: j.ejc.2011.07.003
OpenAlex ID: W2058589564
cites work: Unextendible product bases
cites work: A combinatorial approach for Keller's conjecture
cites work: Unextendible product bases, uncompletable product bases and bound entanglement
cites work: Combinatorial cube packings in the cube and the torus
cites work: Cube packings, second moment and holes
cites work: Q4222329
cites work: Orthonormal bases of exponentials for the \(n\)-cube
cites work: Keller’s cube-tiling conjecture is false in high dimensions
cites work: Keller's conjecture on the existence of columns in cube tilings of \(\mathbb R^n\)
cites work: A cube tiling of dimension eight with no facesharing
cites work: Topics in factorization of Abelian groups.
DOI: 10.1016/J.EJC.2011.07.003
description: scientific article; zbMATH DE number 5982486