Bogdanov, I.I., Grigoryan, O. and Zhukovskii, M. orcid.org/0000-0001-8763-9533 (2026) Covering three-tori with cubes. Australasian Journal of Combinatorics, 95 (Part 1). pp. 33-48. ISSN: 1034-4942
Abstract
Let (ε) be the minimum number of cubes of side ε needed to cover the unit three-torus [R/Z]3. We prove new lower and upper bounds for (ε) and find the exact value for all ε ≥ 7 15 and all ε ∈ 1 r+1/(r2+r+1) , 1 r−1/(r2−1) for any integer r ≥ 3.
Metadata
| Item Type: | Article |
|---|---|
| Authors/Creators: |
|
| Copyright, Publisher and Additional Information: | © 2026 The author(s). Released under the CC BY 4.0 International License - https://creativecommons.org/licenses/by/4.0/ |
| Dates: |
|
| Institution: | The University of Sheffield |
| Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
| Date Deposited: | 24 Apr 2026 10:07 |
| Last Modified: | 15 May 2026 15:06 |
| Published Version: | https://ajc.maths.uq.edu.au/?page=get_volumes&volu... |
| Status: | Published |
| Publisher: | The University of Queensland |
| Refereed: | Yes |
| Related URLs: | |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:240449 |

CORE (COnnecting REpositories)
CORE (COnnecting REpositories)