Towards resolving Keller's cube tiling conjecture in dimension seven

DOI10.1515/advgeom-2022-0001zbMath1486.52053arXiv1701.07155OpenAlexW2580453757WikidataQ113741381 ScholiaQ113741381MaRDI QIDQ2127866

Andrzej P. Kisielewicz

Publication date: 21 April 2022

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.07155

zbMATH Keywords

boxrigiditycube tilingKeller's conjectureKeller graph

Mathematics Subject Classification ID

Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Combinatorial codes (94B25) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (3)

Gluing and cutting cube tiling codes in dimension six ⋮ The resolution of Keller's conjecture ⋮ The resolution of Keller's conjecture

Cites Work

• On Keller's conjecture in dimension seven
• Minimal partitions of a box into boxes
• Cube packings, second moment and holes
• Polyboxes, cube tilings and rigidity
• Cube tiling and covering a complete graph
• Cube-tilings of \(\mathbb{R}^ n\) and nonlinear codes
• Rigid polyboxes and Keller's conjecture
• A reduction of Keller's conjecture
• A cube tiling of dimension eight with no facesharing
• A combinatorial approach for Keller's conjecture
• Über lückenlose Ausfüllung des \(n\)-dimensionalen Raumes durch kongruente Würfel
• Keller’s conjecture on the existence of columns in cube tilings of ℝn
• Keller’s cube-tiling conjecture is false in high dimensions
• The resolution of Keller's conjecture
• Unnamed Item
• Unnamed Item

This page was built for publication: Towards resolving Keller's cube tiling conjecture in dimension seven