On Keller's conjecture in dimension seven

zbMath1305.05042arXiv1401.4689MaRDI QIDQ490321

Magdalena Łysakowska, Andrzej P. Kisielewicz

Publication date: 22 January 2015

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.4689

zbMATH Keywords

boxrigiditycube tilingKeller's conjecture

Mathematics Subject Classification ID

Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items

Towards resolving Keller's cube tiling conjecture in dimension seven ⋮ Partitions and balanced matchings of an \(n\)-dimensional cube ⋮ On the structure of cube tiling codes ⋮ Gluing and cutting cube tiling codes in dimension six ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Extended Keller graph and its properties ⋮ The resolution of Keller's conjecture ⋮ The resolution of Keller's conjecture

Cites Work

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• Partitions and balanced matchings of an \(n\)-dimensional cube
• On the structure of cube tilings and unextendible systems of cubes in low dimensions
• Minimal partitions of a box into boxes
• 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
• On the structure of cube tilings of \(\mathbb R^3\) and \(\mathbb R^4\)
• A reduction of Keller's conjecture
• On partitions of discrete boxes
• 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
• Über einfache und mehrfache Bedeckung des \(n\)-dimensionalen Raumes mit einem Würfelgitter
• Keller’s conjecture on the existence of columns in cube tilings of ℝn
• Keller’s cube-tiling conjecture is false in high dimensions