Polyboxes, cube tilings and rigidity

DOI10.1007/s00454-007-9005-2zbMath1147.52009arXivmath/0609132OpenAlexW2005368674MaRDI QIDQ946683

Andrzej P. Kisielewicz, Krzysztof Przeslawski

Publication date: 24 September 2008

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609132

zbMATH Keywords

boxrigidityindexgenomebinary codeadditive mappingwordcube tilingdichotomous boxespolybox

Mathematics Subject Classification ID

Rigidity and flexibility of structures (aspects of discrete geometry) (52C25) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (13)

Towards resolving Keller's cube tiling conjecture in dimension seven ⋮ Brick partition problems in three dimensions ⋮ New bounds on the maximum number of neighborly boxes in \(\mathbb{R}^d\) ⋮ 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 ⋮ Irreducible subcube partitions ⋮ Rigidity and the chessboard theorem for cube packings ⋮ On the Number of Neighbors in Normal Tiling ⋮ Rigid polyboxes and Keller's conjecture ⋮ On Keller's conjecture in dimension seven ⋮ Partition problems in high dimensional boxes ⋮ The structure of cube tilings under symmetry conditions

Cites Work

• Unnamed Item
• Rigidity and the chessboard theorem for cube packings
• Minimal partitions of a box into boxes
• Cube-tilings of \(\mathbb{R}^ n\) and nonlinear codes
• Finite algebras of finite complexity
• On partitions of discrete boxes
• A cube tiling of dimension eight with no facesharing
• Über lückenlose Ausfüllung des \(n\)-dimensionalen Raumes durch kongruente Würfel
• Über lückenlose Ausfüllung des \(n\)-dimensionalen Raumes durch kongruente Würfel. II
• Keller’s cube-tiling conjecture is false in high dimensions

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