Cube packings, second moment and holes

DOI10.1016/j.ejc.2006.01.008zbMath1111.52017arXivmath/0509100OpenAlexW2005258255WikidataQ56699787 ScholiaQ56699787MaRDI QIDQ872026

Mathieu Dutour Sikirić, Alexei Poyarkov, Yoshiaki Itoh

Publication date: 27 March 2007

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509100

Mathematics Subject Classification ID

Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Combinatorial aspects of packing and covering (05B40) Sub-Riemannian geometry (53C17)

Related Items (11)

Towards resolving Keller's cube tiling conjecture in dimension seven ⋮ Enumerating cube tilings ⋮ On the structure of cube tiling codes ⋮ Gluing and cutting cube tiling codes in dimension six ⋮ Rigidity and the chessboard theorem for cube packings ⋮ Rigid polyboxes and Keller's conjecture ⋮ On the structure of cube tilings and unextendible systems of cubes in low dimensions ⋮ On hypercube packings, blocking sets and a covering problem ⋮ New results on torus cube packings and tilings ⋮ Combinatorial cube packings in the cube and the torus ⋮ The structure of cube tilings under symmetry conditions

Uses Software

• GAP

Cites Work

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• Cube-tilings of \(\mathbb{R}^ n\) and nonlinear codes
• Orthonormal bases of exponentials for the \(n\)-cube
• A reduction of Keller's conjecture
• A cube tiling of dimension eight with no facesharing
• A combinatorial approach for Keller's conjecture
• Keller’s cube-tiling conjecture is false in high dimensions
• What is known about unit cubes
• Monte Carlo strategies in scientific computing

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