A combinatorial approach for Keller's conjecture

DOI10.1007/BF01946848zbMath0718.52017OpenAlexW2044009042WikidataQ56699786 ScholiaQ56699786MaRDI QIDQ2639344

Keresztély Corrádi, Sándor Szabó

Publication date: 1990

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01946848

zbMATH Keywords

cubeKeller's conjecturelattice tilingEuclidean \(n\)-spacefactorization of finite abelian group

Mathematics Subject Classification ID

Finite abelian groups (20K01) Lattice packing and covering (number-theoretic aspects) (11H31) Combinatorial aspects of tessellation and tiling problems (05B45) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (20)

Cube-tilings of \(\mathbb{R}^ n\) and nonlinear codes ⋮ Towards resolving Keller's cube tiling conjecture in dimension seven ⋮ Cube packings, second moment and holes ⋮ Keller’s cube-tiling conjecture is false in high dimensions ⋮ Partitions and balanced matchings of an \(n\)-dimensional cube ⋮ On the structure of cube tiling codes ⋮ 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 ⋮ Unnamed Item ⋮ On Keller's conjecture in dimension seven ⋮ New results on torus cube packings and tilings ⋮ What is known about unit cubes ⋮ Extended Keller graph and its properties ⋮ The structure of cube tilings under symmetry conditions ⋮ The resolution of Keller's conjecture ⋮ On Importance of a Special Sorting in the Maximum-Weight Clique Algorithm Based on Colour Classes ⋮ The resolution of Keller's conjecture ⋮ Test case generators and computational results for the maximum clique problem ⋮ The maximum clique problem

Cites Work

• A reduction of Keller's conjecture
• Über lückenlose Ausfüllung des \(n\)-dimensionalen Raumes durch kongruente Würfel
• Algebraic Tiling

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