Keller's conjecture on the existence of columns in cube tilings of \(\mathbb R^n\) (Q2882936)
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scientific article; zbMATH DE number 6033008
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Keller's conjecture on the existence of columns in cube tilings of \(\mathbb R^n\) |
scientific article; zbMATH DE number 6033008 |
Statements
11 May 2012
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cube tiling
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column
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Keller partition
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Keller's conjecture
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Keller's conjecture on the existence of columns in cube tilings of \(\mathbb R^n\) (English)
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The paper is devoted to cube tilings of the \(n\)-dimensional Euclidean space, where each tile is a translate of the unit cube. It deals with the stronger (and original) form of Keller's conjecture that each cube tiling of \(\mathbb{R}^{n}\) contains a column.NEWLINENEWLINEIn the paper it is shown that for \(n \leq 6\) each cube tiling of \(\mathbb{R}^{n}\) contains a column. All theorems are given with detailed proofs.NEWLINENEWLINEThe authors also introduce a new concept which they call Keller partition and generalize the result in this sense.
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