Keller properties for integer tiling
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916213819441152 |
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| author | Bruce, Benjamin Laba, Izabella |
| author_facet | Bruce, Benjamin Laba, Izabella |
| contents | Keller's conjecture on cube tilings asserted that, in any tiling of $\mathbb{R}^d$ by unit cubes, there must exist two cubes that share a $(d-1)$-dimensional face. This is now known to be true in dimensions $d\leq 7$ and false for $d\geq 8$. In this article, we investigate analogues of Keller's conjecture for integer tilings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12518 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Keller properties for integer tiling Bruce, Benjamin Laba, Izabella Combinatorics 05B45, 52C22 Keller's conjecture on cube tilings asserted that, in any tiling of $\mathbb{R}^d$ by unit cubes, there must exist two cubes that share a $(d-1)$-dimensional face. This is now known to be true in dimensions $d\leq 7$ and false for $d\geq 8$. In this article, we investigate analogues of Keller's conjecture for integer tilings. |
| title | Keller properties for integer tiling |
| topic | Combinatorics 05B45, 52C22 |
| url | https://arxiv.org/abs/2404.12518 |