The Simultaneous Lattice Packing-Covering Constant of Octahedra
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915492666540032 |
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| author | Li, Yiming Zong, Chuanming |
| author_facet | Li, Yiming Zong, Chuanming |
| contents | This paper proves that the simultaneous lattice packing-covering constant of an octahedron is $7/6$. In other words, $7/6$ is the smallest positive number $r$ such that for every octahedron $O$ centered at the origin there is a lattice $Λ$ such that $O+Λ$ is a packing in $\mathbb{E}^3$ and $rO+Λ$ is a covering of $\mathbb{E}^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18643 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Simultaneous Lattice Packing-Covering Constant of Octahedra Li, Yiming Zong, Chuanming Combinatorics 52C17, 11H31 This paper proves that the simultaneous lattice packing-covering constant of an octahedron is $7/6$. In other words, $7/6$ is the smallest positive number $r$ such that for every octahedron $O$ centered at the origin there is a lattice $Λ$ such that $O+Λ$ is a packing in $\mathbb{E}^3$ and $rO+Λ$ is a covering of $\mathbb{E}^3$. |
| title | The Simultaneous Lattice Packing-Covering Constant of Octahedra |
| topic | Combinatorics 52C17, 11H31 |
| url | https://arxiv.org/abs/2310.18643 |