Extensions of integral orthoregular sets and icubes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913971935641600 |
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| author | Erdélyi, Márton Maga, Péter Zábrádi, Gergely |
| author_facet | Erdélyi, Márton Maga, Péter Zábrádi, Gergely |
| contents | In this paper, we study the question when a (rational or Gaussian) integral vector can be extended to an integral orthogonal basis consisting of vectors of equal length. We also study when a set of integral vectors has such an extension. Some necessary conditions are given which are proven to be sufficient in dimensions $3$ and $4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions of integral orthoregular sets and icubes Erdélyi, Márton Maga, Péter Zábrádi, Gergely Number Theory 11E25, 11R52, 52C07 In this paper, we study the question when a (rational or Gaussian) integral vector can be extended to an integral orthogonal basis consisting of vectors of equal length. We also study when a set of integral vectors has such an extension. Some necessary conditions are given which are proven to be sufficient in dimensions $3$ and $4$. |
| title | Extensions of integral orthoregular sets and icubes |
| topic | Number Theory 11E25, 11R52, 52C07 |
| url | https://arxiv.org/abs/2508.01196 |