Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.03212 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908764754411520 |
|---|---|
| author | Cremona, J. E. Koymans, P. |
| author_facet | Cremona, J. E. Koymans, P. |
| contents | We consider the problem of covering $\mathbb{Z}^2$ with a finite number of sublattices of finite index, satisfying a simple minimality or non-degeneracy condition. We show how this problem may be viewed as a projective (or homogeneous) version of the well-known problem of covering systems of congruences. We give a construction of minimal coverings which produces many, but not all, minimal coverings, and determine all minimal coverings with at most $8$ sublattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03212 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lattice coverings and homogeneous covering congruences Cremona, J. E. Koymans, P. Number Theory We consider the problem of covering $\mathbb{Z}^2$ with a finite number of sublattices of finite index, satisfying a simple minimality or non-degeneracy condition. We show how this problem may be viewed as a projective (or homogeneous) version of the well-known problem of covering systems of congruences. We give a construction of minimal coverings which produces many, but not all, minimal coverings, and determine all minimal coverings with at most $8$ sublattices. |
| title | Lattice coverings and homogeneous covering congruences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.03212 |