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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.03212 |
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Table of 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.