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arXiv · 2508.01196

Extensions of integral orthoregular sets and icubes

Márton Erdélyi·Péter Maga·Gergely Zábrádi
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Abstract

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 $4$.

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Márton Erdélyi, Péter Maga, Gergely Zábrádi. 2025-08-02. Extensions of integral orthoregular sets and icubes. https://arxiv.org/abs/2508.01196

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