English

A new description of uniformly spread discrete sets

Metric Geometry 2025-10-14 v1

Abstract

We prove that each discrete set in the Euclidean space that has bounded changes under every translation is a bounded perturbation of a square lattice, i.e., a uniformly spread set in the sense of Laszkovich. In particular, the support of every Fourier quasicrystal with unit masses is uniformly spread.

Keywords

Cite

@article{arxiv.2510.11061,
  title  = {A new description of uniformly spread discrete sets},
  author = {A. Dudko and S. Favorov},
  journal= {arXiv preprint arXiv:2510.11061},
  year   = {2025}
}

Comments

9 pages, 16 references