Cut-and-project quasicrystals, lattices and dense forests
Cut-and-project quasicrystals, lattices and dense forests
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切割投影准晶体、晶格和茂密的森林
DOI：
10.1112/jlms.12534
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Adiceam F
中科院分区：
文献类型：
--
作者：
Adiceam F
稠密森林是欧氏空间的离散子集，它们一致地接近所有足够长的线段。茂密森林的密度是用可见度函数来衡量的。我们表明，切割和投影准晶从来没有稠密的森林，但他们的有限工会可能是一致离散的稠密森林。另一方面，我们表明，有限工会的格通常是茂密的森林，并给出了他们的可见性功能，这是接近最佳的约束。我们还构造了一个明确的有限联盟的格，这是一个一致离散的稠密森林，其可见性明确的限制。
Dense forests are discrete subsets of Euclidean space which are uniformly close to all sufficiently long line segments. The degree of density of a dense forest is measured by its visibility function. We show that cut‐and‐project quasicrystals are never dense forests, but their finite unions could be uniformly discrete dense forests. On the other hand, we show that finite unions of lattices typically are dense forests, and give a bound on their visibility function, which is close to optimal. We also construct an explicit finite union of lattices which is a uniformly discrete dense forest with an explicit bound on its visibility.