发表机构
Central China Normal University; University of Crete; Institute of Computer Science, Foundation for Research and Technology Hellas; San Francisco State University（华中师范大学; 克里特大学; 希腊研究与技术基金会计算机科学研究所; 旧金山州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究非重叠单位立方体并集的弱铺砌，给出Keller定理的弱铺砌类比，并证明特定并集的Fuglede猜想。
AI 中文摘要
我们研究由$\mathbb R^d$中两两非重叠且不一定轴平行的单位立方体的有限并集构成的弱铺砌。我们获得了Keller经典定理的弱铺砌类比，该定理对与单位立方体相关联的任何弱铺砌测度的支撑集给出了结构性限制。这使我们能够推导出对立方体配置的几何限制，这些立方体的并集允许弱铺砌。作为应用，我们证明了$\mathbb R^2$中三个非重叠单位正方形的并集以及任意维度中两个非重叠轴平行单位立方体的并集的Fuglede猜想。
英文摘要
We study weak tiling by finite unions of pairwise non-overlapping unit cubes in $\mathbb R^d$ that are not necessarily axis-parallel. We obtain a weak-tiling analogue of Keller's classical theorem, which gives a structural restriction on the support of any weak tiling measure associated with the unit cube. This allows us to derive geometric restrictions on configurations of cubes whose union admits a weak tiling. As an application, we prove Fuglede's conjecture for unions of three non-overlapping unit squares in $\mathbb R^2$ as well as unions of two non-overlapping axis-parallel unit cubes in any dimension.
Comments41 pages, 15 figures
