Periodicity of tiles in finite abelian groups

发布时间：2024-10-22 作者：浏览次数：

Speaker:	张韬	DateTime:	2024-10-24 14:30-16:30
Brief Introduction to Speaker: 教授，西安电子科技大学		Place:	6号楼二楼报告厅
Abstract:In this talk, we introduce the concept of a periodic tiling group, which is defined as a group where any non-periodic set that tiles the finite abelian group by translation has a periodic tiling complement. This extends the scope of good groups. We establish the implication ``Tile implies Spectral" for such groups. Additionally, we characterize the structures of tiles in periodic tiling groups. This ensure us to show that if an elementary group has periodic tiling property, then a tile must be a complete set of representatives of the cosets of some subgroup.