机构地区: 浙江万里学院计算机与信息学院数学研究所
出 处: 《数学物理学报(A辑)》 2009年第5期1350-1354,共5页
摘 要: 该文借助Tiling的拓扑图和边邻居图,给出了正规Tiling中两个Tiles拥有相同的邻居系的一个充分必要条件,并利用此条件证明了正规Tiling中不可能存在三个不同的Tiles具有相同的邻居系,从而在一定程度上回答了Gr_(u|¨)nbaum的一个公开问题. In this paper,by using the topological graphs and the edge-neighbor graphs of tiling,we give a sufficient and necessary condition of two tiles of normal tiling having a same collection of neighborhoods.And it is proved that there exist impossibly three tiles with a same collection of neighborhoods in every normal tiling via the condition.Therefore,an open problem of Griinbaum is solved in some sense.