正规Tiling的邻居系

数学物理学报 ›› 2009, Vol. 29 ›› Issue (5): 1350-1354.

正规Tiling的邻居系

1.浙江万里学院数学研究所浙江宁波 315101|2.中山大学教学与计算科学学院\quad 广州 510275|3.中山大学岭南学院 |广州 510275

收稿日期:2007-08-15 修回日期:2008-09-02 出版日期:2009-10-25 发布日期:2009-10-25
基金资助:
浙江省教育厅科研项目资助

Collection of Neighborhoods of Normal Tiling

1.Institute of Mathematics, Zhejiang Wanli University, Zhejiang Ningbo 315100|2.School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275|3.Lingnan College, Sun Yat-Sen University, |Guangzhou 510275

Received:2007-08-15 Revised:2008-09-02 Online:2009-10-25 Published:2009-10-25
Supported by:
浙江省教育厅科研项目资助

摘要/Abstract

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Grünbaum 的一个公开问题.

关键词: 正规Tiling, 边邻居, 拓扑图, 邻居系

Abstract:

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 Grünbaum is solved in some sense.

中图分类号:

05B45

李浩, 罗俊, 周作领. 正规Tiling的邻居系[J]. 数学物理学报, 2009, 29(5): 1350-1354.

LI Hao, LUO Jun, ZHOU Zuo-Ling. Collection of Neighborhoods of Normal Tiling[J]. Acta mathematica scientia,Series A, 2009, 29(5): 1350-1354.