Coordination sequences and layer-by-layer growth of periodic structures
Coordination sequences and layer-by-layer growth of periodic structures
复制标题
周期结构的配位序列和逐层生长
DOI：
10.1515/zkri-2018-2144
复制
发表时间：
2018
期刊：
影响因子：
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通讯作者：
A. Maleev
中科院分区：
文献类型：
--
作者：
A. Shutov;A. Maleev
摘要提出了一种求解周期结构协调序列问题的新方法。它是基于逐层生长的概念和对周期图中测地线的研究。我们表示协调数的总和，所谓的部门协调数所产生的增长多边形的图。在每个扇区中，我们得到了测地链的标准形，并将扇区坐标数的计算归结为求解线性丢番图方程。以2-齐次kra图为例说明了该方法。我们得到三种不同的描述协调序列：显式公式，生成函数和经常性关系。
Abstract A new approach to the problem of coordination sequences of periodic structures is proposed. It is based on the concept of layer-by-layer growth and on the study of geodesics in periodic graphs. We represent coordination numbers as sums of so called sector coordination numbers arising from the growth polygon of the graph. In each sector we obtain a canonical form of the geodesic chains and reduce the calculation of the sector coordination numbers to solution of the linear Diophantine equations. The approach is illustrated by the example of the 2-homogeneous kra graph. We obtain three alternative descriptions of the coordination sequences: explicit formulas, generating functions and recurrent relations.