德龙集合中的局部群:一个猜想与结果

IF 1.4 4区数学 Q1 MATHEMATICS

Russian Mathematical Surveys Pub Date : 2021-01-01 DOI:10.1070/RM10037

N. Dolbilin, M. Shtogrin

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引用次数: 1

摘要

在对任意Delone集合局部对称概念的一种新方法的框架下，我们得到了不受任何限制的任意Delone集合的新结果。这些结果对晶格和规则系统具有重要意义。提出了一个关于晶体核的猜想，它极大地推广了三维晶格中五重对称不存在的经典定理。证明了下列与几何晶体学基础有关的定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Local groups in Delone sets: a conjecture and results

In the framework of a new approach to the concept of local symmetry in arbitrary Delone sets we obtain new results for such sets without any restrictions. These results have important consequences for lattices and regular systems. A conjecture about the crystal kernel is stated, which generalises significantly the classical theorem on the non-existence of a five-fold symmetry in three-dimensional lattices. The following theorems related to the foundations of geometric crystallography are proved.

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来源期刊

Russian Mathematical Surveys 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Mathematical Surveys is a high-prestige journal covering a wide area of mathematics. The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The survey articles on current trends in mathematics are generally written by leading experts in the field at the request of the Editorial Board.