关于保持对称的局部运算和保持地图的多面体

IF 0.6 3区 数学 Q3 MATHEMATICS
G. Brinkmann, Heidi Van den Camp
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引用次数: 1

摘要

我们证明了保留所有对称的局部运算,如对偶、截断、中间或连接,以及只保证保留所有保向对称的局部运算,如陀螺或斜面,可以保留简单映射的多面体。这推广了Mohar证明对偶运算的结果。我们基于这些操作的抽象表征给出了证明,证明了这些操作是定义良好的,并证明了这些操作与Delaney-Dress符号之间的密切联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On local operations that preserve symmetries and on preserving polyhedrality of maps
We prove that local operations that preserve all symmetries, as e.g. dual, truncation, medial, or join, as well as local operations that are only guaranteed to preserve all orientation-preserving symmetries, as e.g. gyro or snub, preserve the polyhedrality of simple maps. This generalizes a result by Mohar proving this for the operation dual. We give the proof based on an abstract characterization of these operations, prove that the operations are well defined, and also demonstrate the close connection between these operations and Delaney-Dress symbols.
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来源期刊
Ars Mathematica Contemporanea
Ars Mathematica Contemporanea MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.70
自引率
0.00%
发文量
45
审稿时长
>12 weeks
期刊介绍: Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.
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