On permutation polytopes: notions of equivalence
On permutation polytopes: notions of equivalence
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关于排列多胞形：等价的概念
DOI：
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发表时间：
2013
期刊：
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通讯作者：
Matthias C. Grüninger
中科院分区：
文献类型：
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作者：
B. Baumeister;Matthias C. Grüninger
通过给群分配一个置换多面体，我们得到了新的有趣的多面体。为了有效地使用这种构造方法，需要了解哪些基团导致仿射等效多面体。因此，引入了有效等价的概念（Baumeister et al. in Adv Math 222(2): 431-452, 2009）。在这篇笔记中，我们澄清了有效等价的概念，并对其进行了几何表征。此外，我们给出的例子表明，有效等价置换群并不对应于仿射等价多面体。我们还将表征应用到实例中。在我们的方法中，我们为在置换多面体研究中使用表示理论方法提供了一个框架。
By assigning a permutation polytope to a group, we produce new interesting polytopes. For the effective use of this construction method, it is desirable to understand which groups are leading to affine equivalent polytopes. Therefore, the notion of effective equivalence has been introduced (Baumeister et al. in Adv Math 222(2):431–452, 2009). In this note, we clarify the notion of effective equivalence and characterize it geometrically. Moreover, we present examples showing that the effective equivalent permutation groups do not correspond to affinely equivalent polytopes. We also apply the characterization to the examples. In our approach we provide a framework for the use of representation theoretic methods in the study of permutation polytopes.