图覆盖和（Im）基同调：低阶的例子

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2021-06-21 DOI:10.1080/10586458.2021.1926013

Destine Lee, Iris Rosenblum-Sellers, Jakwanul Safin, Anda Tenie

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引用次数: 0

摘要

摘要给定图的有限覆盖，它并不总是由的基元的提升所跨越的情况。在这篇文章中，我们研究了不是这种情况的图，我们在这里给出了具有这种性质的覆盖的最简单的已知非平凡的例子，覆盖度小到128。我们的第一步是将注意力集中在图覆盖的特殊类上，其中甲板群是有限p群。对于这样的覆盖，有一个表示论准则来识别存在具有该性质的覆盖的甲板组。我们提出了一种算法来确定有限p-群是否满足这个准则，该准则只使用群的字符表。最后，我们提供了满足该准则的所有秩和阶<1000的有限p-群的完整普查，所有这些都是新的例子。

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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Graph Coverings and (Im)primitive Homology: Examples of Low Degree

Abstract Given a finite covering of graphs , it is not always the case that is spanned by lifts of primitive elements of . In this article, we study graphs for which this is not the case, and we give here the simplest known nontrivial examples of covers with this property, with covering degree as small as 128. Our first step is focusing our attention on the special class of graph covers where the deck group is a finite p-group. For such covers, there is a representation-theoretic criterion for identifying deck groups for which there exist covers with the property. We present an algorithm for determining if a finite p-group satisfies this criterion that uses only the character table of the group. Finally, we provide a complete census of all finite p-groups of rank and order < 1000 satisfying this criterion, all of which are new examples.

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来源期刊

Experimental Mathematics 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： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.