有限结构中的有限群胚、有限覆盖与对称性
组合数学
2024-01-15 v5 计算机科学中的逻辑
逻辑
摘要
我们提出了一种基于群胚 Cayley 图的约化积来构造有限超图和关系结构的新方法。为此，我们构造了具有大围长的群胚，其 Cayley 图的大围长不仅具有通常意义，而且是相对于一种折扣距离度量而言的；该度量压缩了同一子群胚（陪集）内任意长的边序列，仅统计陪集之间的转移。与此类群胚的约化积具有足够的通用性，适用于各种由局部粘合操作指定并需要全局有限闭包的构造。在此，我们考察了将局部对称性提升为全局自同构的超图覆盖和扩展任务。
引用
@article{arxiv.1404.4599,
title = {Finite Groupoids, Finite Coverings and Symmetries in Finite Structures},
author = {Martin Otto},
journal= {arXiv preprint arXiv:1404.4599},
year = {2024}
}
备注
The construction of finite n-acyclic groupoids in Section 2.4 is flawed and I know of no direct repair: completion turns out to be incompatible with restriction to proper subsets of the generator set, so that the induction towards Proposition 2.22 does not stabilise as claimed. This problem has been overcome in arxiv:1806.08664. Also compare arxiv:1709.00031 and arXiv:2208.03273