抽象分离系统
Abstract Separation Systems
摘要：
抽象分离系统提供了一个简单的一般框架，在这个框架中，许多组合结构的树形性和高内聚性都可以表达出来，并且证明了它们的对偶性。应用范围从图、拟阵或CW-复形中的缠结型对偶和树结构定理到潜在的图像分割和聚类分析。本文的目的是作为一个简明的共同参考的基本定义和事实抽象分离系统在这些和任何未来的论文使用这个框架。
英文摘要：
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree structure theorems in graphs, matroids or CW-complexes to, potentially, image segmentation and cluster analysis. This paper is intended as a concise common reference for the basic definitions and facts about abstract separation systems in these and any future papers using this framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
