TL;DR
This paper introduces abstract separation systems as a versatile framework for representing and analyzing tree-like and cohesive structures across various fields, providing foundational definitions and duality principles.
Contribution
It offers a concise reference for the fundamental concepts and facts about abstract separation systems, facilitating their application in diverse areas.
Findings
Unified framework for tree-shape and cohesion structures
Duality theorems applicable to graphs, matroids, and complexes
Potential applications in image segmentation and clustering
Abstract
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.
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