Abstract Separation Systems

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.

This is Section 2, considerably expanded, of the predecessor version 4 of this thread. Sections 3-4 on abstract duality have migrated to [8], Section 5 on applications has moved to [9]

Cited by in corpus (5)

• Tangle-tree duality in abstract separation systems
• Tangle-tree duality: in graphs, matroids and beyond
• Trees of tangles in abstract separation systems
• Trees of tangles in infinite separation systems
• Efficiently distinguishing all tangles in locally finite graphs