Representations of infinite tree-sets
J. Pascal Gollin, Jay Lilian Kneip

TL;DR
This paper extends the representation theory of finite tree sets to infinite ones, characterizing which can be represented by infinite trees and introducing a topological generalization to encompass all infinite tree sets.
Contribution
It provides a characterization of infinite tree sets representable by infinite trees and introduces a topological framework for representing all infinite tree sets.
Findings
Characterization of tree sets representable by infinite trees.
Introduction of a topological generalization for infinite trees.
Every infinite tree set can be represented by a suitable topological tree-like space.
Abstract
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets. First we characterise those tree sets that can be represented by tree sets arising from infinite trees; these are precisely those tree sets without a chain of order type . Then we introduce and study a topological generalisation of infinite trees which can have limit edges, and show that every infinite tree set can be represented by the tree set admitted by a suitable such tree-like space.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
