A relationship between trees and Kelly-Mac Lane graphs
Eugenia Cheng
TL;DR
This paper establishes a precise correspondence between combed trees and Kelly-Mac Lane graphs, showing a one-to-one relationship that characterizes their structural equivalence.
Contribution
It provides a novel, exact description of combed trees using Kelly-Mac Lane graphs, bridging two mathematical frameworks.
Findings
Each combed tree corresponds uniquely to an allowable Kelly-Mac Lane graph.
Any Kelly-Mac Lane graph of a certain shape uniquely defines a combed tree.
The correspondence is bijective, establishing a structural equivalence.
Abstract
We give a precise description of combed trees in terms of Kelly-Mac Lane graphs. We show that any combed tree is uniquely expressed as an allowable Kelly-Mac Lane graph of a certain shape. Conversely, we show that any such Kelly-Mac Lane graph uniquely defines a combed tree.
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.
Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Advanced Graph Theory Research