TL;DR
This paper introduces plumbers' knots, a new geometric knot theory framework, and addresses the challenges of distinguishing and counting these knots at specific complexity levels.
Contribution
It develops a novel type of geometric knot theory called plumbers' knots and provides methods for their enumeration and distinction at fixed complexity.
Findings
Successfully constructed the theory of plumbers' knots.
Solved the problem of distinguishing and enumerating knots at fixed complexity.
Revised the framework with substantial updates and added new theorems.
Abstract
We construct a new type of geometric knot theory, plumbers' knots, and solve the problems of distinguishing and enumerating such knots at a fixed level of complexity. (v2) Minor edits, added theorem 3.18. (v3) Substantial revisions, essentially completely rewritten in places.
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
TopicsConnective tissue disorders research