Delta Diagrams
Slavik Jablan, Louis H. Kauffman, Pedro Lopes
TL;DR
This paper introduces Delta Diagrams, a new class of knot/link diagrams with regions of 3 to 5 sides, proves their universal existence, and develops related combinatorial invariants.
Contribution
It establishes that every knot or link can be represented by a Delta Diagram and introduces new combinatorial invariants based on this concept.
Findings
Every knot or link admits a Delta Diagram.
Defined and estimated new combinatorial link invariants.
Provided structural insights into knot diagram representations.
Abstract
We call a Delta Diagram any diagram of a knot or link whose regions (including the unbounded one) have 3, 4, or 5 sides. We prove that any knot or link admits a delta diagram. We define and estimate combinatorial link invariants stemming from this definition.
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 · Advanced Combinatorial Mathematics · Algebraic Geometry and Number Theory