A formula for the Dubrovnik polynomial of rational knots
Carmen Caprau, Katherine Urabe
TL;DR
This paper presents a formula for computing the Dubrovnik polynomial of rational knots directly from their braid-form diagram entries, facilitating easier calculations with computer algebra systems.
Contribution
It introduces a novel explicit formula for the Dubrovnik polynomial of rational knots based on their braid diagram data.
Findings
The formula simplifies polynomial calculations for rational knots.
It enables efficient computer algebra system implementation.
Provides a new tool for knot polynomial analysis.
Abstract
We provide a formula for the Dubrovnik polynomial of a rational knot in terms of the entries of the tuple associated with a braid-form diagram of the knot. Our calculations can be easily carried out using a computer algebra system.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology