A formula for the HOMFLY polynomial of rational links
Sergei Duzhin, Mikhail Shkolnikov
TL;DR
This paper presents an explicit formula for computing the HOMFLY polynomial of rational links using a continued fraction representation of the defining rational number.
Contribution
It introduces a novel explicit formula linking rational links' HOMFLY polynomial to their continued fraction representation.
Findings
Provides a direct computational method for HOMFLY polynomials of rational links.
Simplifies the calculation process for these polynomials.
Enhances understanding of the relationship between rational links and their polynomial invariants.
Abstract
We give an explicit formula for the HOMFLY polynomial of a rational link (in particular, a knot) in terms of a special continued fraction for the rational number that defines the given link.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · semigroups and automata theory