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This is a Quantitative Study study.

October 2, 2025Open Access

A condition on the Jones polynomial for a family of positive links

Key Points

The maximum degree of the Jones polynomial for certain positive links is bounded.
Specifically, this bound applies to positive links with a second Jones coefficient of ±1.
This builds upon previous results concerning positive fibered links and their properties.
These findings enhance understanding of the relations between link characteristics and polynomial properties.

Abstract

We provide a bound on the maximum degree of the Jones polynomial of any positive link with second Jones coefficient equal to 1. This builds on the result of our previous work, in which we found such a bound for positive fibered links.

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Cite This Study

Lizzie Buchanan (Fri,) studied this question.

synapsesocial.com/papers/68de5da783cbc991d0a20ab6 https://doi.org/https://doi.org/10.48550/arxiv.2509.15537

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