The coefficients of the Jones polynomial

TL;DR

This paper investigates the minimal factors needed to convert rational-valued Vassiliev invariants derived from the Jones polynomial into integer-valued invariants, providing a new set of integer invariants.

Contribution

It calculates the minimal multiplying factor for rational Vassiliev invariants from the Jones polynomial to become integer-valued, leading to a new set of integer invariants.

Findings

Determined the minimal multiplying factor for integrality

Established a set of integer-valued Vassiliev invariants

Enhanced understanding of the algebraic structure of Jones polynomial invariants

Abstract

It has been known that, the coefficients of the series expansion of the Jones polynomial evaluated at $e^x$ are rational valued Vassiliev invariants . In this article, we calculate minimal multiplying factor, {\lambda}, needed for these rational valued invariants to become integer valued Vassiliev invariants. By doing that we obtain a set of integer-valued Vassiliev invariants.