Recurrence relation for Jones polynomials

TL;DR

This paper introduces a recurrence relation-based method for computing Jones polynomials of closed braids, providing a new expansion formula and generating function, which aids in estimating degrees and deriving qualitative properties.

Contribution

It presents a novel recurrence relation approach for Jones polynomial computation, including a general expansion formula and rational generating function, enhancing analysis of braid families.

Findings

Derived a recurrence relation for Jones polynomials

Established a general expansion formula and generating function

Estimated degrees of Jones polynomials for braid families

Abstract

Using a simple recurrence relation we give a new method to compute Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for Jones polynomials. The method is used to estimate degree of Jones polynomials for some families of braids and to obtain general qualitative results.