State generatings for Jones and Kauffman-Jones polynomials

TL;DR

This paper introduces a state generating method to compute Jones and Kauffman-Jones polynomials, providing formulas for infinite families of knots and virtual links, including non-alternating cases.

Contribution

The paper presents a novel state generating approach for calculating Jones and Kauffman-Jones polynomials, extending to virtual links and identifying non-alternating families.

Findings

Derived formulas for two infinite families of knots

Proved one family of knots is non-alternating

Extended method to virtual links with explicit examples

Abstract

A state generating is introduced to determine the Jones polynomial of a link. Formulae for two infinite families of knots are shown by applying this method, the second family of which are proved to be non-alternating. Moreover, the method is generalized to compute the Jones-Kauffman polynomial of a virtual link. As examples, formulae for one infinite family of virtual knots are given.