Polynomial representation for long knots

TL;DR

This paper explores polynomial representations of long knots, providing methods to obtain such representations with degree bounds for any knot type, advancing the mathematical understanding of knot parametrizations.

Contribution

It introduces a systematic approach to construct polynomial representations of long knots with degree bounds, applicable to all knot types.

Findings

Established degree bounds for polynomial representations of long knots

Provided explicit methods for constructing polynomial parametrizations

Enhanced understanding of knot representation in polynomial form

Abstract

We discuss the polynomial representation for long knots and elaborate on how to obtain them with a bound on degrees of the defining polynomials, for any knot-type.