Matrix representation of knots and folds: I

TL;DR

This paper introduces a unified mathematical framework to analyze the density of states for knots and folds in polymer chains, applicable to systems from DNA to space-time configurations.

Contribution

It provides a novel matrix representation approach for modeling knots and folds, unifying their treatment across different physical systems.

Findings

Matrix representation effectively models knot and fold density of states.

Applicable to diverse systems like DNA and space-time.

Lays groundwork for further computational and theoretical studies.

Abstract

This report presents a unified treatment of the density of states for the knots and folds of polymer chains. The physical realization of such systems ranges from DNA molecules to the microscopic configurations of space-time.