A New Algorithm for Numerical Calculation of Link Invariants

Abstract

We propose a new method for numerical calculation of link plynomials for knots given in 3 dimensions. We calculate derivatives of the Jones polynomial in a computational time proportional to $N^{\alpha }$ with respect to the system size $N$ . This method gives a new tool for determining topology of knotted closed loops in three dimensions using computers.

20 pages, September 1992

Cited by in corpus (13)

• Average size of random polygons with fixed knot topology
• Characteristic length of random knotting for cylindrical self-avoiding polygons
• Finite-size and asymptotic behaviors of the gyration radius of knotted cylindrical polygons
• Gyration radius of a circular polymer under a topological constraint with excluded volume
• On the Dominance of Trivial Knots among SAPs on a Cubic Lattice
• Knot complexity and the probability of random knotting
• Knotting probability of self-avoiding polygons under a topological constraint
• Scattering functions of knotted ring polymers
• Distribution of the distance between opposite nodes of random polygons with a fixed knot
• Topological entropy of a stiff ring polymer and its connection to DNA knots
• Knot probabilities in equilateral random polygons
• Evaluating the Jones polynomial with tensor networks
• Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent