An Algorithm for Generating a Family of Alternating Knots

Abstract EN

An algorithm for generating a family of alternating knots (which are described by means of a chain code) is presented.

The family of alternating knots is represented on the cubic lattice, that is, each alternating knot is composed of constant orthogonal straight-line segments and is described by means of a chain code.

This chain code is represented by a numerical string of finite length over a finite alphabet, allowing the usage of formal-language techniques for alternating-knot representation.

When an alternating knot is described by a chain, it is possible to obtain its mirroring image in an easy way.

Also, we have a compression efficiency for representing alternating knots, because chain codes preserve information and allow a considerable data reduction.