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ISRN Algebra
Volume 2012 (2012), Article ID 804829, 12 pages
Research Article

An Algorithm for Generating a Family of Alternating Knots

Departamento de Ciencias de la Computación, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado. 20-726, 01000 México City, DF, Mexico

Received 25 September 2011; Accepted 11 October 2011

Academic Editors: C. Munuera and A. Vourdas

Copyright © 2012 Carlos Velarde et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.