An Algorithm for Generating a Family of Alternating Knots. (26th January 2012)

• Record Type: Journal Article
• Authors: Velarde, Carlos; Bribiesca, Ernesto; Aguilar, Wendy
• Other Names: Munuera C. Academic Editor.; Vourdas A. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2012(2012)
• Publication Date: 2012-01-26
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.5402/2012/804829
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : 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.