About this Journal Submit a Manuscript Table of Contents 
ISRN Algebra
Volume 2012 (2012), Article ID 804829, 12 pages
doi:10.5402/2012/804829
Research Article

An Algorithm for Generating a Family of Alternating Knots

Carlos Velarde, Ernesto Bribiesca, and Wendy Aguilar

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.

Linked References

  1. C. Livingston, Knot Theory, vol. 24, Mathematical Association of America, Washington, DC, USA, 1993.
  2. E. Bribiesca, “A method for computing families of discrete knots using knot numbers,” Journal of Knot Theory and Its Ramifications, vol. 14, no. 4, pp. 405–424, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Y. Diao, “Minimal knotted polygons on the cubic lattice,” Journal of Knot Theory and Its Ramifications, vol. 2, no. 4, pp. 413–425, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y. Diao, “The number of smallest knots on the cubic lattice,” Journal of Statistical Physics, vol. 74, no. 5-6, pp. 1247–1254, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. E. J. J. van Rensburg and S. D. Promislow, “Minimal knots in the cubic lattice,” Journal of Knot Theory and Its Ramifications, vol. 4, no. 1, pp. 115–130, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. B. Hayes, “Square knots,” American Scientist, vol. 85, no. 6, pp. 506–510, 1997. View at Scopus
  7. L. H. Kauffman, “Virtual knot theory,” European Journal of Combinatorics, vol. 20, no. 7, pp. 663–690, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. Nakamura and A. Rosenfeld, “Digital knots,” Pattern Recognition, vol. 33, no. 9, pp. 1541–1553, 2000. View at Publisher · View at Google Scholar · View at Scopus
  9. F. Harary, Graph Theory, Addison-Wesley, 1969.
  10. C. R. Jordan and D. A. Jordan, Groups, Arnold, London, UK, 1994.
  11. R. Bird, Introduction to Functional Programming Using Haskell, Prentice Hall, 1998.
  12. S. P. Jones, Ed., Haskell 98 Language and Libraries. The Revised Report, 2002, http://haskell.org.
  13. E. Bribiesca, “A chain code for representing 3D curves,” Pattern Recognition, vol. 33, no. 5, pp. 755–765, 2000. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Guzmán, “Canonical shape description for 3-d stick bodies,” Tech. Rep. ACA-254-87, MCC, Austin, Tex, USA, 1987.