Computer evaluation of Homfly polynomials by using Gauss codes, with a skein-template algorithm

Applied Mathematics and Computation

Volumn 105, Issue 2-3, 1999, Pages 271-289

  Gouesbet, G ^a   Meunier Guttin Cluzel, S ^a   Letellier, C ^a  

^a University of Rouen Normandy   (France)

Author keywords

Gauss codes; Homfly polynomials; Knot invariant; Knot theory

Indexed keywords

EID: 0346906092     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(98)10106-6     Document Type: Article

References (23)

1. J.S. Birman, R.F. Williams, Knotted periodic orbits in dynamical systems, Topology 22 (1) (1983) 47-82.
2. P. Freyd, D. Yetter, J. Hoste, W.B.R. Lickorish, K. Millet, A. Ocneanu, A new polynomial invariant of knots and links, Bulletin (new series) of the American mathematical society 12 (2) (1985) 239-246.
3. C.F. Gauss, Werke, Teubner, Leipzig, 1900.
4. G. Gouesbet, L. Le Sceller, C. Letellier, R. Brown, J.R. Buchler, Z. Kollath, Reconstructing a dynamics from a scalar time series, in: Nonlinear signal and image analysis, Eleventh annual Florida Workshop in nonlinear astronomy, 30 November-2 December 1995, vol. 808 of Annals N.Y. Academy of Sciences, 1997.
5. G. Gouesbet, C. Letellier, Global vector field reconstruction by using a multivariate polynomial L2-approximation on nets, Phys. Rev. E 49 (6) (1994) 4955-4972.
6. G. Gouesbet, J. Maquet, Construction of phenomenological models from numerical scalar time series, Physica D 58 (1992) 202-215.
7. F. Jaeger, Composition products and models for the Homfly polynomial, L'enseignement mathématique 35 (1989) 323-361.
8. V.F.R. Jones, Hecke algebra representations of braid groups and link polynomials, Annals of Mathematics 126 (1987) 335-388.
9. L.H. Kauffman, On knots. Number 115 in Annals of Mathematical Studies, Princeton university press, Princeton, NJ, 1987.
10. L.H. Kauffman, State models for link polynomials, L'enseignement mathématique 36 (1990) 1-37.
11. L.H. Kauffman, Gauss codes, quantum groups and ribbon Hopf algebras, Rev. Math. Phys. 5(4) (1993).
12. L.H. Kauffman, Knots and Physics, vol. 1 of On knots and everything, 2nd ed., World Scientific, Singapore, 1993.
13. B.W. Kernighan, D.M. Ritchie, Le language C, Manuels Informatiques Masson, Masson, 1984.
14. C. Letellier, G. Gouesbet, Topological characterization of reconstructed attractors modding out symmetries, Journal de physique II, France 6 (1996) 1615-163 8.
15. C. Letellier, G. Gouesbet, N. Rulkov, Topological analysis of chaos in equivariant electronic circuits, Int. J. Bifurcation and Chaos 6 (12B) (1996) 2531-2555.
16. C. Letellier, G. Gouesbet, F. Soufi, J.R. Buchler, Z. Kollath, Chaos in variable stars: Topological analysis of W Vir model pulsations, Chaos 6 (3) (1996) 466-476.
17. C. Letellier, L. Le Sceller, P. Dutertre, G. Gouesbet, Z. Fei, J.L. Hudson, Topological characterization and global vector field reconstruction of an experimental electro-chemical system, J. Phys. Chem. 99 (1995) 7016-7027.
18. W.B.R. Lickorish, Polynomials for links, Bull. London Math. Soc. 20 (1988) 558-588.
19. S. Meunier-Guttin-Cluzel, Calcul automatique de polynômes de homfly associés à des nœuds ou à des liens à partir des codes de Gauss, Technical report, LESP-UMR 6614 CNRS -CORIA - INSA de ROUEN, 1997.
20. J.H. Przytycki, P. Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1987) 115-139.
21. K. Reidemeister, Knotentheorie, Chelsea, New York, Copyright 1932, Julius Springer, Berlin, 1948.
22. R.L. Ricca, M.A. Berger, Topological Ideas and Fluid Mechanics, Physics Today, December 1996, pp. 28-34.
23. D. Rolfsen, Knots and links, Number 7 in Mathematical lectures series, Publish or Perish Press, Berkeley, CA, 1976.