Kyungpook Mathematical Journal

  • 제48권3호
  • /
  • Pages.337-357
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  • 2008
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Enumeration of Algebraic Tangles with Applications to Theta-curves and Handcuff Graphs

  • 투고 : 2005.08.22
  • 발행 : 2008.09.30
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초록

We enumerate all algebraic tangles of seven crossings or less up to equivalence. These tangles are mutually distinguished by the corresponding links and their double. The result will be used for enumerating $\theta$-curves and handcuff graphs in a forthcoming paper.

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참고문헌

  1. C. C. Adams, "The Knot Book. An elementary introduction to the mathematical theory of knots", W. H. Freeman and Company, New York, 1994.
  2. A. Caudron, Classification des noeuds et des enlacements, Publications Mathematiques d'Orsay 82, 4(1982). Universite de Paris-Sud, Departement de Mathematique, Orsay.
  3. T. D. Cochran, D. Ruberman, Invariants of tangles, Math. Proc. Cambridge. Philos. Soc., 105(2)(1989) 299-306. https://doi.org/10.1017/S0305004100067785
  4. J. H. Conway, "An enumeration of knots and links, and some of their algebraic properties", Computational Problems in Abstract Algebra (Proc. Conf. Oxford, 1967), Pergamon Press(1970) 329-358.
  5. T. Kanenobu, Tangle surgeries on the double of a tangle and link polynomials, Kobe J. Math., 19(1-2)(2002), 1-19.
  6. T, Kanenobu, T. Sumi, Polynomial invariants of 2-bridge knots through 22 crossings, Math. Comp., 60(202)(1993), 771-778, S17-S28.
  7. T. Kanenobu, H. Saito, S. Satoh, Tangles with up to seven crossings, Proceedings of the Winter Workshop of Topology/Workshop of Topology and Computer (Sendai, 2002/Nara, 2001). Interdiscip. Inform. Sci., 9(1)(2003), 127-140.
  8. L. H. Kauffman, State models and the Jones polynomial, Topology, 26(3)(1987), 395-407. https://doi.org/10.1016/0040-9383(87)90009-7
  9. R. A. Litherland, A table of all prime theta-curves in $S^3$ up to 7 crossings, a letter(1989).
  10. H. Moriuchi, An enumeration of theta-curves with up to 7 crossings (in Japanese), Master Thesis, Osaka City Univ., 2004.
  11. H. Moriuchi, An enumeration of theta-curves with up to seven crossings, submitted.
  12. H. Moriuchi, A table of handcuff graphs with up to seven crossings, OCAMI Studies 1 Knot theory for Science Objects (to appear).
  13. K. Murasugi, Knot Theory and Its Applications, Translated from the 1993 Japanese original by Bohdan Kurpita. BirkhAauser Boston, Inc., Boston, MA, 1996.
  14. Y. Nakanishi, Alexander invariants of links (in Japanese), Master Thesis, Kobe Univ., 1980.
  15. D. Rolfsen, Knots and Links, Mathematics Lecture Series, No. 7. Publish or Perish, Inc., Berkeley, Calif., 1976.
  16. K. Wolcott, The knotting of theta-curves and other graphs in $S^3$, Geometry and topology (Athens, Ga., 1985), Lecture Notes in Pure and Appl. Math., Dekker, New York, 105(1987), 325-346.
  17. H. Yamano, Classification of tangles of 7 crossings or less (in Japanese), Master Thesis, Tokyo Metrop. Univ., 2001.

피인용 문헌

  1. AN ENUMERATION OF THETA-CURVES WITH UP TO SEVEN CROSSINGS vol.18, pp.02, 2009, https://doi.org/10.1142/S0218216509006884
  2. Enumeration of spatial 2-bouquet graphs up to flat vertex isotopy vol.196, 2015, https://doi.org/10.1016/j.topol.2015.05.049