대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제54권6호
  • /
  • Pages.2149-2154
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  • 2017
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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LOWER BOUNDS FOR THE NUMBER OF POSITIVE AND NEGATIVE CROSSINGS IN ORIENTED LINK DIAGRAMS

  • Lei, Fengchun (School of Mathematical Sciences Dalian University of Technology) ;
  • Zhang, Kai (School of Mathematical Sciences Dalian University of Technology)
  • 투고 : 2016.09.29
  • 심사 : 2017.05.23
  • 발행 : 2017.11.30
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초록

In this paper, we obtain a simple lower bound for the number of positive (resp. negative) crossings in oriented link diagrams in terms of the maximal (resp. minimal) degree of the Jones polynomial.

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참고문헌

  1. J. C. Cha and C. Livingston, KnotInfo: Table of Knot Invariants, http://www.indiana.edu/knotinfo.
  2. V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985), no. 1, 103-111. https://doi.org/10.1090/S0273-0979-1985-15304-2
  3. L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), no. 3, 395-407. https://doi.org/10.1016/0040-9383(87)90009-7
  4. K. Murasugi, On invariants of graphs with applications to knot theory, Trans. Amer. Math. Soc. 314 (1989), no. 1, 1-49. https://doi.org/10.1090/S0002-9947-1989-0930077-6
  5. A. Stoimenow, On some restrictions to the values of the Jones polynomial, Indiana Univ. Math. J. 54 (2005), no. 2, 557-574. https://doi.org/10.1512/iumj.2005.54.2624