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2 results

  • An upper bound of arc index of links

  • YONGJU BAE, CHAN-YOUNG PARK
  • Journal:
    Mathematical Proceedings of the Cambridge Philosophical Society / Volume 129 / Issue 3 / November 2000
    Published online by Cambridge University Press:
    17 January 2001, pp. 491-500
    Print publication:
    November 2000

  • In 1996, Cromwell and Nutt [7] found an upper bound on the arc index which is related to the minimal crossing number and conjectured that the upper bound achieves the lowest possible index for alternating links.

    CONJECTURE. Let L be any prime link. Then α(L) [les ] c(L)+2. Moreover this inequality is strict if and only if L is not alternating.

    In this paper, we define a new diagram, called a wheel diagram, of a link and use it to prove this conjecture.

  • Jones polynomials of periodic knots

  • Yongju Bae, Young Kon Kim, Chan-Young Park
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 58 / Issue 2 / October 1998
    Published online by Cambridge University Press:
    17 April 2009, pp. 261-270
    Print publication:
    October 1998
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  • We calculate the Zulli's matrix of a periodic knot and give some necessary conditions for the Jones polynomial of a periodic knot, which are slightly different from Yokota's result.