대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제55권3호
  • /
  • Pages.799-808
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  • 2018
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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KAUFFMAN POLYNOMIAL OF PERIODIC KNOTTED TRIVALENT GRAPHS

  • Aboufattoum, Ayman (Department of Mathematics Faculty of Science Kuwait University) ;
  • Elsakhawy, Elsyed A. (Department of Mathematics Faculty of Science Ain Shams University) ;
  • Istvan, Kyle (Department of Mathematics Louisiana State University) ;
  • Qazaqzeh, Khaled (Department of Mathematics Faculty of Science Kuwait University)
  • 투고 : 2017.03.23
  • 심사 : 2017.11.22
  • 발행 : 2018.05.31
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초록

We generalize some of the congruences in [20] to periodic knotted trivalent graphs. As an application, a criterion derived from one of these congruences is used to obstruct periodicity of links of few crossings for the odd primes p = 3, 5, 7, and 11. Moreover, we derive a new criterion of periodic links. In particular, we give a sufficient condition for the period to divide the crossing number. This gives some progress toward solving the well-known conjecture that the period divides the crossing number in the case of alternating links.

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참고문헌

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