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On the arc index of an adequate link

Published online by Cambridge University Press:  17 April 2009

Chan-Young Park  and
Myoungsoo Seo
Chan-Young Park
Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, South Korea
Myoungsoo Seo
Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, South Korea
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Abstract

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In 1996, Cromwell and Nutt conjectured that α(L) − c (L) = 2 for a link L if and only if L is alternating. In this paper we calculate that α(L) = c (L) for some non-alternating pretzel links L, define a new invariant ρ(L) of adequate links L and show that for each non-negative integer n, there is a prime adequate knot K such that α(K) − c (K) = −2n. We conjecture that α(L) − c (L) = 2ρ(L) for any adequate link L.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 177 - 187
Copyright
Copyright © Australian Mathematical Society 2000

References

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