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Arc index and the Kauffman polynomial

Published online by Cambridge University Press:  01 January 1998

HUGH R. MORTON  and
ELISABETTA BELTRAMI
HUGH R. MORTON
Affiliation:
Department of Mathematical Sciences, University of Liverpool, PO Box 147, Liverpool L69 3BX
ELISABETTA BELTRAMI
Affiliation:
Dipartimento di Matematica, Università di Pisa, Via F. Buonarroti 2, 56127 Pisa, Italy
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Abstract

The arc index α(L) of a link L is shown by a direct combinatorial argument to be related to sprv(FL(v, z)), the Laurent degree of its Kauffman polynomial, by the inequality

α(L)[ges ]sprv (FL(v, z))+2.

Equality is conjectured for alternating links.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 1 , January 1998 , pp. 41 - 48
Copyright
Cambridge Philosophical Society 1998

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