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Some link-polynomial relations

Published online by Cambridge University Press:  24 October 2008

W. B. R. Lickorish
W. B. R. Lickorish
Affiliation:
Department of Pure Mathematics, 16 Mill Lane, Cambridge CB2 1SB
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Extract

The polynomial invariants of classical links that relate to the Jones polynomial have various inter-connections. Here a new one is given: the square of the Jones polynomial is obtained from the F-polynomial by means of a certain substitution of variables. This explains and corrects some similarities between known evaluations of these polynomials. The proof uses the ‘Dubrovnik’ version of the F-polynomial; this is first proved to be equivalent to the F-polynomial. Finally a correlation between the F and P polynomials is included as a provocative curiosity.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 1 , January 1989 , pp. 103 - 107
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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