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Knots, matroids and the Ising model

Published online by Cambridge University Press:  24 October 2008

W. Schwärzler  and
D. J. A. Welsh
W. Schwärzler
Affiliation:
Forschungsinstitut für Diskrete Mathematik, Universität Bonn, Germany
D. J. A. Welsh
Affiliation:
Merton College, Oxford
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Abstract

A polynomial is defined on signed matroids which contains as specializations the Kauffman bracket polynomial of knot theory, the Tutte polynomial of a matroid, the partition function of the anisotropic Ising model, the Kauffman–Murasugi polynomials of signed graphs. It leads to generalizations of a theorem of Lickorish and Thistlethwaite showing that adequate link diagrams do not represent the unknot. We also investigate semi-adequacy and the span of the bracket polynomial in this wider context.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 1 , January 1993 , pp. 107 - 139
Copyright
Copyright © Cambridge Philosophical Society 1993

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