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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Homfly and dichromatic polynomials


Authors: Xian’an Jin and Fuji Zhang
Journal: Proc. Amer. Math. Soc. 140 (2012), 1459-1472
MSC (2000): Primary 57M15, 57M27; Secondary 05CXX
Published electronically: August 1, 2011
MathSciNet review: 2869131
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Abstract: In this paper, we first associate a plane graph with an oriented link via replacing each edge of the graph by an alternatingly oriented 2-tangle. Then we establish a relation between the Homfly polynomial of the associated oriented link and the dichromatic polynomial of the plane graph by assigning suitable edge weights. This result extends work of F. Jaeger and L. Traldi.


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Additional Information

Xian’an Jin
Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, People’s Republic of China
Email: xajin@xmu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11050-5
PII: S 0002-9939(2011)11050-5
Keywords: Link, oriented tangle, graph, Homfly polynomial, dichromatic polynomial.
Received by editor(s): December 29, 2010
Published electronically: August 1, 2011
Communicated by: Jim Haglund
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.