The Homfly and dichromatic polynomials

Jin, Xian’an; Zhang, Fuji

doi:10.1090/S0002-9939-2011-11050-5

The Homfly and dichromatic polynomials
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Proc. Amer. Math. Soc. 140 (2012), 1459-1472 Request permission

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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