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International Mathematics Research Notices Advance Access published online on September 3, 2009
International Mathematics Research Notices, doi:10.1093/imrn/rnp137
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Elementary Combinatorics of the HOMFLYPT Polynomial

Sergei Chmutov1 and Michael Polyak2

1 The Ohio State University, Mansfield, 1680 University Drive, Mansfield, OH 44906, USA
2 Department of Mathematics, Technion, Haifa 32000, Israel

Correspondence: Correspondence to be sent to: polyak{at}math.technion.ac.il

We explore Jaeger's state model for the HOMFLYPT polynomial. We reformulate this model in the language of Gauss diagrams and use it to obtain Gauss diagram formulas for a two-parameter family of Vassiliev invariants coming from the HOMFLYPT polynomial. These formulas are new already for invariants of degree 3.

Communicated by Prof. Anton Alekseev


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