Elementary combinatorics of the HOMFLYPT polynomial

Abstract

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.

12 pages, many figures. v2: multiple changes; part on virtual links removed

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