Elementary combinatorics of the HOMFLYPT polynomial

Mathematics – Geometric Topology

Scientific paper

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

Scientific paper

10.1093/imrn/rnp137

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.

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