Elementary combinatorics of the HOMFLYPT polynomial
arXiv:0810.4105 · doi:10.1093/imrn/rnp137
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