Kauffman polynomial

In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. It is initially defined on a link diagram as

where ${\displaystyle w(K)}$ is the writhe of the link diagram and ${\displaystyle L(K)}$ is a polynomial in a and z defined on link diagrams by the following properties:

Here ${\displaystyle s}$ is a strand and ${\displaystyle s_{r}}$ (resp. ${\displaystyle s_{\ell }}$) is the same strand with a right-handed (resp. left-handed) curl added (using a type I Reidemeister move).

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