Geodesic
The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials
Documenta mathematica, Tome 5 (2000), pp. 275-299.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider vector spaces $\Hvnl$ and $\Fvnl$ spanned by the degree-$n$ coefficients in power series forms of the Homfly and Kauffman polynomials of links with $\ell$ components. Generalizing previously known formulas, we determine the dimensions of the spaces $\Hvnl, \Fvnl$ and $\Hvnl+\Fvnl$ for all values of $n$ and $\ell$. Furthermore, we show that for knots the algebra generated by $\bigoplus_n \Hvne+\Fvne$ is a polynomial algebra with $\dim(\Hvne+\Fvne)-1=n+[n/2]-4$ generators in degree $n\geq 4$ and one generator in degrees 2 and 3.
Classification : 57M25
Keywords: Vassiliev invariants, link polynomials, Brauer algebra, vogelś algebra, dimensions 
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     author = {Lieberum, Jens},
     title = {The number of independent {Vassiliev} invariants in the {Homfly} and {Kauffman} polynomials},
     journal = {Documenta mathematica},
     pages = {275--299},
     publisher = {mathdoc},
     volume = {5},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2000__5__a11/}
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Lieberum, Jens. The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials. Documenta mathematica, Tome 5 (2000), pp. 275-299. http://geodesic.mathdoc.fr/item/DOCMA_2000__5__a11/