Geodesic
The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials
Documenta mathematica, Tome 5 (2000), pp. 275-299
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We consider vector spaces Hn,l​ and Fn,l​ spanned by the degree-n coefficients in power series forms of the Homfly and Kauffman polynomials of links with l components. Generalizing previously known formulas, we determine the dimensions of the spaces Hn,l​,Fn,l​ and Hn,l​+Fn,l​ for all values of n and l. Furthermore, we show that for knots the algebra generated by ⨁n​Hn,1​+Fn,1​ is a polynomial algebra with dim(Hn,1​+Fn,1​)−1=n+[n/2]−4 generators in degree n≥4 and one generator in degrees 2 and 3.
DOI : 10.4171/dm/81
Mots-clés : Brauer algebra, Vassiliev invariants, link polynomials, vogelś algebra, dimensions 
@article{10_4171_dm_81,
     author = {Jens Lieberum},
     title = {The number of independent {Vassiliev} invariants in the {Homfly} and {Kauffman} polynomials},
     journal = {Documenta mathematica},
     pages = {275--299},
     year = {2000},
     volume = {5},
     doi = {10.4171/dm/81},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/81/}
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Jens Lieberum. The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials. Documenta mathematica, Tome 5 (2000), pp. 275-299. doi: 10.4171/dm/81

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