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The number of independent Vassiliev invariants in the Homfly and Kauffman polynomials. (English) Zbl 0953.57007
The author considers the vector spaces $$H_{n,l}$$ and $$F_{n,l}$$ 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, the dimensions of the spaces $$H_{n,l}$$, $$F_{n,l}$$ and $$H_{n,l}+F_{n,l}$$ for all values of $$n$$ and $$l$$ are determined. Furthermore, the author shows that for knots the algebra generated by $$\bigoplus_n H_{n,1}+F_{n,1}$$ is a polynomial algebra with $$\dim(H_{n,1}+F_{n,1})-1=n+[n/2]-4$$ generators in degree $$n\geq 4$$ and one generator in degrees $$2$$ and $$3$$. The author takes care to briefly define the various knot and link polynomials, in addition the article contains a long and useful list of references.

##### MSC:
 57M27 Invariants of knots and $$3$$-manifolds (MSC2010) 57M25 Knots and links in the $$3$$-sphere (MSC2010)
##### Keywords:
link polynomials; Brauer algebra; Vogels algebra; dimensions
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