1998/06/30 by J. Lieberum
Mathematics · #math.QA #math.CO #msc:57M25
published as Documenta Mathematica, Vol 5(2000), 275-299 · 25 pages, 14 figures
arxiv created 2000/06/23 · arxiv updated 2009/11/30
We consider 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, we determine 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. Furthermore, we show that for knots the algebra generated by H(n,1)+F(n,1) (n > 0) is a polynomial algebra with dim(H(n,1)+F(n,1))-1=n+[n/2]-4 generators in degree n>3 and one generator in degrees 2 and 3.