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The prime link 02-0201 which has Jones polynomial V(t)=-t-t^(-1) and HOMFLY polynomial P(z,alpha)=z^(-1)(alpha^(-1)-alpha^(-3))+zalpha^(-1). It has braid word sigma_1^2.

A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of each string in ...

A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...

A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of each string in ...

A link invariant defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components ...

A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.

The substitution of re^(itheta) for z in a polynomial p(z). p(z) is then plotted as a function of theta for a given r in the complex plane. By varying r so that the curve ...

Gives a matrix representation b_i of a braid group in terms of (n-1)×(n-1) matrices. A -t always appears in the (i,i) position. b_1 = [-t 0 0 ... 0; -1 1 0 ... 0; 0 0 1 ... ...

The prime link 05-0201, illustrated above, with braid word sigma_1^2sigma_2^2sigma_1^(-1)sigma_2^(-2) or sigma_1sigma_2^(-1)sigma_1sigma_2^(-2) and Jones polynomial ...

I((chi_s^2)/(sqrt(2(k-1))),(k-3)/2)=(Gamma(1/2chi_s^2,(k-1)/2))/(Gamma((k-1)/2)), where Gamma(x) is the gamma function.