mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered...

knot. The first knot polynomial, the Alexander polynomial, was introduced by James Waddell Alexander II in 1923. Other knot polynomials were not found until...

Touchard polynomials Wilkinson's polynomial Wilson polynomials Zernike polynomials Pseudo-Zernike polynomials Alexander polynomial HOMFLY polynomial Jones...

the Alexander polynomial and the Jones polynomial, both of which can be obtained by appropriate substitutions from HOMFLY. The HOMFLY polynomial is also...

Alexander, and others—studied knots from the point of view of the knot group and invariants from homology theory such as the Alexander polynomial. This...

\left(V-tV^{*}\right),} which is a polynomial of degree at most 2g in the indeterminate t . {\displaystyle t.} The Alexander polynomial is independent of the choice...

corresponding to this projection map. Much like in the construction of the Alexander polynomial, consider H1(Cn) as a module over the group-ring of covering transformations...

In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant...

.) The Alexander polynomial of the trefoil knot is Δ ( t ) = t − 1 + t − 1 , {\displaystyle \Delta (t)=t-1+t^{-1},} and the Conway polynomial is ∇ ( z...

(t)=c_{0}+c_{1}t+\cdots +c_{n}t^{n}+\cdots +c_{0}t^{2n}} be the Alexander polynomial of the knot. Then the Arf invariant is the residue of c n − 1 + c...