Narrow Results

Some evaluations of the Gordian distance from a knot to another knot are given by using three polynomial invariants called the HOMFLY polynomial, the Jones polynomial and the Q-polynomial. Furthermore, Gordian distances between a lot of pairs of knots are determined.

We study the relation between the maximum z-degree of Kauffman polynomial and the determinant for a quasi-alternating link. This gives a stronger criterion for deciding whether a non-alternating link is quasi-alternating or not than the known criterion in terms of Q-polynomials. Also, we determine all quasi-alternating links with determinant 5.

We give necessary and sufficient conditions for a given polynomial to be a plucking polynomial of a rooted tree. We discuss the fact that different rooted trees can have the same polynomial.

Qazaqzeh and Chbili showed that for any quasi-alternating link, the degree of the Q-polynomial is less than its determinant. We give a refinement of their evaluation.