Related papers: An explicit formula for the A-polynomial of twist …
We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the…
We provide explicit formulas for the Alexander polynomial of pretzel knots and establish several immediate corollaries, including the characterization of pretzel knots with a trivial Alexander polynomial. As an application, we construct a…
Twisted torus knots are a generalization of torus knots, obtained by introducing additional full twists to adjacent strands of the torus knots. In this article, we present an explicit formula for the Alexander polynomial of twisted torus…
An explicit formula for the $A$-polynomial of the knot with Conway's notation $C(2n,3)$ is obtained from the explicit Riley-Mednykh polynomial of it.
We extend recent work by Howie, Mathews and Purcell to simplify the calculation of A-polynomials for any family of hyperbolic knots related by twisting. The main result follows from the observation that equations defining the deformation…
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.
Knots obtained by Dehn filling the Whitehead sister link include some of the smallest volume twisted torus knots. Here, using results on A-polynomials of Dehn fillings, we give formulas to compute the A-polynomials of these knots. Our…
We give a formula for Alexander polynomials of doubly primitive knots.
We show that for a twist knot, the A-polynomial can be obtained from recurrences for the summand in Masbaum's formula of the colored Jones polynomial. Our result supports the AJ conjecture due to S.Garoufalidis.
We introduce a version of the Alexander polynomial for singular knots and tangles and show how it can be strengthened considerably by introducing a perturbation. For singular long knots, we also prove that our Alexander polynomial agrees…
We compute the A-polynomial 2-tuple of twisted Whitehead links. As applications, we determine canonical components of twisted Whitehead links and give a formula for the volume of twisted Whitehead link cone-manifolds.
An explicit formula for the $A$-polynomial of the knot having Conway's notation $C(2n,4)$ is computed up to repeated factors. Our polynomial contains exactly the same irreducible factors as the $A$-polynomial defined in~\cite{CCGLS1}.
We give an explicit formula for the HOMFLY polynomial of a rational link (in particular, a knot) in terms of a special continued fraction for the rational number that defines the given link.
We give a simple proof of an explicit formula for Kerov polynomials. This formula is closely related to a formula of Goulden and Rattan.
We calculate the twisted Alexander polynomial with the adjoint action for torus knots and twist knots. As consequences of these calculations, we obtain the formula for the nonabelian Reidemeister torsion of torus knots in \cite{Du} and a…
We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.
We calculate the Chern-Simons invariants of the twist knot orbifolds using the Schl\"{a}fli formula for the generalized Chern-Simons function on the family of the twist knot cone-manifold structures. Following the general instruction of…
We discuss the polynomial representation for long knots and elaborate on how to obtain them with a bound on degrees of the defining polynomials, for any knot-type.
We give explicit formulas for the adjoint twisted Alexander polynomial and the nonabelian Reidemeister torsion of genus one two-bridge knots.
In this paper, we discuss twisted Alexander polynomials of a knot for group extensions of a finite group in two directions. Firstly, we provide a mod $p$ formula for the twisted Alexander polynomial of a knot in the $3$-sphere associated…