An explicit formula for the $A$-polynomial of the knot with Conway's notation $C(2n, 3)$

TL;DR

This paper derives an explicit formula for the $A$-polynomial of a specific family of knots with Conway's notation $C(2n,3)$, using the Riley-Mednykh polynomial, advancing understanding of knot invariants.

Contribution

The paper provides the first explicit formula for the $A$-polynomial of the $C(2n,3)$ knots, connecting it to the Riley-Mednykh polynomial.

Findings

Explicit $A$-polynomial formula for $C(2n,3)$ knots

Connection established between $A$-polynomial and Riley-Mednykh polynomial

Enhanced computational tools for knot invariants

Abstract

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.