An explicit formula for the $A$-polynomial of the knot with Conway's notation $C(2n, 4)$

TL;DR

This paper derives an explicit formula for the $A$-polynomial of the knot with Conway notation $C(2n,4)$, matching the factors of previously known $A$-polynomials, aiding in knot theory analysis.

Contribution

It provides a new explicit formula for the $A$-polynomial of a specific family of knots, expanding computational tools in knot theory.

Findings

The formula matches the irreducible factors of known $A$-polynomials.

The explicit expression simplifies the computation of $A$-polynomials for these knots.

The polynomial is computed up to repeated factors.

Abstract

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}.