Hirasawa–Murasugi's fibering conjecture for Dean knots

Let

$$K(p,q\mid r,rs)$$

be the Dean knot represented by the closed $p$-braid

$$(\sigma_{p-1}\sigma_{p-2}\cdots\sigma_1)^q(\sigma_1\sigma_2\cdots\sigma_{r-1})^{rs},$$

where $p>r>1$ and $q,s$ are nonzero integers with $\gcd(q,p)=1$. Let $\Delta_K$ be the Alexander polynomial of $K$. Hirasawa–Murasugi's conjecture. The Dean knot $K(p,q\mid r,rs)$ is fibred if and only if its Alexander polynomial is monic:

$$\max\operatorname{cf}\Delta_K=\pm1.$$

Here $\max\operatorname{cf}\Delta_K$ denotes the maximum absolute coefficient of the Alexander polynomial, as used in the source. The conjecture links fibredness of these generalized Dean knots to monicity of their Alexander polynomials; the source reports only partial results and gives no resolution status.