Exceptional versus $\tau$-exceptional sequences for the Auslander algebra of $K[x]\mathrm{/}(x^t)$

For ${\mathcal{A}}_t$, the Auslander algebra of $K[x]\mathrm{/}(x^t)$, it is shown that every complete exceptional sequence of ${\mathcal{A}}_t$-modules is a complete $\tau$-exceptional sequence. Moreover, it is established that the mutation of complete $\tau$-exceptional sequences generalises the mutation of complete exceptional sequences in the category of ${\mathcal{A}}_t$-modules.