Classifying Nakayama algebras with a braid group action on $\tau$-exceptional sequences

We characterise those basic and connected Nakayama algebras $\mathrm{\Lambda }$ for which the mutation of $\tau$-exceptional sequences respects the braid group relations. We show that this is the case if and only if $\mathrm{\Lambda }$ is hereditary or all indecomposable projective $\mathrm{\Lambda }$-modules have length at least $\mathrm{\mid }\mathrm{\Lambda }\mathrm{\mid }$.