Mutation of torsion pairs in cluster categories of Dynkin type $D$

Mutation of torsion pairs in triangulated categories and its combinatorial interpretation for the cluster category of Dynkin type $A_n$ and of type $A_{\mathrm{\infty }}$ have been studied by Zhou and Zhu. In this paper we present a combinatorial model for mutation of torsion pairs in the cluster category of Dynkin type $D_n$, using Ptolemy diagrams of Dynkin type $D_n$ which were introduced by Holm, J{\o}rgensen and Rubey.