Ptolemy diagrams and torsion pairs in m-cluster categories of type D

In this paper, we give a complete classification of torsion pairs in m-cluster categories of type D when m is odd, denoted by CDnm, via a bijection to combinatorial objects called Ptolemy diagrams of type D. As applications, we classify m-rigid subcategories of CDnm, which gives Jacquet-Malo's classification of m-cluster tilting subcategories of CDnm. When m = 1, we generalizes the work of Holm, Jørgensen and Rubey [ Citation14] for the classification of torsion pairs in cluster categories of type Dn.