Ptolemy diagrams and cotorsion pairs in m-cluster categories of type A.

In this paper, we give a complete classification of cotorsion pairs in m -cluster categories of type A , denoted by A n − 1 m , via certain configurations of m -diagonals, called Ptolemy diagrams. As applications, we classify m -rigid subcategories of A n − 1 m , which gives Jacquet–Malo's classification of m -cluster tilting subcategories of A n − 1 m . When m = 1 , this generalizes the work of Holm et al. [Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type A n , J. Algebraic Combin. 34 (3) (2011) 507–523] for the classification of torsion pairs in cluster categories of type A n − 1 . [ABSTRACT FROM AUTHOR]