Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type An

@inproceedings{Holm2011PtolemyDA,
  title={Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type An},
  author={Thorsten Holm and Peter V. J\orgensen and Martin Rubey},
  year={2011}
}
We give a complete classification of torsion pairs in the cluster category of Dynkin type An. Along the way we give a new combinatorial description of Ptolemy diagrams, an infinite version of which was introduced by Ng in [15]. This allows us to count the number of torsion pairs in the cluster category of type An. We also count torsion pairs up to Auslander-Reiten translation. 

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