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