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

@article{Holm2010PtolemyDA,
title={Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type An},
author={T. Holm and P. J{\o}rgensen and M. Rubey},
journal={Journal of Algebraic Combinatorics},
year={2010},
volume={34},
pages={507-523}
}
• Published 2010
• Mathematics
• Journal of Algebraic Combinatorics
• 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 (1005.4364v1 [math.RT], 2010). 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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