# Cyclic Sieving for torsion pairs in the cluster category of Dynkin type A_n

@inproceedings{Kluge2011CyclicSF, title={Cyclic Sieving for torsion pairs in the cluster category of Dynkin type A_n}, author={Stefan Kluge and Martin Rubey}, year={2011} }

Recently, a combinatorial model for torsion pairs in the cluster category of Dynkin type A_n was introduced, and used to derive an explicit formula for their number. In this article we determine the number of torsion pairs that are invariant under b-fold application of Auslander-Reiten translation. It turns out that the set of torsion pairs together with Auslander-Reiten translation, and a natural q-analogue of the formula for the number of all torsion pairs exhibits the cyclic sieving… CONTINUE READING

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## Torsion pairs in cluster tubes

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