Cyclic Sieving for torsion pairs in the cluster category of Dynkin type An
Abstract
Recently, a combinatorial model for torsion pairs in the cluster category of Dynkin type An 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 phenomenon.
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