  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 phenomenon.
