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

Abstract

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.

arXiv comment17 pages, 4 pdf-Figures

References in corpus (1)

• Cyclic sieving phenomenon in non-crossing connected graphs

Cited by in corpus (1)

• Torsion pairs in cluster tubes