Abstract

Abstract. We give a complete classification of torsion pairs in the cluster cat-egories associated to tubes of finite rank. The classification is in terms of com-binatorial objects called Ptolemy diagrams which already appeared in our earlier work on torsion pairs in cluster categories of Dynkin type A. As a consequence of our classification we establish closed formulae enumerating the torsion pairs in cluster tubes, and obtain that the torsion pairs in cluster tubes exhibit a cyclic sieving phenomenon. Dedicated to Idun Reiten on the occasion of her 70th birthday. 1.