Geodesic
Torsion pairs in cluster tubes
Journal of Algebraic Combinatorics, Tome 39 (2014) no. 3, pp. 587-605.

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We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial 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 find that the torsion pairs in cluster tubes exhibit a cyclic sieving phenomenon.
Classification : 05E10, 18E30
Keywords: Auslander-Reiten quiver, cluster category, cluster tilting object, triangulated category, tube 
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     title = {Torsion pairs in cluster tubes},
     journal = {Journal of Algebraic Combinatorics},
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Holm, Thorsten; Jørgensen, Peter; Rubey, Martin. Torsion pairs in cluster tubes. Journal of Algebraic Combinatorics, Tome 39 (2014) no. 3, pp. 587-605. http://geodesic.mathdoc.fr/item/JAC_2014__39_3_a8/