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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.
Author(s): Holm T, Jorgensen P, Rubey M
Publication type: Article
Publication status: Published
Journal: Journal of Algebraic Combinatorics
Year: 2014
Volume: 39
Issue: 3
Pages: 587-605
Print publication date: 01/05/2014
ISSN (print): 0925-9899
ISSN (electronic): 1572-9192
Publisher: Springer
URL: http://dx.doi.org/10.1007/s10801-013-0457-6
DOI: 10.1007/s10801-013-0457-6
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