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Torsion pairs in cluster tubes

Lookup NU author(s): Professor Peter Jorgensen

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Abstract

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.

Publication metadata

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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