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Journal of Algebraic Combinatorics

, Volume 34, Issue 3, pp 507–523 | Cite as

Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type A n

  • Thorsten Holm
  • Peter JørgensenEmail author
  • Martin Rubey
Article

Abstract

We give a complete classification of torsion pairs in the cluster category of Dynkin type A n . Along the way we give a new combinatorial description of Ptolemy diagrams, an infinite version of which was introduced by Ng (1005.4364v1 [math.RT], 2010). This allows us to count the number of torsion pairs in the cluster category of type A n . We also count torsion pairs up to Auslander–Reiten translation.

Keywords

Clique Cluster algebra Cluster tilting object Generating function Recursively defined set Species Triangulated category 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und PhysikLeibniz Universität HannoverHannoverGermany
  2. 2.School of Mathematics and StatisticsNewcastle UniversityNewcastle upon TyneUK

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