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Ptolemy diagrams and torsion pairs in the cluster categories of Dynkin type D

Lookup NU author(s): Professor Peter Jorgensen

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Abstract

We give a complete classification of torsion pairs in the cluster category of Dynkin type D-n, via a bijection to new combinatorial objects called Ptolemy diagrams of type D. For the latter we give along the way different combinatorial descriptions. One of these allows us to count the number of torsion pairs in the cluster category of type Dn by providing their generating function explicitly. (C) 2013 Elsevier Inc. All rights reserved.

Publication metadata

Author(s): Holm T, Jorgensen P, Rubey M

Publication type: Article

Publication status: Published

Journal: Advances in Applied Mathematics

Year: 2013

Volume: 51

Issue: 5

Pages: 583-605

Print publication date: 01/10/2013

Online publication date: 09/09/2013

Acceptance date: 26/07/2013

ISSN (print): 0196-8858

ISSN (electronic): 1090-2074

Publisher: Academic Press

URL: http://dx.doi.org/10.1016/j.aam.2013.07.005

DOI: 10.1016/j.aam.2013.07.005

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