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

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Ptolemy Diagrams and Torsion Pairs in the Cluster Categories of Dynkin Type D

We give a complete classification of torsion pairs in the cluster category of Dynkin type Dn, 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.

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ژورنال

عنوان ژورنال: Advances in Applied Mathematics

سال: 2013

ISSN: 0196-8858

DOI: 10.1016/j.aam.2013.07.005