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

Details Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type A_n Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type A_n

2010-10-06

arxiv.org/abs/1010.1184v3

Mathematics

Representation Theory

14 pages; v2: Major simplification of the formula in Theorem B for the number of Ptolemy diagrams; v3: 17 pages; revision foll

Scientific paper

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. 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.

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