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

2010/10/06 by Thorsten Holm, Holm, Thorsten, Peter Jørgensen +3
Mathematics · #05A15 #05E15 #13F60 #18E30 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1010.1184

openalex publication_date 2010/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. 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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