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

2013/03/07 by Thorsten Holm, Holm, Thorsten, Peter Jørgensen +3
Mathematics · #05A15 #05E15 #13F60 #16G10 #16G70 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1303.1684

openalex publication_date 2013/03/07 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We give a complete classification of torsion pairs in the cluster category of\nDynkin type D_n, via a bijection to new combinatorial objects called Ptolemy\ndiagrams of type D. For the latter we give along the way different\ncombinatorial descriptions. One of these allows us to count the number of\ntorsion pairs in the cluster category of type D_n by providing their generating\nfunction explicitly.\n

Related

• Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type A_n
• Ptolemy diagrams and torsion pairs in m-cluster categories of type D
• Torsion pairs in repetitive cluster categories of type A_n
• Cluster tilting subcategories and torsion pairs in Igusa--Todorov cluster categories of Dynkin type A _∞
• Cotorsion pairs in cluster categories of type A_∞^∞