Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type A n
نویسندگان
چکیده
منابع مشابه
Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type An
We give a complete classification of torsion pairs in the cluster category of Dynkin type An. Along the way we give a new combinatorial description of Ptolemy diagrams, an infinite version of which was introduced by Ng (1005.4364v1 [math.RT], 2010). This allows us to count the number of torsion pairs in the cluster category of type An. We also count torsion pairs up to Auslander–Reiten translat...
متن کاملPtolemy 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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The Periodicity Conjecture for Pairs of Dynkin Diagrams
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We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptolemy diagrams which already appeared in our earlier work on torsion pairs in cluster categories of Dynkin type A. As a consequence of our classification we establish closed formulae enumerating the torsion pairs in clu...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2011
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-011-0280-x