Details
| Original language | English |
|---|---|
| Pages (from-to) | 583-605 |
| Number of pages | 23 |
| Journal | Advances in applied mathematics |
| Volume | 51 |
| Issue number | 5 |
| Publication status | Published - Oct 2013 |
Abstract
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.
Keywords
- Clique, Cluster algebra, Cluster category, Cluster tilting object, Dynkin type D, Generating function, Species, Triangulated category
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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In: Advances in applied mathematics, Vol. 51, No. 5, 10.2013, p. 583-605.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Ptolemy diagrams and torsion pairs in the cluster categories of Dynkin type D
AU - Holm, Thorsten
AU - Jørgensen, Peter
AU - Rubey, Martin
N1 - Funding Information: This work has been carried out in the framework of the research priority programme SPP 1388 Darstellungstheorie of the Deutsche Forschungsgemeinschaft (DFG). We gratefully acknowledge financial support through the grants HO 1880/4-1 and HO 1880/5-1.
PY - 2013/10
Y1 - 2013/10
N2 - 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.
AB - 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.
KW - Clique
KW - Cluster algebra
KW - Cluster category
KW - Cluster tilting object
KW - Dynkin type D
KW - Generating function
KW - Species
KW - Triangulated category
UR - http://www.scopus.com/inward/record.url?scp=84886721101&partnerID=8YFLogxK
U2 - 10.1016/j.aam.2013.07.005
DO - 10.1016/j.aam.2013.07.005
M3 - Article
AN - SCOPUS:84886721101
VL - 51
SP - 583
EP - 605
JO - Advances in applied mathematics
JF - Advances in applied mathematics
SN - 0196-8858
IS - 5
ER -