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

Thorsten Holm; Peter Jørgensen; Martin Rubey

doi:10.1016/j.aam.2013.07.005

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

Thorsten Holm^*
, Peter Jørgensen
, Martin Rubey

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

11 Citationer (Scopus)

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.

Originalsprog	Engelsk
Tidsskrift	Advances in Applied Mathematics
Vol/bind	51
Nummer	5
Sider (fra-til)	583-605
Antal sider	23
ISSN	0196-8858
DOI	https://doi.org/10.1016/j.aam.2013.07.005
Status	Udgivet - okt. 2013
Udgivet eksternt	Ja

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title = "Ptolemy diagrams and torsion pairs in the cluster categories of Dynkin type D",

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",

author = "Thorsten Holm and Peter J{\o}rgensen and Martin Rubey",

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T1 - Ptolemy diagrams and torsion pairs in the cluster categories of Dynkin type D

AU - Holm, Thorsten

AU - Jørgensen, Peter

AU - Rubey, Martin

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 - https://www.scopus.com/pages/publications/84886721101

U2 - 10.1016/j.aam.2013.07.005

DO - 10.1016/j.aam.2013.07.005

M3 - Journal article

AN - SCOPUS:84886721101

SN - 0196-8858

VL - 51

SP - 583

EP - 605

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 5

ER -

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

Abstract

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