arXiv Analytics

Sign in

arXiv:1010.1184 [math.RT]AbstractReferencesReviewsResources

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

Thorsten Holm, Peter Jorgensen, Martin Rubey

Published 2010-10-06, updated 2011-03-14Version 3

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.

Comments: 14 pages; v2: Major simplification of the formula in Theorem B for the number of Ptolemy diagrams; v3: 17 pages; revision following referee's very helpful comments; more details for some arguments added; formula in Prop. 3.5 (formerly 3.4) corrected; final version, to appear in J. Algebraic Combin
Categories: math.RT, math.CO
Subjects: 05A15, 05E15, 13F60, 18E30
Related articles: Most relevant | Search more
arXiv:1303.1684 [math.RT] (Published 2013-03-07)
Ptolemy diagrams and torsion pairs in the cluster categories of Dynkin type D
arXiv:1706.06778 [math.RT] (Published 2017-06-21)
A geometric realization of the $m$-cluster categories of type $\tilde{D_n}$
arXiv:1111.4431 [math.RT] (Published 2011-11-18, updated 2012-03-07)
Generic bases for cluster algebras from the cluster category

Links

Toolbox