Cyclic Sieving for torsion pairs in the cluster category of Dynkin type A_n
Abstract
Recently, a combinatorial model for torsion pairs in the cluster category of Dynkin type A_n was introduced, and used to derive an explicit formula for their number. In this article we determine the number of torsion pairs that are invariant under bfold application of AuslanderReiten translation. It turns out that the set of torsion pairs together with AuslanderReiten translation, and a natural qanalogue of the formula for the number of all torsion pairs exhibits the cyclic sieving phenomenon.
 Publication:

arXiv eprints
 Pub Date:
 January 2011
 arXiv:
 arXiv:1101.1020
 Bibcode:
 2011arXiv1101.1020K
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 17 pages, 4 pdfFigures