# MathSciDoc: An Archive for Mathematician ∫

#### CombinatoricsRepresentation Theorymathscidoc:2204.06001

Journal of Combinatorial Theory, Series A, 156, 119-141, 2018.5
In this paper, we give a complete classification of cotorsion pairs in a cluster category C of type A^\infty_\infty via certain configurations of arcs, called τ-compact Ptolemy diagrams, in an infinite strip with marked points. As applications, we classify t-structures and functorially finite rigid subcategories in C, respectively. We also deduce Liu-Paquette's classification of cluster tilting subcategories of C and Ng's classification of torsion pairs in the cluster category of type A^\infty_\infty.
@inproceedings{huimin2018cotorsion,
title={Cotorsion pairs in cluster categories of type A^\infty_\infty},
author={Huimin Chang, Yu Zhou, and Bin Zhu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429164329030432175},
booktitle={Journal of Combinatorial Theory, Series A},
volume={156},
pages={119-141},
year={2018},
}

Huimin Chang, Yu Zhou, and Bin Zhu. Cotorsion pairs in cluster categories of type A^\infty_\infty. 2018. Vol. 156. In Journal of Combinatorial Theory, Series A. pp.119-141. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429164329030432175.