This thesis explores some questions regarding the combinatorial structure of cluster
algebras and cluster categories, with a strong focus on cluster algebras and cluster …

We formalize the way in which one can think about cluster algebras of infinite rank by
showing that every rooted cluster algebra of infinite rank can be written as a colimit of rooted …

We apply our previous work on cluster characters for Hom-infinite cluster categories to the
theory of cluster algebras. We give a new proof of Conjectures 5.4, 6.13, 7.2, 7.10 and 7.12 …

Introduction to Cluster Algebras Chapters 4–5 Page 1 arXiv:1707.07190v3 [math.CO] 30 Aug
2021 Introduction to Cluster Algebras Chapters 4–5 (preliminary version) Sergey Fomin Lauren …

We prove the existence of cluster characters for Hom-infinite cluster categories. For this
purpose, we introduce a suitable mutation-invariant subcategory of the cluster category. We …

In the cluster algebra literature, the notion of a graded cluster algebra has been implicit
since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra …

Motivated by existing results about the Kronecker cluster algebra, this thesis is concerned
with two families of cluster algebras, which are two different ways of generalizing the …

For a skew-symmetrizable cluster algebra, which was actually verified in Gross et
al.(Canonical bases for cluster algebras, J. Amer. Math. Soc. 31 (2)(2018), 497–608) …

Unistructurality of cluster algebras Page 1 Unistructurality of cluster algebras Peigen Cao
and Fang Li Compositio Math. 156 (2020), 946–958. doi:10.1112/S0010437X20007113 …

Cluster algebras were introduced by Fomin and Zelevinsky [FZ] in 2002. Their original
motivation was coming from canonical bases in Lie Theory. Today the theory of cluster …