Open Access Dissertation
Date of Award
Lots of research focuses on the combinatorics behind various bases of cluster
algebras. This thesis studies the natural basis of a type A cluster algebra, which consists of all cluster monomials. We introduce a new kind of combinatorial formulas for the cluster monomials in terms of globally compatible collections and broken lines. We give bijective proofs of these formulas by comparing with the well-known combinatorial models of the T-paths and of the perfect matchings in a snake diagram.
Nguyen, Ba, "Some New Combinatorial Formulas For Cluster Monomials Of Type A Quivers" (2016). Wayne State University Dissertations. 1568.