Access Type
Open Access Dissertation
Date of Award
January 2016
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
Kyungyong Lee
Second Advisor
Frank Okoh
Abstract
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.
Recommended Citation
Nguyen, Ba, "Some New Combinatorial Formulas For Cluster Monomials Of Type A Quivers" (2016). Wayne State University Dissertations. 1568.
https://digitalcommons.wayne.edu/oa_dissertations/1568