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Some New Combinatorial Formulas For Cluster Monomials Of Type A Quivers, Ba Nguyen
Some New Combinatorial Formulas For Cluster Monomials Of Type A Quivers, Ba Nguyen
Wayne State University Dissertations
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.