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.

Included in

Mathematics Commons

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