m-Colored Exchange Graphs and Associated Combinatorial Objects

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m-Colored Exchange Graphs and Associated Combinatorial Objects

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2022-12

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In this thesis we provide exposition and conjectures regarding acyclic type A m-colored oriented exchange graphs of m-colored quivers and related combinatorial objects. These related objects include the m-Cambrian lattice, flip graphs of (m+2)-angulated polygons, Stokes poset, and the H-triangle of the type A cluster complex. The main conjectures stated are that the m-colored oriented exchange graph of a quiver is isomorphic to the m-Cambrian lattice for the corresponding Coxeter element, and to the flip graph of the corresponding (m+2)-angulated polygon. Additionally, a conjecture is made regarding an isomorphism between Stokes poset and what we refer to as the green oriented exchange graph of a quiver, and a combinatorial interpretation of the H-triangle of the type A cluster complex in terms of m-colored quivers is also conjectured.

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University of Minnesota M.S. thesis. December 2022. Major: Mathematics. Advisor: Gregg Musiker. 1 computer file (PDF); iv, 41 pages.

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Farrell, Libby. (2022). m-Colored Exchange Graphs and Associated Combinatorial Objects. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/252481.

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