Combinatorics of Cluster Algebras from Surfaces
2016-08
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Combinatorics of Cluster Algebras from Surfaces
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2016-08
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We construct a periodic infinite frieze using a class of peripheral elements of a cluster algebra of type D or affine A. We discover new symmetries and formulas relating the entries of this frieze and bracelet elements. We also present a correspondence between Broline, Crowe and Isaacs’s classical matching tuples and various recent interpretations of elements of cluster algebras from surfaces. We extend a T-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of type D. We further generalize our work and present T-path formulas for tagged arcs with one or two notchings on a marked surface with punctures.
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University of Minnesota Ph.D. dissertation. August 2016. Major: Mathematics. Advisor: Gregg Musiker. 1 computer file (PDF); viii, 183 pages.
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Gunawan, Emily. (2016). Combinatorics of Cluster Algebras from Surfaces. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/182830.
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