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Cluster Algebras And Maximal Green Sequences For Closed Surfaces, Eric Bucher
Cluster Algebras And Maximal Green Sequences For Closed Surfaces, Eric Bucher
LSU Doctoral Dissertations
Given a marked surface (S,M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider orientable surfaces of genus n with two interior marked points and no boundary component. We will construct a specific triangulation of this surface which yields a quiver. Then in the sense of work by Keller we will produce a maximal green sequence for this quiver. Since all finite mutation type cluster algebras can be associated to a surface, with some rare exceptions, this work …
Combinatorial Minimal Free Resolutions Of Ideals With Monomial And Binomial Generators, Trevor Mcguire
Combinatorial Minimal Free Resolutions Of Ideals With Monomial And Binomial Generators, Trevor Mcguire
LSU Doctoral Dissertations
In recent years, the combinatorial properties of monomials ideals and binomial ideals have been widely studied. In particular, combinatorial interpretations of minimal free resolutions have been given in both cases. In this present work, we will generalize existing techniques to obtain two new results. If Lambda is an integer lattice in the n-dimensional integers satisfying some mild conditions, S is the polynomial ring with n variables and R is the group algebra of S[Lambda], then the first result is resolutions of Lambda-invariant submodules of the Laurent polynomial ring in n variables as R-modules. A consequence will be the ability to …