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Showing 1 to 9 of 9 for “"Cluster algebra"”.
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Query processing in heterogeneous distributed database management systems
… addressed the first issue by developing an algebraic query language called cluster algebra. The cluster algebra consists of the following operations: (a) Selection, union, intersection and difference, which are extensions of their relational algebraic counterparts to heterogeneous databases; …
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Cluster Algebras and Maximal Green Sequences for Closed Surfaces
… 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 …
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Applications of graded methods to cluster variables in arbitrary types
… properties of gradings on several examples of cluster algebras, primarily of infinite type. We start by considering two classes of finite type cluster algebras: those of type Bn and Cn. We give the number of cluster variables of each occurring degree and verify that the grading is balanced. …
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Categorifications of Cluster Varieties
… thesis we study additive categorifications of algebraic varieties whose coordinate rings admit a cluster algebra structure. The presence of a cluster structure has important implications for the geometry of a variety including the existence of canonical linearly independent sets of regular …
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Cluster Structure for Mirkovic-Vilonen Cycles and Polytopes
… Mirkovic-Vilonen (MV) basis for semisimple Lie algebras and compare this to the associated cluster algebra to investigate the question of whether or not the cluster variables are in the MV basis. We begin with finding analogues of the cluster structure among MV cycles and MV polytopes. In …
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Cluster algebras and discrete integrable systems
This dissertation presents connections between cluster algebras and discrete integrable systems, especially T-systems and their specializations/generalizations. We give connections between the T-system or the octahedron relation, and the pentagram map and its various generalizations. A solution to …
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Arrangement of minors in the positive Grassmannian
… to the positive Grassmannian and the associated cluster algebra. However, we also construct examples of arrangements of smallest minors which are not weakly separated using chain reactions of mutations of plabic graphs. In the second chapter, we investigate arrangements of tth largest minors and …
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Cluster algebras from surfaces and their bases
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-20 without embargo terms
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Nakajima's (Q, T)-characters as quantum cluster variables
This Dissertation was approved for publication on 2017-05-03 at 09:13.