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Articles 1 - 8 of 8
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Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach
Patterns, Symmetries, And Mathematical Structures In The Arts, Sarah C. Deloach
Honors College Theses
Mathematics is a discipline of academia that can be found everywhere in the world around us. Mathematicians and scientists are not the only people who need to be proficient in numbers. Those involved in social sciences and even the arts can benefit from a background in math. In fact, connections between mathematics and various forms of art have been discovered since as early as the fourth century BC. In this thesis we will study such connections and related concepts in mathematics, dances, and music.
Gallai-Ramsey Number For Classes Of Brooms, Benjamin J. Hamlin
Gallai-Ramsey Number For Classes Of Brooms, Benjamin J. Hamlin
Electronic Theses and Dissertations
Given a graph $G$, we consider the problem of finding the minimum number $n$ such that any $k$ edge colored complete graph on $n$ vertices contains either a rainbow colored triangle or a monochromatic copy of the graph $G$, denoted $gr_k(K_{3}:G)$. More precisely we consider $G=B_{m,\ell}$ where $B_{m,\ell}$ is a broom graph with $m$ representing the number of vertices on the handle and $\ell$ representing the number of bristle vertices. We develop a technique to reduce the difficulty of finding $gr_{k}(K_{3}:B_{m,\ell})$, and use the technique to prove a few cases with a fixed handle length, but arbitrarily many bristles. Further, …
Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier
Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier
Electronic Theses and Dissertations
We explore a relatively new concept in edge-colored graphs called conflict-free connectivity. A conflict-free path is a (edge-) colored path that has an edge with a color that appears only once. Conflict-free connectivity is the maximal number of internally disjoint conflict-free paths between all pairs of vertices in a graph. We also define the c-conflict-free-connection of a graph G. This is the maximum conflict-free connectivity of G over all c-colorings of the edges of G. In this paper we will briefly survey the works related to conflict-free connectivity. In addition, we will use the probabilistic method to achieve a bound …
The Relationship Between Housing Affordability And Demographic Factors: Case Study For The Atlanta Beltline, Chapman T. Lindstrom
The Relationship Between Housing Affordability And Demographic Factors: Case Study For The Atlanta Beltline, Chapman T. Lindstrom
Electronic Theses and Dissertations
Housing affordability has been a widely examined subject for populations residing in major metropolitan regions around the world. The relationship between housing affordability and the city’s demographics and its volume of urban development are important to take into consideration. In the past two decades there has been an increasing volume of literature detailing Atlanta Georgia’s large-scale redevelopment project, the Atlanta BeltLine (ABL), and its relationship with Atlanta’s Metropolitan population and housing affordability. The first objective of this paper is to study the relationship between housing affordability at two scales within the Atlanta Metropolitan Area (AMA) for both renters and homeowners. …
Taking A Canon To The Adjunction Formula, Paul M. Harrelson
Taking A Canon To The Adjunction Formula, Paul M. Harrelson
Electronic Theses and Dissertations
In this paper, we show how the canonical divisor of a graph is related to the canonical divisor of its subgraph. The use of chip firing and the adjunction formula for graphs ex- plains said relation and even completes it. We go on to show the difference between the formula for full subgraphs and that of non-full subgraphs. Examples are used to simplify these results and to see the adjunction formula in action. Finally, we show that though the adjunction formula seems simple at first glance, it is somewhat complex and rather useful.
Homological Constructions Over A Ring Of Characteristic 2, Michael S. Nelson
Homological Constructions Over A Ring Of Characteristic 2, Michael S. Nelson
Electronic Theses and Dissertations
We study various homological constructions over a ring $R$ of characteristic $2$. We construct chain complexes over a field $K$ of characteristic $2$ using polynomials rings and partial derivatives. We also provide a link from the homology of these chain complexes to the simplicial homology of simplicial complexes. We end by showing how to construct all finitely-generated commutative differential graded $R$-algebras using polynomial rings and partial derivatives.
Totally Acyclic Complexes, Holly M. Zolt
Totally Acyclic Complexes, Holly M. Zolt
Electronic Theses and Dissertations
We consider the following question: when is every exact complex of injective modules a totally acyclic one? It is known, for example, that over a commutative Noetherian ring of finite Krull dimension this condition is equivalent with the ring being Iwanaga-Gorenstein. We give equivalent characterizations of the condition that every exact complex of injective modules (over arbitrary rings) is totally acyclic. We also give a dual result giving equivalent characterizations of the condition that every exact complex of flat modules is F-totally acyclic over an arbitrary ring.
Inverse Problems Related To The Wiener And Steiner-Wiener Indices, Matthew Gentry
Inverse Problems Related To The Wiener And Steiner-Wiener Indices, Matthew Gentry
Electronic Theses and Dissertations
In a graph, the generalized distance between multiple vertices is the minimum number of edges in a connected subgraph that contains these vertices. When we consider such distances between all subsets of $k$ vertices and take the sum, it is called the Steiner $k$-Wiener index and has important applications in Chemical Graph Theory. In this thesis we consider the inverse problems related to the Steiner Wiener index, i.e. for what positive integers is there a graph with Steiner Wiener index of that value?