Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 11 of 11 for “"Matroid Theory"”.
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Lattice Subdivisions and Tropical Oriented Matroids, Featuring Products of Simplices
… lattice subdivisions and tropical oriented matroid theory. The first chapter describes desirable combinatorial properties of subdivisions of lattice polytopes, and how they can be used to address algebraic questions. Chapter two discusses tropical hyperplane arrangements and the tropical …
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A Dual Fano, and Dual Non-Fano Matroidal Network
<p>Matroidal networks are useful tools in furthering research in network coding. They have been used to show the limitations of linear coding solutions. In this paper we examine the basic information on network coding and matroid theory. We then go over the method of creating matroidal networks. …
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Tutte's first colour-cycle conjecture
… of W. T. Tutte's paper "A contribution to the theory of chromatic polynomials''. It is believed that this conjecture has not previously been resolved. Sections 25 and 38 are original. The remainder of the thesis is a summary of the requisite graph theory and matroid theory. Most of the material …
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Regular Round Matroids
<p>A matroid <em>M</em> is a finite set <em>E</em>, called the ground set of <em>M</em>, together with a notion of what it means for subsets of <em>E</em> to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors …
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Selected Problems on Matroid Minors
This dissertation begins with an introduction to matroids and graphs. In the first chapter, we develop matroid and graph theory definitions and preliminary results sufficient to discuss the problems presented in the later chapters. These topics include duality, connectivity, matroid minors, and …
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Classification of Ideal Secret Sharing Schemes
… between ideal secret sharing schemes and matroids. Therefore matroid theory is a natural tool to understand the structure of ideal secret sharing schemes. This thesis contributes to the characterization of ideal secret sharing schemes and the forensic aspects of secret sharing. We focus on …
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Probabilistic Topologies with Applications in Security and Resilience of Multi-Robot Systems
… diagrams, convolutional neural networks, matroid theory and more to tackle the problems related to probabilistic security and resilience where we find exact solutions, calculate bounds, solve optimization problems, and compute informative paths for exploration.
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Generating secret in a network
This monograph studies the theory of information through the multiuser secret key agreement problem. A general notion of mutual dependence is established for the secrecy capacity, as a natural generalization of Shannon's mutual information to the multivariate case. Under linear-type source models, …
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Applications of Powerset Operators, Especially to Matroids
… One of the fundamental theorems of vector space theory states that, \((\mathcal{S}^{\perp_v})^{\perp_v}\) is the subspace \textit{spanned} by \(\mathcal{S}\). Thus the ``spanning'' operator on the subsets of a vector space is the square of the ``orthogonal complement'' operator.</p><p>In matroid …
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Capturing elements in matroid minors
… dissertation, we begin with an introduction to a matroid as the natural generalization of independence arising in three different fields of mathematics. In the first chapter, we develop graph theory and matroid theory terminology necessary to the topic of this dissertation. In Chapter 2 and …
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Ramsey Theory Using Matroid Minors
This thesis considers a Ramsey Theory question for graphs and regular matroids. Specifically, how many elements N are required in a 3-connected graphic or regular matroid to force the existence of certain specified minors in that matroid? This question cannot be answered for an arbitrary collection …