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 9 of 9 for “"combinatorial geometry"”.
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Some Results in Combinatorics and Combinatorial Geometry
… results in combinatorics and combnatorial geometry. In Chapter 2, we discuss union-closed families. For a given number of k-sets, how should we choose them so as to minimise the union-closed family that they generate? In this chapter we show that, if $\mathcal{A}$ is a family of k-sets of …
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Extremal problems in combinatorial geometry and Ramsey theory
… We describe diverse facets of interplay between geometry and combinatorics and consider several questions about existence of structures in various combinatorial settings. We make contributions to specific problems in combinatorial geometry, Ramsey theory and graph theory. We first study extremal …
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Topics in metric geometry, combinatorial geometry, extremal combinatorics and additive combinatorics
In this thesis, we consider several combinatorial topics, belonging to the areas appearing in the thesis title. Given a non-empty complete metric space $(X,d)$, a family of $n$ continuous maps $f_1,f_2,\dots,f_n\colon X\to X$ is a \emph{contractive family} if there exists $\lambda<1$ such that for …
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Probabilistic Methods
… very useful to solve problems in number theory, combinatorial geometry, linear algebra and real analysis. More recently, it has been applied in the development of efficient algorithms and in the study of various computational problems.Broadly, the probabilistic method is somewhat opposite of the …
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Tilings and other combinatorial results
… three tiling problems and three problems in combinatorial geometry, extremal graph theory and sparse Ramsey theory. We first consider tilings of $\mathbb{Z}^n$. In this setting a tile $T$ is just a finite subset of $\mathbb{Z}^n$. We say that $T$ tiles $\mathbb{Z}^n$ if the latter set admits …
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The inverse problem to the Voronoi diagram
The primary purpose of this thesis is to address the problem of solving the Inverse Problem for the Voronoi Diagram where the Inverse Problem is: Given a diagram that is in fact a Voronoi Diagram find the set of points X = {x1, x2, x3,…,x n} in R2 that will generate the diagram. In formulating a …
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Lights out game with cellular automation
1 PDF file (x, 53 pages)
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Extremal results for graphs and hypergraphs and other combinatorial problems
In this dissertation we present several combinatorial results, primarily concerning extremal problems for graphs and hypergraphs, but also covering some additional topics. In Chapter 2, we consider the following geometric problem of Croft. Let K be a convex body in R^d that contains a copy of …