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 20 of 284 for “"combinatorics"”.
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Topics in metric geometry, combinatorial geometry, extremal combinatorics and additive combinatorics
… we answer a question of Nathanson in additive combinatorics about sums, differences and products of sets in $\mathbb{Z}_N$ (the integers modulo $N$). For all $\epsilon>0$ and $k\in\mathbb{N}$, we construct a subset $A\subset\mathbb{Z}_N$ for some $N$, such that $|A^2+kA|\leq\epsilon N$, while …
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Topics In Probabilistic Combinatorics
This paper is a compilation of results in combinatorics utilizing the probabilistic method. Below is a brief description of the results highlighted in each chapter. Chapter 1 provides basic definitions, lemmas, and theorems from graph theory, asymptotic analysis, and probability which will be used …
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Topics in Probabilistic Combinatorics
This thesis consists of an introduction and eight chapters, each devoted to a different combinatorial problem. In Chapter 2, we study problems regarding reconstructing the entirety, or a large subset, of a point set $V$ embedded in either $\mathbb{R}$ or $\mathbb{R}^d$, where the only information …
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Problems in extremal combinatorics
We consider a variety of problems in extremal graph and set theory. Given a property $\Gamma$ and a family of sets ${\mathcal F}$, let $f({\mathcal F},\Gamma)$ be the size of the largest subfamily of ${\mathcal F}$ having property $\Gamma$. Let $f(m,\Gamma)$ be the minimum of $f({\mathcal …
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Combinatorics of finite sets
Let $\lbrack n\rbrack = \{1,2,\..., n\},A$ and let $2\sp{\lbrack n\rbrack}$ represent the subset lattice of (n) with sets ordered by inclusion. A collection I of subsets of (n) is called an ideal if every subset of a member of I is also in I. An intersecting family S in 2$\sp{\lbrack n\rbrack }$ is …
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Polynomials in algebraic combinatorics
A long-standing theme in algebraic combinatorics is to study bases of the rings of symmetric functions, quasisymmetric functions, and polynomials. Classically, these bases are homogeneous functions, however, the introduction of K-theoretic combinatorics has led to increased interest in finding …
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Combinatorics and Metric Geometry
This thesis consists of an introduction and seven chapters, each devoted to a different combinatorial problem. In Chapters 1 and 2, we consider the main subject of this thesis; the sharp stability of the Brunn-Minkowski inequality (BM). This celebrated theorem from the 19th century asserts that for …
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Topics in arithmetic combinatorics
This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L^1-norm of the Fourier transform, and the closely related idempotent theorem. The vast majority of the results regarding these problems are, in some sense, qualitative or at the very least infinitary and it …
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Combinatorics of ribbon tableaux
This thesis begins with the study of a class of symmetric functions ... Which are generating functions for ribbon tableaux (hereon called ribbon functions), first defined by Lascoux, Leclerc and Thibon. Following work of Fomin and Greene, I introduce a set of operators called ribbon Schur operators …
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Studies in projective combinatorics
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.
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The combinatorics of adinkras
Adinkras are graphical tools created to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown nontrivial connections with coding theory and Clifford algebras. Furthermore, adinkras offer many easy-to-state and …
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Combinatorics of determinantal identities
In this thesis, we apply combinatorial means for proving and generalizing classical determinantal identities. In Chapter 1, we present some historical background and discuss the algebraic framework we employ throughout the thesis. In Chapter 2, we construct a fundamental bijection between certain …
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Forcing in Analysis and Combinatorics
… forcing technique in the context of Analysis and Combinatorics by: (1) Constructing a model of Set Theory in which strong measure zero subsets of the real line are meager-additive while Borel’s conjecture fails, answering a long-standing question due to Bartoszy\'nski and Judah. (2) Constructing a …
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Topics in combinatorics and algorithms
This thesis studies several topics in theoretical computer science. First, the author shows that $5n-4$ is a tight lower bound on the number of edges in the visibility graph of n non-intersecting line segments in the plane.
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Two topics in arithmetic combinatorics
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms
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Extremal Combinatorics and Universal Algorithms
… different areas of mathematics: automata theory, combinatorics of partially ordered sets and extremal combinatorics. Firstly, we focus on some new automata that do not seem to have occurred much in the literature, that of solvability of mazes. For our model, a maze is a countable strongly …
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Algebraic combinatorics of hyperplane arrangements
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987.
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Free resolutions, combinatorics, and geometry
Boij-Söderberg theory is the study of two cones: the first is the cone of graded Betti tables over a polynomial ring, and the second is the cone of cohomology tables of coherent sheaves over projective space. Each cone has a triangulation induced from a certain partial order. Our first result gives …
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The combinatorics of reduced decompositions
This thesis examines several aspects of reduced decompositions in finite Coxeter groups. Effort is primarily concentrated on the symmetric group, although some discussions are subsequently expanded to finite Coxeter groups of types B and D. In the symmetric group, the combined frameworks of …
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Extremal Graph Theory and Enumerative Combinatorics
<p>This thesis consists of research on two topics.The first topic is about different middle parts of trees, such as center, centroid, subtree core. In this work, we considered how far apart (with given order of the tree) two different `middle points' can be and when such maximum distances are …
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