Results 71 to 80 of about 125 (122)
Probabilistic and extremal studies in additive combinatorics
, 2023 The results in this thesis concern extremal and probabilistic topics in number theoretic settings. We prove sufficient conditions on when certain types of integer solutions to linear systems of equations in binomial random sets are distributed normally, results on the typical approximate structure of pairs of integer subsets with a given sumset ...
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Structure and randomness in extremal combinatorics
, 2017 In this thesis we prove several results in extremal combinatorics from areas including Ramsey theory, random graphs and graph saturation. We give a random graph analogue of the classical Andr´asfai, Erd˝os and S´os theorem showing that in some ways subgraphs of sparse random graphs typically behave in a somewhat similar way to dense graphs.
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Topics in metric geometry, combinatorial geometry, extremal combinatorics and additive combinatorics
, 2018 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 any $x,y\in X$ we have $d(f_i(x),f_i(y))\leq\lambda ...
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Continuous optimisation in extremal combinatoricst
, 2017 In this thesis we explore instances in which tools from continuous optimisation can be used to solve problems in extremal graph and hypergraph theory. We begin by introducing a generalised notion of hypergraph Lagrangian and use tools from the theory of nonlinear optimisation to explore some of its properties.
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Extremal combinatorics in generalized Kneser graphs
, 2009 This thesis focuses on the interplay of extremal combinatorics and finite geometry. Combinatorics is concerned with discrete (and usually finite) objects. Extremal combinatorics studies how large or how small a collection of finite objects can be under certain restrictions. Those objects can be sets, graphs, vectors, etc.
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Problems in extremal and probabilistic combinatorics
, 2018 In this thesis we consider some problems in extremal and probabilistic combinatorics. In Chapter 2 we determine the maximum number of induced cycles that can be contained in a graph on n ≥ n0 vertices, and show that there is a unique graph that achieves this maximum. This answers a question of Tuza. Let Qd denote the hypercube of dimension d. Given d ≥
Morrison, N, Noel, J
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Problems in Positional Games and Extremal Combinatorics
, 2017 Diese Dissertation besteht aus 5 Kapiteln. Das erste Kapitel dient als Einleitung und stellt die in der Dissertation behandelten Themen und Ergebnisse vor. Das zweite Kapitel befasst sich mit sogenannten ”strong Ramsey games”, bei denen zwei Spieler ab- wechselnd Kanten des vollst ̈andigen (Hyper-)Graphen beanspruchen. Gewinner des Spiels ist der erste
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Extremal combinatorics, graph limits and computational complexity
, 2016 This thesis is primarily focused on problems in extremal combinatorics, although we will also consider some questions of analytic and algorithmic nature. The d-dimensional hypercube is the graph with vertex set {0,1}d where two vertices are adjacent if they differ in exactly one coordinate.
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Preface: Levon Khachatrian’s legacy in extremal combinatorics
Discrete Applied Mathematics, 2017 Füredi, Zoltán, Katona, Gyula
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Theory of combinatorial limits and extremal combinatorics
In the past years, techniques from different areas of mathematics have been successfully applied in extremal combinatorics problems. Examples include applications of number theory, geometry and group theory in Ramsey theory and analytical methods to different problems in extremal combinatorics.\ud By providing an analytic point of view of many discrete
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