Results 171 to 180 of about 934 (196)

Applications of Continuous Combinatorics to Quasirandomness and Extremal Combinatorics

2021
The theory of limits of dense combinatorial objects studies the asymptotic behavior of densities of small templates in an increasing sequence of combinatorial objects. The inaugural limit theory of graphons captures limits of graph sequences in a semantic limit object that can be thought of as a fractional version of an adjacency matrix. Since graphons
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Several problems in extremal combinatorics

This thesis presents three distinct contributions to extremal combinatorics. First, it resolves a conjecture by Bollobás, Brightwell, and Leader on the prevalence of unate k-SAT functions, proving that for all fixed k≥2, almost all k-SAT functions on n variables are unate (i.e., monotone after negating certain variables).
Dong, Dingding
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IV.19 Extremal and Probabilistic Combinatorics

2010
Noga Alon, Michael Krivelevich
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Remark on one problem in extremal combinatorics

Problems of Information Transmission, 2012
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Several problems in extremal combinatorics

2023
In this thesis, we study several problems from combinatorial probability theory, discrete geometry and extremal graph theory. We establish several extremal results towards our problems. Some of the theorems extend or generalize previous results, and others resolve open problems in the literature.
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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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Challenges and Results in Extremal Combinatorics.

2023
In this thesis, we address several questions in extremal, probabilisitic, and additive combinatorics, with applications to theoretical computer science. We start by addressing the sunflower lemma of Erd ̋os and Rado, and some related problems about set systems. A sunflower with r petals is a collection of r sets so that the intersection of each pair is
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Several problems in extremal and probabilistic combinatorics

2023
This thesis consists of four parts, each on a different problem in extremal or probabilistic combinatorics. Chapters 2 and 3 center around hypergraph versions of foundational problems in extremal combinatorics. Chapter 4 concerns algorithmic and structural results for a probabilistic model motivated by statistical physics, and Chapter 5 details the use
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Extremal problems in combinatorics and geometry

This thesis is comprised of four chapters relating to combinatorics and geometry. More specifically, the main topics of the dissertation are incidence geometry and Euclidean Ramsey theory. In Chapter 2, we study the Erdős unit distance problem. In particular, we prove a structural result for pointsets determining many unit distances from a small ...
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Sumsets, Zero-Sums and Extremal Combinatorics

2006
This thesis develops and applies a method of tackling zero-sum additive questions, especially those related to the Erdos-Ginzburg-Ziv Theorem (EGZ), through the use of partitioning sequences into sets, i.e., set partitions. Much of the research can alternatively be found in the literature spread across nine separate articles, but is here collected into
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