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On a Bound in Extremal Combinatorics
Doklady Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Raigorodskii, A. M., Sagdeev, A. A.
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Extremal Combinatorics of Reaction Systems
2014Extremal combinatorics is the study of the size that a certain collection of objects must have in order to certainly satisfy a property. Reaction systems are a recent formalism for computation inspired by chemical reactions. This work is a first contribution to the study of the behaviour of large reaction systems by means of extremal combinatorics.
Dennunzio Alberto +2 more
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Applications of Continuous Combinatorics to Quasirandomness and Extremal Combinatorics
2021The 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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Fully Computer-Assisted Proofs in Extremal Combinatorics
Proceedings of the AAAI Conference on Artificial Intelligence, 2023We present a fully computer-assisted proof system for solving a particular family of problems in Extremal Combinatorics. Existing techniques using Flag Algebras have proven powerful in the past, but have so far lacked a computational counterpart to derive matching constructive bounds.
Olaf Parczyk +3 more
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Several problems in extremal combinatorics
2023In 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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New results in extremal combinatorics
2021Extremal problems, in general, ask for the optimal size of certain finite objects when some restrictions are imposed. In extremal combinatorics, a major field in combinatorics, one studies how global properties guarantee the existence of local substructures, or equivalently, how avoiding local substructures poses a constraint on global quantities.
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Sumsets, Zero-Sums and Extremal Combinatorics
2006This 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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Several problems in extremal and probabilistic combinatorics
2023This 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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Algebraic, Extremal and Metric Combinatorics 1986
1988This book represents a comprehensive overview of the present state of progress in three related areas of combinatorics. It comprises selected papers from a conference held at the University of Montreal. Topics covered in the articles include association schemes, extremal problems, combinatorial geometrics and matroids, and designs.
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