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New results in extremal combinatorics [PDF]
, 2021 Extremal 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.
C. Wong
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On a Bound in Extremal Combinatorics
Doklady Mathematics, 2018A new statement of a recent theorem of [1, 2] on the maximum number of edges in a hypergraph with forbidden cardinalities of edge intersections is given. This statement is fundamentally simpler than the original one, which makes it possible to obtain important corollaries in combinatorial geometry and Ramsey theory.
A. Raigorodskii, A. Sagdeev
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Problems in Coding Theory and Extremal Combinatorics
, 2020This dissertation consists of ?five papers whose subjects are mostly disjoint. Below are their abstracts and citation information.On a fractional version of Haemers' bound.
Christopher Cox
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Structure and randomness in extremal combinatorics
, 2017In 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 ...
Barnaby Roberts
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The combinatorics and extreme value statistics of protein threading [PDF]
Annals of Combinatorics, 1999 In protein threading, one is given a protein sequence, together with a database of protein core structures that may contain the natural structure of the sequence. The object of protein threading is to correctly identify the structure(s) corresponding to the sequence.
John L. Spouge +2 more
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Sumsets, Zero-Sums and Extremal Combinatorics [PDF]
, 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
David J. Grynkiewicz
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Remark on one problem in extremal combinatorics
Problems of Information Transmission, 2012 We reduce the problem of determining the maximum number of permutations of a finite set such that any pair of permutations has at least t common transpositions to the problem of determining the maximum number of permutations of finite set such that any pair has at least t common fixed points. The latter problem was solved by the author in [1].
Vladimir Blinovsky
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Continuous optimisation in extremal combinatorics
, 2017In 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
Matthew Jenssen
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Algebraic, Extremal and Metric Combinatorics 1986
, 1988 This 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.
Michel Deza +3 more
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