Results 161 to 170 of about 887,124 (211)
Substructure Densities in Extremal Combinatorics [PDF]
, 2021 One of the primary goals of combinatorial mathematics is to understand how an object's properties are influenced by the presence or multiplicity of a given substructure. Over time, it has become popular to highlight the asymptotic behaviour of objects by expressing results in terms of the density of substructures.
Timothy F. N. Chan
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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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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.
Barnaby Roberts
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Extremal combinatorics and universal algorithms
, 2018 In this dissertation we solve several combinatorial problems in 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.
S. David
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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. In this note, we present a fractional version of Haemers' bound on the Shannon capacity of a graph, which is originally due to Blasiak.
Christopher Cox
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Local to Global Phenomenon and Other Topics in Probabilistic and Extremal Combinatorics
, 2021 Matija Bucić
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Continuous optimisation in extremal combinatorics
, 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.
Matthew Jenssen
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An Experimental Evaluation of a Function in Extremal Combinatorics*
2021 International Conference on Computational Science and Computational Intelligence (CSCI), 2021We investigate the validity of a candidate formula for an extremal function introduced by Ferrara et al. The function is defined to be the minimum degree sum such that every bigraphic pair with a given number of terms in each part and at least this ...
Kai Wang, Hong Zhang
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