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Substructure Densities in Extremal Combinatorics

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thesis
posted on 19.06.2021, 00:31 by TIMOTHY FONG NAM CHAN
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. In this thesis, we investigate three topics concerning combinatorial density: We study the interplay between the densities of cycles of length 3 and 4 in large tournaments, we characterise quasirandomness in permutations, and we solve two open problems about the inducibility of trees.

History

Campus location

Australia

Principal supervisor

David Wood

Additional supervisor 1

Daniel Kráľ

Year of Award

2021

Department, School or Centre

Mathematics

Additional Institution or Organisation

University of Warwick

Course

Doctor of Philosophy (Joint award with the University of Warwick)

Degree Type

DOCTORATE

Faculty

Faculty of Science