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Matchings and Representation Theory

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Lindzey_Nathan.pdf (688.04 KB)

Date

2018-12-20

Authors

Lindzey, Nathan

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Publisher

University of Waterloo

Abstract

In this thesis we investigate the algebraic properties of matchings via representation theory. We identify three scenarios in different areas of combinatorial mathematics where the algebraic structure of matchings gives keen insight into the combinatorial problem at hand. In particular, we prove tight conditional lower bounds on the computational complexity of counting Hamiltonian cycles, resolve an asymptotic version of a conjecture of Godsil and Meagher in Erdos-Ko-Rado combinatorics, and shed light on the algebraic structure of symmetric semidefinite relaxations of the perfect matching problem

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Keywords

Representation Theory, Extremal Combinatorics, Symmetric Functions

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URI

http://hdl.handle.net/10012/14267

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Theses
Combinatorics and Optimization