Matchings and Representation Theory
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Date
2018-12-20
Authors
Lindzey, Nathan
Journal Title
Journal ISSN
Volume Title
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