Matchings and Representation Theory

Representation Theory;Extremal Combinatorics;Symmetric Functions

Lindzey, Nathanadvisor:Cheriyan, Joseph ; affiliation1:Faculty of Mathematics ; advisor:Godsil, Christopher ; Cheriyan, Joseph ; Godsil, Christopher ;

University of Waterloo

关键词: Extremal Combinatorics;    Symmetric Functions;    Doctoral Thesis;    Representation Theory;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/14267/3/Lindzey_Nathan.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

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