My friends My family Acknowledgements

The following people contributed to the creation of this thesis. I would like to thank Anthony Henderson, who supervised my Honours thesis and set me on the path on re-search by encouraging me to start a PhD, and also for his latex code. I would also like to thank David Easdown for giving me the opportunity to start a PhD topic with him. Most of all, to Alex Molev: I still vividly remember the 2nd year introduction to modern algebra exam you set, which caused me to take a one year hiatus from pure mathematics. No one would believe me when I told them I had started doing a PhD with you. But the truth is this. You taught symmetric functions with such vigour and enthusiasm, and I was hooked immediately. Thank you for your dedication and hard work in supervising me, and for getting me out of tough spots when the chips were down. Thank you also for your willingness to share what you know and for listening to what I had to say. Without your advice none of this would have been possible. I am grateful to have had the opportunity to spend the last four years in research. During this time, I was able to develop my interests in coffee, cooking, bicycles, an