Acknowledgements

To John Shareshian, for being an excellent advisor and valued mentor; I could not have done this without your guidance. To the faculty in the mathematics department from whom I’ve learned so much, especially Renato Feres, Gary Jensen, Mohan Kumar, John McCarthy, Rachel Roberts, and David Wright. To the other graduate students who have been great friends and colleagues, especially Kim, Jeff and Paul. To Matthias Beck and Sinai Robins for teaching me about Ehrhart theory and writing a great book; special thanks to Matt for introducing me to open problems re-garding Ehrhart polynomial roots and coefficients. To Mike Develin for collaborating and sharing his good ideas. To all of the members of the combinatorics community who I have had the pleasure of working with and learning from over the last fe