Add to ORKGTo my advisor, John Shareshian. I am grateful for our many conversations and the chance to experience your viewpoint of learning and doing mathematics. Thank you for inspiring me and forming me into a better mathematician. To Jesús De Loera, from whom I learned about my thesis problem. You have been a constant source of encouragement and assistance. To Weixong Zhang for granting me access to great computing resources, without which I could not have completed this research. Thanks also to Sharlee Climer for providing me this connection and for her patience in answering my questions about CPLEX. To the Monticello College Foundation and the Mr. and Mrs. Spencer T. Olin Fellowship program, not only for providing me funding for my years of gradu...