Equality of P-partition Generating Functions

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

The Persistence of Shattered Dreams: a Comparative Study of the Audacity of the American Dream

In my thesis, I use historical and literary analysis to study how the concept of the American Dream was popularized during the Great Depression and how cultural understanding of the term has changed following the 2008 Recession. By comparing popular media, literature, and political documents within a historical framework from the 1930s and after 2008 through the present day, I analyze how the term ¿American Dream¿ has persisted as an element of the United States¿ national ethos. I explore why the language of the American Dream does not appear to carry the same resonance in American society as in the 1930s, even though the post-2008 economic environment is somewhat comparable to conditions created by the Great Depression and associated reform measures. This comparative historical approach in scholarly studies of the American Dream is unique because the two periods have not previously been discussed in relation to one another in order to show transformations in cultural understanding of the Dream. The American Dream, both embodying a dual identity as an aspiration to aspire to and also as a delusional fantasy which can lead to cynicism, is a highly complex idea in lived experience. The concept¿s ambiguous nature allows for individuals to interpret it differently, allowing for the term to remain resilient throughout different periods in United States history. While the meaning of the term has been subject to change, it is grounded upon an idealistic concept of American individualism and hope that through one¿s merit, one will be able to achieve one¿s vision of success. Through interdisciplinary analysis, I show that the American Dream will alter to suit the needs of contemporary society and the term¿s power will continue to endure in society despite evidence of rising cynicism since 2008.

Health, Justice, and Fairness

In this study I will endeavor to show that the American system of health care violates any conception of distributive justice understood as equality of opportunity. This system fails to provide equal access through a lack of universal insurance, a consumer driven conception of quality, and a system wide focus on cost control, leaving millions of Americans exposed to the ravages of disease. However, if health is understood as an antecedent for one's ability to function across a number of categories that have been objectively deemed as vital to engage in a life that is fully human than the commitment our nation has to the protection of fair equality of opportunity, established by our adoption of a Rawlsian conception of justice, necessitates a revision of our nation's conception of quality to encapsulate health outcomes as well as the advent of a system of universal coverage. Quality care will come to be understood as care that returns to the patient the ability to function across those categories of functioning that illness has jeopardized, and this conception of quality will precipitate system wide reform geared at the creation of positive health outcomes. This paper will articulate this argument by reconstructing and synthesizing precepts from the contemporary philosophical sources and then applying these to the practical workings of our healthcare system, while concurrently demonstrating that a system of distributive justice is compatible with the creation of a universal system of healthcare.