\contentsline {section}{\numberline {1}Introduction}{2}{section.1}
\contentsline {section}{\numberline {2}Subsets with no sum-dominant sets}{4}{section.2}
\contentsline {section}{\numberline {3}Subsets with Finitely Many sum-dominant Sets}{6}{section.3}
\contentsline {subsection}{\numberline {3.1}Special Sum-Dominant Sets}{6}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Finitely Many Sum-Dominant Sets on a Sequence}{7}{subsection.3.2}
\contentsline {subsection}{\numberline {3.3}Proof of Theorem \ref {thm:finite}}{7}{subsection.3.3}
\contentsline {section}{\numberline {4}Sum-Dominant subsets of the prime numbers}{12}{section.4}
\contentsline {subsection}{\numberline {4.1}Admissible Prime Tuples and Prime Constellations}{13}{subsection.4.1}
\contentsline {subsection}{\numberline {4.2}Infinitude of sum-dominant subsets of the primes}{13}{subsection.4.2}
\contentsline {section}{\numberline {5}Future Work}{14}{section.5}
\contentsline {section}{\numberline {6}Acknowledgments}{14}{section.6}