\contentsline {section}{\numberline {1}Introduction}{2}{section.1}
\contentsline {section}{\numberline {2}Background}{3}{section.2}
\contentsline {subsection}{\numberline {2.1}Compositions and partitions}{3}{subsection.2.1}
\contentsline {subsection}{\numberline {2.2}Skew shapes and ribbons}{4}{subsection.2.2}
\contentsline {subsection}{\numberline {2.3}Skew Schur functions and ribbon Schur functions}{5}{subsection.2.3}
\contentsline {subsection}{\numberline {2.4}Box diagonal diagrams}{9}{subsection.2.4}
\contentsline {section}{\numberline {3}Ribbon operations for Schur-positivity}{12}{section.3}
\contentsline {subsection}{\numberline {3.1}Moving a cell from the first row}{13}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Exchanging adjacent rows}{17}{subsection.3.2}
\contentsline {section}{\numberline {4}Totally ordered equitable ribbons}{22}{section.4}
\contentsline {section}{\numberline {5}Large ribbons and short end rows}{31}{section.5}
\contentsline {section}{\numberline {6}Large ribbons and even distribution of long rows}{36}{section.6}
\contentsline {subsection}{\numberline {6.1}Minimal equitable ribbons}{47}{subsection.6.1}
