\contentsline {section}{\tocsection {}{1}{Introduction}}{1}
\contentsline {section}{\tocsection {}{2}{Generalized permutation patterns}}{2}
\contentsline {subsection}{\tocsubsection {}{2.1}{Mesh patterns and barred patterns}}{3}
\contentsline {subsubsection}{\tocsubsubsection {}{}{Describing the simple permutations with mesh patterns}}{4}
\contentsline {subsection}{\tocsubsection {}{2.2}{Marked mesh patterns}}{5}
\contentsline {subsection}{\tocsubsection {}{2.3}{Decorated patterns}}{6}
\contentsline {subsubsection}{\tocsubsubsection {}{}{More bars in more places}}{7}
\contentsline {subsection}{\tocsubsection {}{2.4}{Other generalizations}}{7}
\contentsline {section}{\tocsection {}{3}{Finding preimages of patterns}}{7}
\contentsline {subsection}{\tocsubsection {}{3.1}{The stack-sort operator}}{7}
\contentsline {subsubsection}{\tocsubsubsection {}{}{Stack-sortable permutations}}{8}
\contentsline {subsubsection}{\tocsubsubsection {}{}{West-$2$-stack-sortable permutations}}{8}
\contentsline {subsection}{\tocsubsection {}{3.2}{The bubble-sort operator}}{10}
\contentsline {section}{\tocsection {}{4}{Describing West-$3$-stack sortable permutations}}{11}
\contentsline {section}{\tocsection {}{5}{Open problems}}{18}
\contentsline {subsection}{\tocsubsection {}{}{Acknowledgements}}{19}
\contentsline {section}{\tocsection {}{}{References}}{19}