\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Preliminaries}{}% 2
\BOOKMARK [2][-]{subsection.2.1}{Basic definitions and notation}{section.2}% 3
\BOOKMARK [2][-]{subsection.2.2}{Auxiliary results}{section.2}% 4
\BOOKMARK [1][-]{section.3}{Finiteness proof for irreducible matrices}{}% 5
\BOOKMARK [1][-]{section.4}{Counting quasi-idempotent matrices}{}% 6
\BOOKMARK [2][-]{subsection.4.1}{Analysis of the asymptotics}{section.4}% 7
\BOOKMARK [3][-]{subsubsection.4.1.1}{Asymptotics of generalized partitions}{subsection.4.1}% 8
\BOOKMARK [1][-]{section.5}{Acknowledgments}{}% 9