\BOOKMARK [1][-]{section.1}{Introduction and statement of main results}{}% 1
\BOOKMARK [1][-]{section.2}{Definitions and background material}{}% 2
\BOOKMARK [1][-]{section.3}{Proofs}{}% 3
\BOOKMARK [2][-]{subsection.3.1}{Recurrence for the M\366bius numbers}{section.3}% 4
\BOOKMARK [2][-]{subsection.3.2}{Building the generating functions}{section.3}% 5
\BOOKMARK [2][-]{subsection.3.3}{The initial value problem}{section.3}% 6
\BOOKMARK [2][-]{subsection.3.4}{Verifying the generating functions both solve the initial value problem}{section.3}% 7
\BOOKMARK [1][-]{section.4}{Acknowledgements}{}% 8