\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Preliminaries}{}% 2
\BOOKMARK [1][-]{section.3}{Higher-order conjugation}{}% 3
\BOOKMARK [2][-]{subsection.3.1}{The extended line graph}{section.3}% 4
\BOOKMARK [1][-]{section.4}{The conjugate height}{}% 5
\BOOKMARK [1][-]{section.5}{Reciprocal compositions and recursive conjugation}{}% 6
\BOOKMARK [1][-]{section.6}{Zig-zag graphs and higher-order conjugates}{}% 7
\BOOKMARK [1][-]{section.7}{Enumeration}{}% 8
\BOOKMARK [2][-]{subsection.7.1}{Formulas for the number of conjugable compositions}{section.7}% 9
\BOOKMARK [3][-]{subsubsection.7.1.1}{Recurrence relations}{subsection.7.1}% 10
\BOOKMARK [2][-]{subsection.7.2}{Number of compositions with a fixed conjugate height}{section.7}% 11
\BOOKMARK [1][-]{section.8}{Combinatorial identities}{}% 12
\BOOKMARK [1][-]{section.9}{Acknowledgment}{}% 13