\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Combinatorial background}{}% 2
\BOOKMARK [1][-]{section.3}{Marczinzik's conjecture and its refinement}{}% 3
\BOOKMARK [1][-]{section.4}{Dyck paths and 321-avoiding permutations}{}% 4
\BOOKMARK [1][-]{section.5}{321-avoiding permutations and Motzkin paths}{}% 5
\BOOKMARK [1][-]{section.6}{Acknowledgments}{}% 6