It was three grad students of Arizona
To learning much inclined,
Who went to study genus zero one-face maps,
Though not all were of like mind.

The first was enticed by the graphical representation,
and its eigenvalues he set out to calculate.
The second was a fan of dyck paths,
and a dyck path representation he did create.
The third chose to study pair partitions,
in his mind, the best representation without debate.

What a fortuitous day it was indeed,
when these three students decided to share.
For what interesting results can be found
if all three representations are examined with care.