TITLE: Normal form(s) for the elements of hyperbolic triangle groups
QUESTION [5 upvotes]: I'm seeking a reference or a sketch for any sort of normal form that would enable rapid enumeration without redundancies of the elements of hyperbolic triangle groups and/or von Dyck groups.

REPLY [3 votes]: The general reference for this topic is "Word processing in groups", Epstein et. al., MR1161694 (93i:20036). Your groups all have automatic structures, and that book gives an enumeration method as you ask for, which applies to any automatic structure on a group.