In this paper we analyze O'Hara's partition bijection. We present three type
of results. First, we show that O'Hara's bijection can be viewed geometrically
as a certain scissor congruence type result. Second, we obtain a number of new
complexity bounds, proving that O'Hara's bijection is efficient in several
special cases and mildly exponential in general. Finally, we prove that for
identities with finite support, the map of the O'Hara's bijection can be
computed in polynomial time, i.e. much more efficiently than by O'Hara's
construction.Comment: 20 pages, 4 figure