Geometry and complexity of O'Hara's algorithm

Details Geometry and complexity of O'Hara's algorithm Geometry and complexity of O'Hara's algorithm

2007-10-08

arxiv.org/abs/0710.1459v2

Mathematics

Combinatorics

20 pages, 4 figures

Scientific paper

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.

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