Geometry and complexity of O'Hara's algorithm
In this paper we analyze O'Hara's partition bijection. We present three type of results. First, we see that O'Hara's bijection can be viewed geometrically as a certain scissor congruence type result. Second, we present a number of new complexity bounds, proving that O'Hara&#...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2009-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2692/pdf |
| Summary: | In this paper we analyze O'Hara's partition bijection. We present three type of results. First, we see that O'Hara's bijection can be viewed geometrically as a certain scissor congruence type result. Second, we present a number of new complexity bounds, proving that O'Hara's bijection is efficient in most cases and mildly exponential in general. Finally, we see 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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| ISSN: | 1365-8050 |