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 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&#...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier
2015
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| Online Access: | http://hdl.handle.net/1721.1/96288 |
| _version_ | 1811083475805011968 |
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| author | Konvalinka, Matjaz Pak, Igor |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Konvalinka, Matjaz Pak, Igor |
| author_sort | Konvalinka, Matjaz |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:33:40Z |
| format | Article |
| id | mit-1721.1/96288 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:33:40Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/962882022-10-01T09:46:36Z Geometry and complexity of O'Hara's algorithm Konvalinka, Matjaz Pak, Igor Massachusetts Institute of Technology. Department of Mathematics Konvalinka, Matjaz 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. National Science Foundation (U.S.) 2015-03-31T18:01:45Z 2015-03-31T18:01:45Z 2008-09 2007-10 Article http://purl.org/eprint/type/JournalArticle 01968858 1090-2074 http://hdl.handle.net/1721.1/96288 Konvalinka, Matjaz, and Igor Pak. “Geometry and Complexity of O’Hara’s Algorithm.” Advances in Applied Mathematics 42, no. 2 (February 2009): 157–175. © 2008 Elsevier Inc. en_US http://dx.doi.org/10.1016/j.aam.2008.06.005 Advances in Applied Mathematics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Elsevier Elsevier |
| spellingShingle | Konvalinka, Matjaz Pak, Igor Geometry and complexity of O'Hara's algorithm |
| title | Geometry and complexity of O'Hara's algorithm |
| title_full | Geometry and complexity of O'Hara's algorithm |
| title_fullStr | Geometry and complexity of O'Hara's algorithm |
| title_full_unstemmed | Geometry and complexity of O'Hara's algorithm |
| title_short | Geometry and complexity of O'Hara's algorithm |
| title_sort | geometry and complexity of o hara s algorithm |
| url | http://hdl.handle.net/1721.1/96288 |
| work_keys_str_mv | AT konvalinkamatjaz geometryandcomplexityofoharasalgorithm AT pakigor geometryandcomplexityofoharasalgorithm |