Inequalities Between Ranks and Cranks
Higher moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms. This paper proves the first several cases of (and strengthens) a conjecture due to Garvan, whic...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Mathematical Society
2009
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| Online Access: | http://hdl.handle.net/1721.1/49528 |
| _version_ | 1826206211427532800 |
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| author | Bringmann, Kathrin Mahlburg, Karl Eugene |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bringmann, Kathrin Mahlburg, Karl Eugene |
| author_sort | Bringmann, Kathrin |
| collection | MIT |
| description | Higher moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms. This paper proves the first several cases of (and strengthens) a conjecture due to Garvan, which states that the moments of the crank function are always larger than the moments of the rank function. Furthermore, asymptotic estimates for these differences are also proven. |
| first_indexed | 2024-09-23T13:25:51Z |
| format | Article |
| id | mit-1721.1/49528 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:25:51Z |
| publishDate | 2009 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/495282022-09-28T14:08:59Z Inequalities Between Ranks and Cranks Bringmann, Kathrin Mahlburg, Karl Eugene Massachusetts Institute of Technology. Department of Mathematics Mahlburg, Karl Eugene Mahlburg, Karl Eugene Higher moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms. This paper proves the first several cases of (and strengthens) a conjecture due to Garvan, which states that the moments of the crank function are always larger than the moments of the rank function. Furthermore, asymptotic estimates for these differences are also proven. National Security Administration National Science Foundation 2009-11-04T16:43:22Z 2009-11-04T16:43:22Z 2009-02 2008-10 Article http://purl.org/eprint/type/SubmittedJournalArticle 0002-9939 1088-6826 http://hdl.handle.net/1721.1/49528 Bringmann, Kathrin, and Karl Mahlburg. “Inequalities between ranks and cranks.” 137 (2009): 2567-2574. en_US http://dx.doi.org/10.1090/S0002-9939-09-09806-2 Proceedings of The American Mathematical Society 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 American Mathematical Society Karl Mahlburg |
| spellingShingle | Bringmann, Kathrin Mahlburg, Karl Eugene Inequalities Between Ranks and Cranks |
| title | Inequalities Between Ranks and Cranks |
| title_full | Inequalities Between Ranks and Cranks |
| title_fullStr | Inequalities Between Ranks and Cranks |
| title_full_unstemmed | Inequalities Between Ranks and Cranks |
| title_short | Inequalities Between Ranks and Cranks |
| title_sort | inequalities between ranks and cranks |
| url | http://hdl.handle.net/1721.1/49528 |
| work_keys_str_mv | AT bringmannkathrin inequalitiesbetweenranksandcranks AT mahlburgkarleugene inequalitiesbetweenranksandcranks |