Asymptotic inequalities for k-ranks and their cumulation functions
Asymptotic formulas for the positive moments of rank and crank of partitions were obtained by K. Bringmann and K. Mahlburg recently. Mo-tivated by their works, in this paper, we prove asymptotic formulas for the k-ranks and their cumulation functions. Asymptotic inequalities between these combinat...
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| Format: | Journal Article |
| Language: | English |
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2014
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| Online Access: | https://hdl.handle.net/10356/102157 http://hdl.handle.net/10220/20357 |
| _version_ | 1811676830573264896 |
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| author | Mao, Renrong |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Mao, Renrong |
| author_sort | Mao, Renrong |
| collection | NTU |
| description | Asymptotic formulas for the positive moments of rank and crank of partitions were obtained by K. Bringmann and K. Mahlburg recently. Mo-tivated by their works, in this paper, we prove asymptotic formulas for the k-ranks and their cumulation functions. Asymptotic inequalities between these
combinatorial objects are also discovered. In particular, we show that, for fixed integer l and su ciently large N,
M(l;N) N(l;N)
and
M(l;N) < N(l;N);
whereM(l;N) (resp. N(l;N)) denotes the number partitions of N with crank (resp. rank) l. |
| first_indexed | 2024-10-01T02:27:42Z |
| format | Journal Article |
| id | ntu-10356/102157 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:27:42Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1021572023-02-28T19:33:46Z Asymptotic inequalities for k-ranks and their cumulation functions Mao, Renrong School of Physical and Mathematical Sciences DRNTU::Science::Mathematics Asymptotic formulas for the positive moments of rank and crank of partitions were obtained by K. Bringmann and K. Mahlburg recently. Mo-tivated by their works, in this paper, we prove asymptotic formulas for the k-ranks and their cumulation functions. Asymptotic inequalities between these combinatorial objects are also discovered. In particular, we show that, for fixed integer l and su ciently large N, M(l;N) N(l;N) and M(l;N) < N(l;N); whereM(l;N) (resp. N(l;N)) denotes the number partitions of N with crank (resp. rank) l. Accepted version 2014-08-21T01:49:27Z 2019-12-06T20:50:31Z 2014-08-21T01:49:27Z 2019-12-06T20:50:31Z 2013 2013 Journal Article Mao, R. (2013). Asymptotic inequalities for -ranks and their cumulation functions. Journal of Mathematical Analysis and Applications, 409(2), 729-741. 0022-247X https://hdl.handle.net/10356/102157 http://hdl.handle.net/10220/20357 10.1016/j.jmaa.2013.07.057 en Journal of mathematical analysis and applications © 2013 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Mathematical Analysis and Applications, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.jmaa.2013.07.057 ]. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics Mao, Renrong Asymptotic inequalities for k-ranks and their cumulation functions |
| title | Asymptotic inequalities for k-ranks and their cumulation functions |
| title_full | Asymptotic inequalities for k-ranks and their cumulation functions |
| title_fullStr | Asymptotic inequalities for k-ranks and their cumulation functions |
| title_full_unstemmed | Asymptotic inequalities for k-ranks and their cumulation functions |
| title_short | Asymptotic inequalities for k-ranks and their cumulation functions |
| title_sort | asymptotic inequalities for k ranks and their cumulation functions |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/102157 http://hdl.handle.net/10220/20357 |
| work_keys_str_mv | AT maorenrong asymptoticinequalitiesforkranksandtheircumulationfunctions |