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https://hdl.handle.net/10356/102157
Title: | Asymptotic inequalities for k-ranks and their cumulation functions | Authors: | Mao, Renrong | Keywords: | DRNTU::Science::Mathematics | Issue Date: | 2013 | Source: | Mao, R. (2013). Asymptotic inequalities for -ranks and their cumulation functions. Journal of Mathematical Analysis and Applications, 409(2), 729-741. | Series/Report no.: | Journal of mathematical analysis and applications | Abstract: | 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. | URI: | https://hdl.handle.net/10356/102157 http://hdl.handle.net/10220/20357 |
ISSN: | 0022-247X | DOI: | 10.1016/j.jmaa.2013.07.057 | Schools: | School of Physical and Mathematical Sciences | Rights: | © 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 ]. | Fulltext Permission: | open | Fulltext Availability: | With Fulltext |
Appears in Collections: | SPMS Journal Articles |
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jmaa (2).pdf | 332.23 kB | Adobe PDF | View/Open |
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