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Asymptotic inequalities for -ranks and their cumulation functions.
- Source :
-
Journal of Mathematical Analysis & Applications . Jan2014, Vol. 409 Issue 2, p729-741. 13p. - Publication Year :
- 2014
-
Abstract
- Abstract: Asymptotic formulas for the positive moments of rank and crank of partitions were obtained by K. Bringmann and K. Mahlburg recently. Motivated by their works, in this paper, we prove asymptotic formulas for the -ranks and their cumulation functions. Asymptotic inequalities between these combinatorial objects are also discovered. In particular, we show that, for fixed integer and sufficiently large , and where (resp. ) denotes the number partitions of with crank (resp. rank) . [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 409
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 90390913
- Full Text :
- https://doi.org/10.1016/j.jmaa.2013.07.057