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: | Article |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/102157 http://hdl.handle.net/10220/20357 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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