Asymptotic inequalities for k-ranks and their cumulation functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Mao, Renrong

关键词: Asymptotic;    Cumulation functions;    Circle method;    k-ranks;    Inequalities;    Partial theta functions;    q-series;   

DOI  :  10.1016/j.jmaa.2013.07.057

来源: Elsevier

【 摘 要 】

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 k-ranks and their cumulation functions. Asymptotic inequalities between these combinatorial objects are also discovered. In particular, we show that, for fixed integer land sufficiently large N, M(l, N) similar to N(l, N) and M(l, N) < N(l, N), where, M(I, N) (resp. (l, N)) denotes the number partitions of N with crank (resp. rank) l. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free