Some inequalities for Garvan's bicrank function of 2-colored partitions
作者: Shane ChernDazhao TangLiuquan Wang
作者单位: 1Department of Mathematics The Pennsylvania State University University Park, PA 16802, U.S.A.
2College of Mathematics and Statistics Chongqing University 401331, Chongqing, P.R. China
3School of Mathematics and Statistics Wuhan University 430072, Wuhan, P.R. China
刊名: Acta Arithmetica, 2019, Vol.190 , pp.171-191
来源数据库: Institute of Mathematics Polish Academy of Sciences
DOI: 10.4064/aa180507-7-11
原始语种摘要: In order to provide a unified combinatorial interpretation of congruences modulo $5$ for 2-colored partition functions, Garvan introduced a bicrank statistic in terms of weighted vector partitions. In this paper, we obtain some inequalities between the bicrank counts $M^{*}(r,m,n)$ for $m=2$, $3$ and $4$ via their asymptotic formulas and some $q$-series techniques. These inequalities are parallel to Andrews and Lewis’ results on the rank and crank counts for ordinary partitions.
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  • statistic 统计量
  • asymptotic 渐近的
  • colored 有色的
  • function 函数
  • formulas 公式
  • terms 术语
  • crank 曲柄
  • combinatorial 组合
  • counts 计数
  • provide 规定