论文标题
Bressoud-Subbarao类型的加权分区身份
Bressoud-Subbarao type weighted partition identities for a generalized divisor function
论文作者
论文摘要
1984年，Bressoud和Subbarao通过组合参数获得了广义的除数函数的有趣加权分区身份。最近，最后三名命名的作者发现了Bressoud和Subbarao的上述身份的分析证明，从Ramanujan的$ Q $ Series身份开始。在本文中，我们重新审视了Bressoud和Subbarao的组合论证，并获得了更一般的加权分区身份。此外，借助分数差异操作员，我们建立了一些Bressoud-Subbarao型加权分区身份，从Andrews，Garvan和Liang的身份开始。我们还发现了与贝尔多项式相关的uchimura身份的一般概括。
In 1984, Bressoud and Subbarao obtained an interesting weighted partition identity for a generalized divisor function, by means of combinatorial arguments. Recently, the last three named authors found an analytic proof of the aforementioned identity of Bressoud and Subbarao starting from a $q$-series identity of Ramanujan. In the present paper, we revisit the combinatorial arguments of Bressoud and Subbarao, and derive a more general weighted partition identity. Furthermore, with the help of a fractional differential operator, we establish a few more Bressoud-Subbarao type weighted partition identities beginning from an identity of Andrews, Garvan and Liang. We also found a one-variable generalization of an identity of Uchimura related to Bell polynomials.
