论文标题
与双分会对的双变量生成函数相关的组合身份
Combinatorial identities associated with a bivariate generating function for overpartition pairs
论文作者
论文摘要
我们获得了三参数$ q $ series的身份，该身份概括了Chan和Mao的两个结果。通过专门提高我们的身份，我们获得了与$ N（R，S，M，N）$相关的组合意义的新结果，该功能计算了Bringmann，Lovejoy和Osburn最近引入的某些过度分支对。例如，我们的一个身份之一就第二种的Chebyshev多项式对双重系列进行了封闭式评估，从而导致了Euler的五角形编号定理的类似物。我们的另一个结果表达了涉及$ n（r，s，m，n）$的多功能，仅分区功能$ p（n）$。使用Shimura的结果，我们还将某个双重系列与重量为7/2 Theta系列相关联。
We obtain a three-parameter $q$-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with $N(r, s, m, n)$, a function counting certain overpartition pairs recently introduced by Bringmann, Lovejoy and Osburn. For example, one of our identities gives a closed-form evaluation of a double series in terms of Chebyshev polynomials of the second kind, thereby resulting in an analogue of Euler's pentagonal number theorem. Another of our results expresses a multi-sum involving $N(r, s, m, n)$ in terms of just the partition function $p(n)$. Using a result of Shimura we also relate a certain double series with a weight 7/2 theta series.
