论文标题
等级分区功能和截断的theta身份
Rank partition functions and truncated theta identities
论文作者
论文摘要
弗里曼·戴森（Freeman Dyson）以1944美元的价格定义了整数分区的等级概念，并在没有定义的整数分区曲柄的情况下引入了排名。 G. E. Andrews和F. G. Garvan在1988年发现了Dyson假设的曲柄的定义。在本文中，我们引入了两个theta身份的截短形式，涉及具有非负等级和非负曲柄的分区的生成功能。作为推论，我们为分区功能$ p（n）$衍生出新的无限线性不平等家庭。在这种情况下，还考虑了伊甸园分区花园的数量，以便以$ p（n）$提供其他无限的线性不平等家庭。
In $1944$, Freeman Dyson defined the concept of rank of an integer partition and introduced without definition the term of crank of an integer partition. A definition for the crank satisfying the properties hypothesized for it by Dyson was discovered in 1988 by G. E. Andrews and F. G. Garvan. In this paper, we introduce truncated forms for two theta identities involving the generating functions for partitions with non-negative rank and non-negative crank. As corollaries we derive new infinite families of linear inequalities for the partition function $p(n)$. The number of Garden of Eden partitions are also considered in this context in order to provide other infinite families of linear inequalities for $p(n)$.
