论文标题
对安德鲁斯和纽曼的扩展最小排除者的概括
Generalization of the Extended Minimal Excludant of Andrews and Newman
论文作者
论文摘要
在最近的开创性工作中，安德鲁斯（Andrews）和纽曼（Newman）定义了一个扩展功能$ p_ {a，a}（n）$的最小排除物或分区功能的“ mex”。通过考虑特殊情况$ p_ {k，k}（n）$和$ p_ {2k，k}（n）$，它们发掘了与分区和一些限制分区的等级和曲柄的连接。在本文中，我们以他们的工作为基础，并获得更一般的结果，将扩展的MEX功能与整数分区的数量相关联，并在等级和曲柄上进行任意界限。我们还得出了一个新的结果，该结果表达了Andrews的最小零件函数，作为以奇怪的系数考虑的扩展MEX函数的有限总和。我们还获得了一些限制的分区身份，使人联想到转移的分区身份。最后，我们定义并探索了一个新的最小排除物，以使其过度分区。
In a recent pioneering work, Andrews and Newman defined an extended function $p_{A,a}(n)$ of their minimal excludant or "mex" of a partition function. By considering the special cases $p_{k,k}(n)$ and $p_{2k,k}(n)$, they unearthed connections to the rank and crank of partitions and some restricted partitions. In this paper, we build on their work and obtain more general results associating the extended mex function with the number of partitions of an integer with arbitrary bound on the rank and crank. We also derive a new result expressing the smallest parts function of Andrews as a finite sum of the extended mex function in consideration with a curious coefficient. We also obtain a few restricted partition identities with some reminiscent of shifted partition identities. Finally, we define and explore a new minimal excludant for overpartitions.
