论文标题
一系列分区，并具有上线指定的汇总
A rank of partitions with overline designated summands
论文作者
论文摘要
安德鲁斯（Andrews），刘易斯（Lewis）和洛夫乔伊（Lovejoy）将分区功能$ pd（n）$作为$ n $的分区数，并带有指定的汇总。在最近的一项工作中，林研究了一个分区函数$ pd_ {t}（n）$，该函数计算了所有$ n $分区中标记的零件的数量，并指定了指定的汇总。他证明$ pd_ {t}（3n+2）$可除以$ 3 $。在本文中，我们首先介绍了一个名为“分区”的结构，该结构用划定的汇总，由$ pd_t（n）$计数。然后，我们定义了具有跨海指定求和的广义分区等级，并对$ pd_t（3n+2）$的一致性进行组合解释。
Andrews, Lewis and Lovejoy introduced the partition function $PD(n)$ as the number of partitions of $n$ with designated summands. In a recent work, Lin studied a partition function $PD_{t}(n)$ which counts the number of tagged parts over all the partitions of $n$ with designated summands. He proved that $PD_{t}(3n+2)$ is divisible by $3$. In this paper, we first introduce a structure named partitions with overline designated summands, which is counted by $PD_t(n)$. We then define a generalized rank of partitions with overline designated summands and give a combinatorial interpretation of the congruence for $PD_t(3n+2)$.
