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 $P{D}_t(n)$ which counts the number of tagged parts over all the partitions of n with designated summands. He proved that $P{D}_t(3n+2)$ is divisible by 3. In this paper, we first introduce a structure named partitions with overline designated summands, which is counted by $P{D}_t(n)$. We then define a generalized rank of partitions with overline designated summands and give a combinatorial interpretation of the congruence for $P{D}_t(3n+2)$.

中文翻译：

---

带有上划线指定被加数的分区等级

Andrews、Lewis 和 Lovejoy 介绍了分区函数 $磷D(n)$作为具有指定加数的n的分区数。在最近的一项工作中，Lin 研究了一个分区函数$磷D_{吨}(n)$它计算具有指定加数的n 的所有分区上标记部分的数量。他证明了$磷D_{吨}(3n+2)$ 可被 3 整除。 在本文中，我们首先介绍一个名为 partitions 的结构，其上划线指定被加数，其计数为 $磷D_{吨}(n)$. 然后，我们定义了具有上划线指定被加数的分区的广义秩，并给出了同余的组合解释$磷D_{吨}(3n+2)$.