论文标题
受限制的k色分区，ii
Restricted k-color partitions, II
论文作者
论文摘要
我们考虑$（k，j）$ - 彩色分区，其中存在$ k $的颜色，但最多可以选择$ j $颜色。特别是这些概括的过度分区。在先前的工作中，我们找到了新的一致性，包括在以前未开发的案例中，$ k $和$ j $不是企业，以及某些非企业。除此之外，我们为具有给定数量的零件尺寸的$ n \ times m $ box中的分区数量提供了明显的新生成功能，并扩展到多种颜色的dousse和kim的猜想在过度分区中的单段性。
We consider $(k,j)$-colored partitions, partitions in which $k$ colors exist but at most $j$ colors may be chosen per size of part. In particular these generalize overpartitions. Advancing previous work, we find new congruences, including in previously unexplored cases where $k$ and $j$ are not coprime, as well as some noncongruences. As a useful aside, we give the apparently new generating function for the number of partitions in the $N \times M$ box with a given number of part sizes, and extend to multiple colors a conjecture of Dousse and Kim on unimodality in overpartitions.
