Restricted k-color partitions, II

Abstract

We consider [Formula: see text]-colored partitions, partitions in which [Formula: see text] colors exist but at most [Formula: see text] 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 [Formula: see text] and [Formula: see text] 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 [Formula: see text] box with a given number of part sizes, and extend to multiple colors a conjecture of Dousse and Kim on unimodality in overpartitions.