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Restricted -color partitions, II
Abstract
We consider -colored partitions, partitions in which colors exist but at most 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 and 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 box with a given number of part sizes, and extend to multiple colors a conjecture of Dousse and Kim on unimodality in overpartitions.
AMSC: 05A17, 11P83
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