Restricted k-color partitions, II

Document Type

Article

Publication Date

10-21-2020

Department

Department of Mathematical Sciences

Abstract

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 × M box with a given number of part sizes, and extend to multiple colors a conjecture of Dousse and Kim on unimodality in overpartitions.

Publisher's Statement

© 2020 World Scientific Publishing Company. Publisher’s version of record: https://doi.org/10.1142/S1793042120400151

Publication Title

International Journal of Number Theory

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