Some inequalities for k-colored partition functions

Abstract

Motivated by a partition inequality of Bessenrodt and Ono, we obtain analogous inequalities for k-colored partition functions $$p_{-k}(n)$$ for all $$k\ge 2$$ . This enables us to extend the k-colored partition function multiplicatively to a function on k-colored partitions and characterize when it has a unique maximum. We conclude with one conjectural inequality that strengthens our results.