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 $k\geq2$. 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2017
- DOI:
- 10.48550/arXiv.1709.06735
- arXiv:
- arXiv:1709.06735
- Bibcode:
- 2017arXiv170906735C
- Keywords:
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- Mathematics - Combinatorics;
- 05A17;
- 11P83
- E-Print:
- 11 pages, 1 table