Restricted k-color partitions
Combinatorics
2014-08-19 v1
Abstract
We generalize overpartitions to (k,j)-colored partitions: k-colored partitions in which each part size may have at most j colors. We find numerous congruences and other symmetries. We use a wide array of tools to prove our theorems: generating function dissections, modular forms, bijections, and other combinatorial maps. We find connections to divisor sums, the Han/Nekrasov-Okounkov hook length formula and a possible approach to a finitization, and other topics, suggesting that a rich mine of results is available.
Cite
@article{arxiv.1408.4089,
title = {Restricted k-color partitions},
author = {William J. Keith},
journal= {arXiv preprint arXiv:1408.4089},
year = {2014}
}
Comments
17 pages. I thank Jeremy Rouse for a particular lemma on MathOverflow