Restricted k-color partitions

2014/08/18 by Keith, William J. · 3 citations
#05A17 #11P83 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.4089

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.

Cited by

• On recent Partition function of Kaur and Rana
• Colored base-3 partitions, sequences of polynomials, and perfect numbers
• Combinatorial proof of a congruence for partitions into two sizes of part

Related

• Restricted k-color partitions, II
• Two-color partitions and overpartitions: a combinatorial proof
• Combinatorial Proofs for Two-Color Partition Identities Involving Overpartitions and Minimal Excludants
• Combinatorial Proofs for Overpartitions and Two-Colored Partitions II
• Stanley--Elder--Fine theorems for colored partitions