Stanley--Elder--Fine theorems for colored partitions

Abstract

We give a new proof of a partition theorem popularly known as Elder's theorem, but which is also credited to Stanley and Fine. We extend the theorem to the context of colored partitions (or prefabs). More specifically, we give analogous results for $b$-colored partitions, where each part occurs in $b$ colors; for $b$-colored partitions with odd parts (or distinct parts); for partitions where the part $k$ comes in $k$ colors; and, overpartitions.

arXiv comment11 Pages (Minor update of a reference)

References in corpus (2)

• The Partition-Frequency Enumeration Matrix
• Generalization of a few results in Integer Partitions

Cited by in corpus (1)

• The Partition-Frequency Enumeration Matrix