Stanley–Elder–Fine theorems for colored partitions [article]

Hartosh Singh Bal, Gaurav Bhatnagar
2021 arXiv   pre-print
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:2102.03486v2 fatcat:b5va67p5kjcqjn3cil5z7mojle