English

Stanley--Elder--Fine theorems for colored partitions

Combinatorics 2021-03-05 v2 Number Theory

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 bb-colored partitions, where each part occurs in bb colors; for bb-colored partitions with odd parts (or distinct parts); for partitions where the part kk comes in kk colors; and, overpartitions.

Keywords

Cite

@article{arxiv.2102.03486,
  title  = {Stanley--Elder--Fine theorems for colored partitions},
  author = {Hartosh Singh Bal and Gaurav Bhatnagar},
  journal= {arXiv preprint arXiv:2102.03486},
  year   = {2021}
}

Comments

11 Pages (Minor update of a reference)

R2 v1 2026-06-23T22:53:38.419Z