bibkey: bal2021stanley
authors: Hartosh Singh Bal, Gaurav Bhatnagar
year: 2021
title: 'Stanley–Elder–Fine theorems for colored partitions'
doi: 10.48550/arXiv.2102.03486
url: https://arxiv.org/abs/2102.03486v2
claim: "Section 6 provides the ordinary/distinct decomposition of overpartitions, nonoverlined frequency counts, and threshold-one and threshold-three ingredients."
strata_touched:
  - D5/S3/Combinatorics/Partitions/OverpartitionThreshold
license: citation-only
triage: anchor

Stanley–Elder–Fine theorems for colored partitions

Section 6 treats overpartitions as an ordinary-partition component together with a distinct-part component. Its nonoverlined frequency decomposes by removing positive numbers of unmarked occurrences. Equation (6.2) identifies overpartitions containing a specified nonoverlined size with overpartitions of the reduced integer. Theorem 6.2 compares the threshold-one and threshold-three statistics.

These are prior ingredients of the finite counting argument; they are not attributed as new results. No claim of exhaustive literature absence follows from these sources.

Verified locator

DOI: 10.48550/arXiv.2102.03486

URL: https://arxiv.org/abs/2102.03486v2

Locator: https://arxiv.org/html/2102.03486v2 , Section 6, equations (6.1)–(6.2), Theorems 6.1–6.2.