{
  "abstract": "We introduce P(g)=∏(1−gn)−1 for partitions ∑gn=1 and the index U=1−e/P∈[0,1). P has universal infimum e at the infinitesimal equal partition and diverges at monopoly. Its log L=log⁡P=∑Sk/k, Sk=∑gnk, is the generating function of HHI, Simpson, R\\'enyi, Shannon and Berger-Parker indices. U is additive, strictly Schur-convex, continuous and non-saturating, resolving infinite-tailed geometric vs harmonic decays where Gini collapses to 1. A finite-size normalization UN∗=1−Pmin/P recovers population invariance.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Benito Vinuesa Guerrero",
      "orcid": "0009-0009-3581-0269"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgzymenc5mz4j.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23592342",
  "fulltext_url": null,
  "id": "bgzymenc5mz4j",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23592342",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23592342/files/Vinuesa_Universal_Inequality_Index_2026.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgzymenc5mz4j.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:43Z",
      "native_id": "23592342",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23592342"
    }
  ],
  "subjects": [],
  "title": "A universal inequality index: U = 1 - e/P, P = ∏ 1/(1-g_n). From Γ(x)Γ(3-x) to the generating function of HHI, Shannon, Rényi, and Gini",
  "title_text": "A universal inequality index: U = 1 - e/P, P = ∏ 1/(1-g_n). From Γ(x)Γ(3-x) to the generating function of HHI, Shannon, Rényi, and Gini",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:43Z",
  "url": "https://research.draconitic.com/paper/bgzymenc5mz4j",
  "venue": "Zenodo",
  "versions": []
}