{
  "abstract": "Zhang and Yeung (IEEE Trans. Inf. Theory, 1998) established the first non-Shannon-type inequality that holds for all entropic vectors. Chan and Yeung (IEEE Trans. Inf. Theory, 2002) showed that there is a one-to-one relation between linear entropy inequalities and multiplicative inequalities involving cardinalities of subgroups of a finite group. The Shannon inequality admits a simple proof in the group theoretic setting, but a direct proof of the translation of Zhang--Yeung's inequality to the group-theoretic setting remained elusive. We resolve this open problem, giving a direct proof of the group-theoretic Zhang--Yeung inequality for cardinalities of subgroups of finite groups, using elementary group-theoretic and counting arguments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35451",
  "author_total": 2,
  "authors": [
    {
      "name": "Harold Nieuwboer"
    },
    {
      "name": "Lubashan Pathirana"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1he6ee0ft0anr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35451",
  "fulltext_url": null,
  "id": "1he6ee0ft0anr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35451",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7214771859",
  "pdf_url": "https://arxiv.org/pdf/2609.35451",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1he6ee0ft0anr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35451",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35451"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Finite Group Theory Research",
      "subfield": "combinatorics"
    }
  ],
  "title": "A simple proof of the group-theoretic Zhang-Yeung inequality",
  "title_text": "A simple proof of the group-theoretic Zhang-Yeung inequality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/1he6ee0ft0anr",
  "venue": "arXiv",
  "versions": []
}