{
  "abstract": "In this note, we prove that the noncommutative AM-GM inequality holds if $n\\ge 2\\lceil m/2 \\rceil^2$. The motivation comes from counterexamples constructed in [De Sa, Random reshuffling is not always better, NeurIPS2020]. The proof constructs a vertex measure based on the Chebyshev nodes on the Boolean cube to extract the distinct indices. The main difficulty is that the measure is not positive on non-integer nodes. The key technique comes from [Grigoriev, Complexity of Positivstellensatz proofs for the knapsack, Computational Complexity (2001)] and eventually transforms the problem into a quadrature estimate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04874",
  "author_total": 1,
  "authors": [
    {
      "name": "Yimin Zhong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fh7watjdtc9qm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04874",
  "fulltext_url": null,
  "id": "fh7watjdtc9qm",
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  "landing_url": "https://arxiv.org/abs/2610.04874",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
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      "arxiv",
      "math.PR"
    ],
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      "openalex",
      "2604|Mathematical Inequalities and Applications"
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  "openalex": "W7220674060",
  "pdf_url": "https://arxiv.org/pdf/2610.04874",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fh7watjdtc9qm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04874",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04874"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "When the noncommutative AM-GM inequality holds",
  "title_text": "When the noncommutative AM-GM inequality holds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/fh7watjdtc9qm",
  "venue": "arXiv",
  "versions": []
}