{
  "abstract": "We present an exposition of an argument, discovered by GPT-6 Pro, that gives an optimal bound for the polynomial Littlewood-Offord problem. Namely, let $F$ be a degree-$d$ multilinear polynomial that contains $r$ degree-$d$ monomials involving disjoint sets of variables. Then, for i.i.d. Rademacher random variables $ξ_1, \\ldots, ξ_n$, we have $\\mathbb{P}[F(ξ_1, \\ldots, ξ_n) = 0] = O_d(r^{-1/2})$. This improves upon the previous bound of $(\\log r)^{O_d(1)} r^{-1/2}$ due to Meka, O. Nguyen, and Vu, and resolves a conjecture attributed to H. Nguyen and Vu. The key part of the proof is an estimate for the total influence of bounded-degree rational functions, which resolves a recent conjecture of Kothari, Kovacs-Deak, Wang, and Yang.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08708",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexandr Grebennikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8age4x85djznc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08708",
  "fulltext_url": null,
  "id": "8age4x85djznc",
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  "landing_url": "https://arxiv.org/abs/2610.08708",
  "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/",
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  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
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  "pdf_url": "https://arxiv.org/pdf/2610.08708",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8age4x85djznc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.08708",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08708"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Optimal bound for the polynomial Littlewood-Offord problem",
  "title_text": "Optimal bound for the polynomial Littlewood-Offord problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/8age4x85djznc",
  "venue": "arXiv",
  "versions": []
}