{
  "abstract": "We show that there exist infinitely many polynomials $F\\in\\mathbb{Q}[x]$ with exactly $m$ nonzero coefficients such that every irreducible factor of \\(F\\) over \\(\\mathbb{Q}\\) has \\(\\exp\\) \\(\\!\\bigl(Ω(\\sqrt{m/\\log m})\\bigr)\\) nonzero coefficients. This places multiplication in a sharply different category from powers, composition, and other algebraic operations for which reverse-sparsity principles are known. It also gives an unconditional, degree-free obstruction to sparse factorization, complementing positive factor-sparsity results that impose hypotheses on coefficient height, exponent positions, reciprocal structure, or degree bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22286",
  "author_total": 1,
  "authors": [
    {
      "name": "Bhawesh Mishra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/et4m440175sb0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22286",
  "fulltext_url": null,
  "id": "et4m440175sb0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22286",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "1703|Polynomial and algebraic computation"
    ]
  ],
  "openalex": "W7214030674",
  "pdf_url": "https://arxiv.org/pdf/2609.22286",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/et4m440175sb0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22286",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22286"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Superpolynomially Large Support in Every Irreducible Factor of Lacunary Polynomials",
  "title_text": "Superpolynomially Large Support in Every Irreducible Factor of Lacunary Polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/et4m440175sb0",
  "venue": "arXiv",
  "versions": []
}