{
  "abstract": "We prove an $Ω(n^2)$ lower bound on the determinantal complexity of the power sum polynomial $\\sum_{i=1}^n x_i^n$ over the field of complex numbers. A similar result was claimed in a recent paper of Sheshadri (arXiv:2606.13628), via an AI-assisted and AI-written proof. Assuming its correctness, this was the first super-linear lower bound for this fundamental algebraic problem for any explicit polynomial. However, the authors of this note were unable to follow the details and verify the argument in arXiv:2606.13628, in spite of considerable effort on their part. The proof we provide here is short, (almost) self-contained and seemingly simpler.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34462",
  "author_total": 2,
  "authors": [
    {
      "name": "Mrinal Kumar"
    },
    {
      "name": "Ben Lee Volk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/95mc3xpegec6z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34462",
  "fulltext_url": null,
  "id": "95mc3xpegec6z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34462",
  "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.CC"
    ],
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7214755385",
  "pdf_url": "https://arxiv.org/pdf/2609.34462",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/95mc3xpegec6z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34462",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34462"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Quadratic Lower Bound on Determinantal Complexity",
  "title_text": "A Quadratic Lower Bound on Determinantal Complexity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/95mc3xpegec6z",
  "venue": "arXiv",
  "versions": []
}